how to reject a hypothesis in a lab report

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How to Write a Lab Report – with Example/Template

April 11, 2024

Perhaps you’re in the midst of your challenging AP chemistry class in high school, or perhaps college you’re enrolled in biology , chemistry , or physics at university. At some point, you will likely be asked to write a lab report. Sometimes, your teacher or professor will give you specific instructions for how to format and write your lab report, and if so, use that. In case you’re left to your own devices, here are some guidelines you might find useful. Continue reading for the main elements of a lab report, followed by a detailed description of the more writing-heavy parts (with a lab report example/lab report template). Lastly, we’ve included an outline that can help get you started.

What is a lab report?

A lab report is an overview of your experiment. Essentially, it explains what you did in the experiment and how it went. Most lab reports end up being 5-10 pages long (graphs or other images included), though the length depends on the experiment. Here are some brief explanations of the essential parts of a lab report:

Title : The title says, in the most straightforward way possible, what you did in the experiment. Often, the title looks something like, “Effects of ____ on _____.” Sometimes, a lab report also requires a title page, which includes your name (and the names of any lab partners), your instructor’s name, and the date of the experiment.

Abstract : This is a short description of key findings of the experiment so that a potential reader could get an idea of the experiment before even beginning.

Introduction : This is comprised of one or several paragraphs summarizing the purpose of the lab. The introduction usually includes the hypothesis, as well as some background information.

Lab Report Example (Continued)

Materials : Perhaps the simplest part of your lab report, this is where you list everything needed for the completion of your experiment.

Methods : This is where you describe your experimental procedure. The section provides necessary information for someone who would want to replicate your study. In paragraph form, write out your methods in chronological order, though avoid excessive detail.

Data : Here, you should document what happened in the experiment, step-by-step. This section often includes graphs and tables with data, as well as descriptions of patterns and trends. You do not need to interpret all of the data in this section, but you can describe trends or patterns, and state which findings are interesting and/or significant.

Discussion of results : This is the overview of your findings from the experiment, with an explanation of how they pertain to your hypothesis, as well as any anomalies or errors.

Conclusion : Your conclusion will sum up the results of your experiment, as well as their significance. Sometimes, conclusions also suggest future studies.

Sources : Often in APA style , you should list all texts that helped you with your experiment. Make sure to include course readings, outside sources, and other experiments that you may have used to design your own.

How to write the abstract

The abstract is the experiment stated “in a nutshell”: the procedure, results, and a few key words. The purpose of the academic abstract is to help a potential reader get an idea of the experiment so they can decide whether to read the full paper. So, make sure your abstract is as clear and direct as possible, and under 200 words (though word count varies).

When writing an abstract for a scientific lab report, we recommend covering the following points:

• Background : Why was this experiment conducted?
• Objectives : What problem is being addressed by this experiment?
• Methods : How was the study designed and conducted?
• Results : What results were found and what do they mean?
• Conclusion : Were the results expected? Is this problem better understood now than before? If so, how?

How to write the introduction

The introduction is another summary, of sorts, so it could be easy to confuse the introduction with the abstract. While the abstract tends to be around 200 words summarizing the entire study, the introduction can be longer if necessary, covering background information on the study, what you aim to accomplish, and your hypothesis. Unlike the abstract (or the conclusion), the introduction does not need to state the results of the experiment.

Here is a possible order with which you can organize your lab report introduction:

• Intro of the intro : Plainly state what your study is doing.
• Background : Provide a brief overview of the topic being studied. This could include key terms and definitions. This should not be an extensive literature review, but rather, a window into the most relevant topics a reader would need to understand in order to understand your research.
• Importance : Now, what are the gaps in existing research? Given the background you just provided, what questions do you still have that led you to conduct this experiment? Are you clarifying conflicting results? Are you undertaking a new area of research altogether?
• Prediction: The plants placed by the window will grow faster than plants placed in the dark corner.
• Hypothesis: Basil plants placed in direct sunlight for 2 hours per day grow at a higher rate than basil plants placed in direct sunlight for 30 minutes per day.
• How you test your hypothesis : This is an opportunity to briefly state how you go about your experiment, but this is not the time to get into specific details about your methods (save this for your results section). Keep this part down to one sentence, and voila! You have your introduction.

How to write a discussion section

Here, we’re skipping ahead to the next writing-heavy section, which will directly follow the numeric data of your experiment. The discussion includes any calculations and interpretations based on this data. In other words, it says, “Now that we have the data, why should we care?”  This section asks, how does this data sit in relation to the hypothesis? Does it prove your hypothesis or disprove it? The discussion is also a good place to mention any mistakes that were made during the experiment, and ways you would improve the experiment if you were to repeat it. Like the other written sections, it should be as concise as possible.

Here is a list of points to cover in your lab report discussion:

• Weaker statement: These findings prove that basil plants grow more quickly in the sunlight.
• Stronger statement: These findings support the hypothesis that basil plants placed in direct sunlight grow at a higher rate than basil plants given less direct sunlight.
• Factors influencing results : This is also an opportunity to mention any anomalies, errors, or inconsistencies in your data. Perhaps when you tested the first round of basil plants, the days were sunnier than the others. Perhaps one of the basil pots broke mid-experiment so it needed to be replanted, which affected your results. If you were to repeat the study, how would you change it so that the results were more consistent?
• Implications : How do your results contribute to existing research? Here, refer back to the gaps in research that you mentioned in your introduction. Do these results fill these gaps as you hoped?
• Questions for future research : Based on this, how might your results contribute to future research? What are the next steps, or the next experiments on this topic? Make sure this does not become too broad—keep it to the scope of this project.

How to write a lab report conclusion

This is your opportunity to briefly remind the reader of your findings and finish strong. Your conclusion should be especially concise (avoid going into detail on findings or introducing new information).

Here are elements to include as you write your conclusion, in about 1-2 sentences each:

• Restate your goals : What was the main question of your experiment? Refer back to your introduction—similar language is okay.
• Restate your methods : In a sentence or so, how did you go about your experiment?
• Key findings : Briefly summarize your main results, but avoid going into detail.
• Limitations : What about your experiment was less-than-ideal, and how could you improve upon the experiment in future studies?
• Significance and future research : Why is your research important? What are the logical next-steps for studying this topic?

Template for beginning your lab report

Here is a compiled outline from the bullet points in these sections above, with some examples based on the (overly-simplistic) basil growth experiment. Hopefully this will be useful as you begin your lab report.

1) Title (ex: Effects of Sunlight on Basil Plant Growth )

2) Abstract (approx. 200 words)

• Background ( This experiment looks at… )
• Objectives ( It aims to contribute to research on…)
• Methods ( It does so through a process of…. )
• Results (Findings supported the hypothesis that… )
• Conclusion (These results contribute to a wider understanding about…)

3) Introduction (approx. 1-2 paragraphs)

• Intro ( This experiment looks at… )
• Background ( Past studies on basil plant growth and sunlight have found…)
• Importance ( This experiment will contribute to these past studies by…)
• Hypothesis ( Basil plants placed in direct sunlight for 2 hours per day grow at a higher rate than basil plants placed in direct sunlight for 30 minutes per day.)
• How you will test your hypothesis ( This hypothesis will be tested by a process of…)

4) Materials (list form) (ex: pots, soil, seeds, tables/stands, water, light source )

5) Methods (approx. 1-2 paragraphs) (ex: 10 basil plants were measured throughout a span of…)

6) Data (brief description and figures) (ex: These charts demonstrate a pattern that the basil plants placed in direct sunlight…)

7) Discussion (approx. 2-3 paragraphs)

• Support or reject hypothesis ( These findings support the hypothesis that basil plants placed in direct sunlight grow at a higher rate than basil plants given less direct sunlight.)
• Factors that influenced your results ( Outside factors that could have altered the results include…)
• Implications ( These results contribute to current research on basil plant growth and sunlight because…)
• Questions for further research ( Next steps for this research could include…)
• Restate your goals ( In summary, the goal of this experiment was to measure…)
• Restate your methods ( This hypothesis was tested by…)
• Key findings ( The findings supported the hypothesis because…)
• Limitations ( Although, certain elements were overlooked, including…)
• Significance and future research ( This experiment presents possibilities of future research contributions, such as…)
• Sources (approx. 1 page, usually in APA style)

Final thoughts – Lab Report Example

Hopefully, these descriptions have helped as you write your next lab report. Remember that different instructors may have different preferences for structure and format, so make sure to double-check when you receive your assignment. All in all, make sure to keep your scientific lab report concise, focused, honest, and organized. Good luck!

For more reading on coursework success, check out the following articles:

• How to Write the AP Lang Argument Essay (With Example)
• How to Write the AP Lang Rhetorical Analysis Essay (With Example)
• 49 Most Interesting Biology Research Topics
• 50 Best Environmental Science Research Topics
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Hypothesis Testing (cont...)

Hypothesis testing, the null and alternative hypothesis.

In order to undertake hypothesis testing you need to express your research hypothesis as a null and alternative hypothesis. The null hypothesis and alternative hypothesis are statements regarding the differences or effects that occur in the population. You will use your sample to test which statement (i.e., the null hypothesis or alternative hypothesis) is most likely (although technically, you test the evidence against the null hypothesis). So, with respect to our teaching example, the null and alternative hypothesis will reflect statements about all statistics students on graduate management courses.

The null hypothesis is essentially the "devil's advocate" position. That is, it assumes that whatever you are trying to prove did not happen ( hint: it usually states that something equals zero). For example, the two different teaching methods did not result in different exam performances (i.e., zero difference). Another example might be that there is no relationship between anxiety and athletic performance (i.e., the slope is zero). The alternative hypothesis states the opposite and is usually the hypothesis you are trying to prove (e.g., the two different teaching methods did result in different exam performances). Initially, you can state these hypotheses in more general terms (e.g., using terms like "effect", "relationship", etc.), as shown below for the teaching methods example:

Depending on how you want to "summarize" the exam performances will determine how you might want to write a more specific null and alternative hypothesis. For example, you could compare the mean exam performance of each group (i.e., the "seminar" group and the "lectures-only" group). This is what we will demonstrate here, but other options include comparing the distributions , medians , amongst other things. As such, we can state:

Now that you have identified the null and alternative hypotheses, you need to find evidence and develop a strategy for declaring your "support" for either the null or alternative hypothesis. We can do this using some statistical theory and some arbitrary cut-off points. Both these issues are dealt with next.

Significance levels

The level of statistical significance is often expressed as the so-called p -value . Depending on the statistical test you have chosen, you will calculate a probability (i.e., the p -value) of observing your sample results (or more extreme) given that the null hypothesis is true . Another way of phrasing this is to consider the probability that a difference in a mean score (or other statistic) could have arisen based on the assumption that there really is no difference. Let us consider this statement with respect to our example where we are interested in the difference in mean exam performance between two different teaching methods. If there really is no difference between the two teaching methods in the population (i.e., given that the null hypothesis is true), how likely would it be to see a difference in the mean exam performance between the two teaching methods as large as (or larger than) that which has been observed in your sample?

So, you might get a p -value such as 0.03 (i.e., p = .03). This means that there is a 3% chance of finding a difference as large as (or larger than) the one in your study given that the null hypothesis is true. However, you want to know whether this is "statistically significant". Typically, if there was a 5% or less chance (5 times in 100 or less) that the difference in the mean exam performance between the two teaching methods (or whatever statistic you are using) is as different as observed given the null hypothesis is true, you would reject the null hypothesis and accept the alternative hypothesis. Alternately, if the chance was greater than 5% (5 times in 100 or more), you would fail to reject the null hypothesis and would not accept the alternative hypothesis. As such, in this example where p = .03, we would reject the null hypothesis and accept the alternative hypothesis. We reject it because at a significance level of 0.03 (i.e., less than a 5% chance), the result we obtained could happen too frequently for us to be confident that it was the two teaching methods that had an effect on exam performance.

Whilst there is relatively little justification why a significance level of 0.05 is used rather than 0.01 or 0.10, for example, it is widely used in academic research. However, if you want to be particularly confident in your results, you can set a more stringent level of 0.01 (a 1% chance or less; 1 in 100 chance or less).

One- and two-tailed predictions

When considering whether we reject the null hypothesis and accept the alternative hypothesis, we need to consider the direction of the alternative hypothesis statement. For example, the alternative hypothesis that was stated earlier is:

The alternative hypothesis tells us two things. First, what predictions did we make about the effect of the independent variable(s) on the dependent variable(s)? Second, what was the predicted direction of this effect? Let's use our example to highlight these two points.

Sarah predicted that her teaching method (independent variable: teaching method), whereby she not only required her students to attend lectures, but also seminars, would have a positive effect (that is, increased) students' performance (dependent variable: exam marks). If an alternative hypothesis has a direction (and this is how you want to test it), the hypothesis is one-tailed. That is, it predicts direction of the effect. If the alternative hypothesis has stated that the effect was expected to be negative, this is also a one-tailed hypothesis.

Alternatively, a two-tailed prediction means that we do not make a choice over the direction that the effect of the experiment takes. Rather, it simply implies that the effect could be negative or positive. If Sarah had made a two-tailed prediction, the alternative hypothesis might have been:

In other words, we simply take out the word "positive", which implies the direction of our effect. In our example, making a two-tailed prediction may seem strange. After all, it would be logical to expect that "extra" tuition (going to seminar classes as well as lectures) would either have a positive effect on students' performance or no effect at all, but certainly not a negative effect. However, this is just our opinion (and hope) and certainly does not mean that we will get the effect we expect. Generally speaking, making a one-tail prediction (i.e., and testing for it this way) is frowned upon as it usually reflects the hope of a researcher rather than any certainty that it will happen. Notable exceptions to this rule are when there is only one possible way in which a change could occur. This can happen, for example, when biological activity/presence in measured. That is, a protein might be "dormant" and the stimulus you are using can only possibly "wake it up" (i.e., it cannot possibly reduce the activity of a "dormant" protein). In addition, for some statistical tests, one-tailed tests are not possible.

Rejecting or failing to reject the null hypothesis

Let's return finally to the question of whether we reject or fail to reject the null hypothesis.

If our statistical analysis shows that the significance level is below the cut-off value we have set (e.g., either 0.05 or 0.01), we reject the null hypothesis and accept the alternative hypothesis. Alternatively, if the significance level is above the cut-off value, we fail to reject the null hypothesis and cannot accept the alternative hypothesis. You should note that you cannot accept the null hypothesis, but only find evidence against it.

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Writing Lab Reports: Discussion

Keys to the discussion .

Purpose : Why do we care? Relative size : 40-45% of total Scope : Narrow to broad: the bottom of the hourglass Verb Tense : Use the past tense to refer to results from your experiment or from other studies (e.g., the results supported my hypothesis that). Use the present to suggest implication of your study (e.g., these results suggest that...). Use the future or conditional to suggest what you will study in the future (e.g., future studies should investigate...)

The discussion offers an analysis of the experiment.

The purpose of the discussion section is to provide a brief summary of your results, relate them to your hypotheses, and put them into context within the field of research. This is the most substantial section of your report, and where you will include your unique interpretations and ideas. The discussion must therefore address the following essential questions: 

• Did find what you expected to?
• How do your findings compare to those of previous studies?
• What are the implications of your findings?
• What should be studied next?

Remember that this section forms the bottom of the hourglass – it should mirror the introduction by first focusing on your hypotheses and interpretation of results, and then gradually expanding to make comparisons with previous research, to provide implications of your study and to pose questions for future work – and completes the cycle of the scientific method.

Discussion Section Details

Support or reject hypotheses : Begin by stating whether your results supported your hypotheses or not; remember not to say that you proved anything – you can only support or reject hypotheses. You may also briefly summarize your results.

Interpret and compare results : Do your results make sense? Why do you think you found what you did? Compare your results to those of other studies. Do they differ? If so, how and why? Use literature to support your arguments, statements, and generalizations.

Discuss factors influencing results : Were there any anomalies in your data? Discuss any errors, inconsistencies, assumptions, or other factors that may have influenced the outcome of your study. If you were to repeat your study, would you do anything differently?

Discuss implications : How do your results contribute to existing research? Why was your study important?

Propose ideas for future research : Did your research generate questions for future research? What are the next steps in this field of study?

A good discussion section should…

• Mirror the introduction in structure and scope
• Support or reject your hypotheses
• Explain how your results compare with existing research
• Discuss any issues with your study
• Propose questions for future research

A good discussion section should NOT…

• Repeat detailed results
• Refer to tables, figures, or appendices
• State that anything was “proven”
• Extrapolate beyond the scope of the paper

Back to Writing Lab Reports

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• How to Write a Strong Hypothesis | Steps & Examples

How to Write a Strong Hypothesis | Steps & Examples

Published on May 6, 2022 by Shona McCombes . Revised on November 20, 2023.

A hypothesis is a statement that can be tested by scientific research. If you want to test a relationship between two or more variables, you need to write hypotheses before you start your experiment or data collection .

Example: Hypothesis

Daily apple consumption leads to fewer doctor’s visits.

Table of contents

What is a hypothesis, developing a hypothesis (with example), hypothesis examples, other interesting articles, frequently asked questions about writing hypotheses.

A hypothesis states your predictions about what your research will find. It is a tentative answer to your research question that has not yet been tested. For some research projects, you might have to write several hypotheses that address different aspects of your research question.

A hypothesis is not just a guess – it should be based on existing theories and knowledge. It also has to be testable, which means you can support or refute it through scientific research methods (such as experiments, observations and statistical analysis of data).

Variables in hypotheses

Hypotheses propose a relationship between two or more types of variables .

• An independent variable is something the researcher changes or controls.
• A dependent variable is something the researcher observes and measures.

If there are any control variables , extraneous variables , or confounding variables , be sure to jot those down as you go to minimize the chances that research bias  will affect your results.

In this example, the independent variable is exposure to the sun – the assumed cause . The dependent variable is the level of happiness – the assumed effect .

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Step 1. ask a question.

Writing a hypothesis begins with a research question that you want to answer. The question should be focused, specific, and researchable within the constraints of your project.

Step 2. Do some preliminary research

Your initial answer to the question should be based on what is already known about the topic. Look for theories and previous studies to help you form educated assumptions about what your research will find.

At this stage, you might construct a conceptual framework to ensure that you’re embarking on a relevant topic . This can also help you identify which variables you will study and what you think the relationships are between them. Sometimes, you’ll have to operationalize more complex constructs.

Step 3. Formulate your hypothesis

Now you should have some idea of what you expect to find. Write your initial answer to the question in a clear, concise sentence.

4. Refine your hypothesis

You need to make sure your hypothesis is specific and testable. There are various ways of phrasing a hypothesis, but all the terms you use should have clear definitions, and the hypothesis should contain:

• The relevant variables
• The specific group being studied
• The predicted outcome of the experiment or analysis

5. Phrase your hypothesis in three ways

To identify the variables, you can write a simple prediction in  if…then form. The first part of the sentence states the independent variable and the second part states the dependent variable.

In academic research, hypotheses are more commonly phrased in terms of correlations or effects, where you directly state the predicted relationship between variables.

If you are comparing two groups, the hypothesis can state what difference you expect to find between them.

6. Write a null hypothesis

If your research involves statistical hypothesis testing , you will also have to write a null hypothesis . The null hypothesis is the default position that there is no association between the variables. The null hypothesis is written as H 0 , while the alternative hypothesis is H 1 or H a .

• H 0 : The number of lectures attended by first-year students has no effect on their final exam scores.
• H 1 : The number of lectures attended by first-year students has a positive effect on their final exam scores.

If you want to know more about the research process , methodology , research bias , or statistics , make sure to check out some of our other articles with explanations and examples.

• Sampling methods
• Simple random sampling
• Stratified sampling
• Cluster sampling
• Likert scales
• Reproducibility

 Statistics

• Null hypothesis
• Statistical power
• Probability distribution
• Effect size
• Poisson distribution

Research bias

• Optimism bias
• Cognitive bias
• Implicit bias
• Hawthorne effect
• Anchoring bias
• Explicit bias

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A hypothesis is not just a guess — it should be based on existing theories and knowledge. It also has to be testable, which means you can support or refute it through scientific research methods (such as experiments, observations and statistical analysis of data).

Null and alternative hypotheses are used in statistical hypothesis testing . The null hypothesis of a test always predicts no effect or no relationship between variables, while the alternative hypothesis states your research prediction of an effect or relationship.

Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics. It is used by scientists to test specific predictions, called hypotheses , by calculating how likely it is that a pattern or relationship between variables could have arisen by chance.

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Writing a scientific lab report is significantly different from writing for other classes like philosophy, English, and history. The most prominent form of writing in biology, chemistry, and environmental science is the lab report, which is a formally written description of results and discoveries found in an experiment. College lab reports should emulate and follow the same formats as reports found in scholarly journals, such as Nature , Cell , and The American Journal of Biochemistry .

Report Format

Title: The title says what you did. It should be brief (aim for ten words or less) and describe the main point of the experiment or investigation.

• Example:  Caffeine Increases Amylase Activity in the Mealworm ( Tenebrio molitar).
• If you can, begin your title using a keyword rather than an article like “The” or “A.”

Abstract: An abstract is a very concise summary of the purpose of the report, data presented, and major conclusions in about 100 - 200 words.  Abstracts are also commonly required for conference/presentation submissions because they summarize all of the essential materials necessary to understand the purpose of the experiment. They should consist of a background sentence , an introduction sentence , your hypothesis/purpose of the experiment, and a sentence about the results and what this means.

Introduction: The introduction of a lab report defines the subject of the report, provides background information and relevant studies, and outlines scientific purpose(s) and/or objective(s).

• The introduction is a place to provide the reader with necessary research on the topic and properly cite sources used.
• Summarizes the current literature on the topic including primary and secondary sources.
• Introduces the paper’s aims and scope.
• States the purpose of the experiment and the hypothesis.

Materials and Methods: The materials and methods section is a vital component of any formal lab report. This section of the report gives a detailed account of the procedure that was followed in completing the experiment as well as all important materials used. (This includes bacterial strains and species names in tests using living subjects.)

• Discusses the procedure of the experiment in as much detail as possible.
• Provides information about participants, apparatus, tools, substances, location of experiment, etc.
• For field studies, be sure to clearly explain where and when the work was done.
• It must be written so that anyone can use the methods section as instructions for exact replications.
• Don’t hesitate to use subheadings to organize these categories.
• Practice proper scientific writing forms. Be sure to use the proper abbreviations for units. Example: The 50mL sample was placed in a 5ºC room for 48hrs.

Results: The results section focuses on the findings, or data, in the experiment, as well as any statistical tests used to determine their significance.

• Concentrate on general trends and differences and not on trivial details.
• Summarize the data from the experiments without discussing their implications (This is where all the statistical analyses goes.)
• Organize data into tables, figures, graphs, photographs, etc.  Data in a table should not be duplicated in a graph or figure. Be sure to refer to tables and graphs in the written portion, for example, “Figure 1 shows that the activity....”
• Number and title all figures and tables separately, for example, Figure 1 and Table 1 and include a legend explaining symbols and abbreviations. Figures and graphs are labeled below the image while tables are labeled above.

  Discussion: The discussion section interprets the results, tying them back to background information and experiments performed by others in the past.This is also the area where further research opportunities shold be explored.

• Interpret the data; do not restate the results.
• Observations should also be noted in this section, especially anything unusual which may affect your results.

For example, if your bacteria was incubated at the wrong temperature or a piece of equipment failed mid-experiment, these should be noted in the results section.

• Relate results to existing theories and knowledge.This can tie back to your introduction section because of the background you provided.
• Explain the logic that allows you to accept or reject your original hypotheses.
• Include suggestions for improving your techniques or design, or clarify areas of doubt for further research.

Acknowledgements and References: A references list should be compiled at the end of the report citing any works that were used to support the paper. Additionally, an acknowledgements section should be included to acknowledge research advisors/ partners, any group or person providing funding for the research and anyone outside the authors who contributed to the paper or research.

General Tips

• In scientific papers, passive voice is perfectly acceptable. On the other hand, using “I” or “we” is not.

          Incorrect: We found that caffeine increased amylase levels in Tenebrio molitar.  Correct: It was discovered that caffeine increased amylase levels in Tenebrio molitar.   

• It is expected that you use as much formal (bland) language and scientific terminology as you can. There should be no emphasis placed on “expressing yourself” or “keeping it interesting”; a lab report is not a narrative.
• In a lab report, it is important to get to the point. Be descriptive enough that your audience can understand the experiment, but strive to be concise.
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Lab reports are an essential part of all laboratory courses and usually a significant part of your grade. If your instructor gives you an outline for how to write a lab report, use that. Some instructors require a lab report to be included in a lab notebook , while others will request a separate report. Here's how to write a lab report you can use if you aren't sure what to write or need an explanation of what to include in the different parts of the report.

A lab report is how you explain what you did in ​your experiment, what you learned, and what the results meant.

Lab Report Essentials

Not all lab reports have title pages, but if your instructor wants one, it would be a single page that states:​

• The title of the experiment.
• Your name and the names of any lab partners.
• Your instructor's name.
• The date the experiment was performed or the date the report was submitted.

The title says what you did. It should be brief (aim for ten words or less) and describe the main point of the experiment or investigation. An example of a title would be: "Effects of Ultraviolet Light on Borax Crystal Growth Rate". If you can, begin your title using a keyword rather than an article like "The" or "A".

Introduction or Purpose

Usually, the introduction is one paragraph that explains the objectives or purpose of the lab. In one sentence, state the hypothesis. Sometimes an introduction may contain background information, briefly summarize how the experiment was performed, state the findings of the experiment, and list the conclusions of the investigation. Even if you don't write a whole introduction, you need to state the purpose of the experiment, or why you did it. This would be where you state your hypothesis .

List everything needed to complete your experiment.

Describe the steps you completed during your investigation. This is your procedure. Be sufficiently detailed so that anyone can read this section and duplicate your experiment. Write it as if you were giving directions for someone else to do the lab. It may be helpful to provide a figure to diagram your experimental setup.

Numerical data obtained from your procedure usually presented as a table. Data encompasses what you recorded when you conducted the experiment. It's just the facts, not any interpretation of what they mean.

Describe in words what the data means. Sometimes the Results section is combined with the Discussion.

Discussion or Analysis

The Data section contains numbers; the Analysis section contains any calculations you made based on those numbers. This is where you interpret the data and determine whether or not a hypothesis was accepted. This is also where you would discuss any mistakes you might have made while conducting the investigation. You may wish to describe ways the study might have been improved.

Conclusions

Most of the time the conclusion is a single paragraph that sums up what happened in the experiment, whether your hypothesis was accepted or rejected, and what this means.

Figures and Graphs

Graphs and figures must both be labeled with a descriptive title. Label the axes on a graph, being sure to include units of measurement. The independent variable is on the X-axis, and the dependent variable (the one you are measuring) is on the Y-axis. Be sure to refer to figures and graphs in the text of your report: the first figure is Figure 1, the second figure is Figure 2, etc.

If your research was based on someone else's work or if you cited facts that require documentation, then you should list these references.

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A lab report documents the theory, methods, and results of your experiment to demonstrate your understanding of research and scientific methodology. In this article, we’ll tell you how to write a lab report with the help of some useful examples.

For many students, writing a lab report can be confusing: how to format it, what to include and not include, and so on. The questions are endless! Just remember that your lab report will allow others to reproduce your results and draw their own conclusions. This will help you write a lab report that’s well-formatted and organized.

In true Resource Center fashion, let’s start with the basics: What exactly is a lab report?

Need help creating a perfect lab report? Learn more

What is a lab report? 

A laboratory report is a document written to describe and analyze an experiment that addresses a scientific inquiry. A lab report helps you conduct an experiment and then systematically design a conclusion based on your hypothesis. 

Note: A lab report is not the same as a lab notebook. A notebook is a detailed log you keep throughout the study. A lab report is a concise summary that you submit after the study is done, usually for a final grade. 

A lab report typically follows this format:  

• Title 

Introduction 

• Equipment/Materials 
• Methods 
• Discussion 
• References 

This is a broad list of sections you might have to include in your lab report, but by no means is this compulsory or exhaustive. You should always refer to the course or university guidelines to understand the desired format. 

How to Write a Lab Report

A lab report should be clear, concise, and well-organized, and it should include all the necessary information for others to replicate your experiment. Since the lab report format is designed to serve this purpose, you must follow it to the bone while writing your report.

Let’s start with learning how to title a lab report.

Title  

The title of your lab report should:

• Be clear, direct, and informative.
• Include keywords that clarify your objectives and involved variables.
• Be under ten words (ideally).

It’s a good idea to avoid phrasing the title as a question. Remember, your title doesn’t have to be witty or clever, just descriptive and to the point. Here are a few title examples that can clarify this for you:

• Unraveling the genetic code through gel electrophoresis.
• Hot and cold: How temperature affects enzymes yeast cells
• Impervious alloys of Aluminium
• How fast does Hydrogen Peroxide decompose?
• The speed of growth: An Analysis of bacterial growth rates in different culture media

Analysis of DNA fragment lengths using gel electrophoresis

The effects of temperature on enzyme activity in yeast cells

Investigating the corrosion resistance of Aluminum alloys

Study of chemical kinetics through the decomposition of Hydrogen Peroxide

Quantifying bacterial growth rates in different culture media

While it’s not necessary to dedicate an entire page to the title, some universities might ask for a title page. If you’ve been asked to make this, include the following details:

• The experiment title 
• Your name and student details 
• Course and program details 
• Date and year of submission 

An abstract is a brief but comprehensive overview of the purpose, findings, and larger relevance of your experiment. It communicates the essential details of your study to your readers, whether it’s evaluators or peers.

Follow these tips to write a lab report abstract:

• Clearly state the topic of your experiment.
• Briefly describe the conditions of your study, the variables involved, and the method(s) used to collect data.
• Lay out the major findings of your study and your interpretations of them.
• Mention the relevance and importance of your study in brief.

An abstract is usually only a page long (typically between 100 and 250 words), so your writing must be concise and crisp.

Bonus tip: Although the abstract is the first section of your report, it’s best to write it toward the end. Much easier to summarize the report afte r it’s been written!

Lab report abstract example

This experiment aimed to investigate the corrosion resistance of two different aluminum alloys: 6061-T6 and 7075-T6. The experiment involved exposing samples of each alloy to a 3% NaCl solution for a period of 72 hours and then measuring the weight loss of the samples. The results showed that 6061-T6 had a weight loss of 0.10 g, while 7075-T6 had a weight loss of 0.25 g, indicating that 6061-T6 was more corrosion resistant. These findings suggest that the composition of the alloy has a significant impact on its resistance to corrosion. This information is important for industries that use aluminum alloys in environments that are prone to corrosion, such as marine applications or chemical processing. Further research could explore the specific mechanisms that contribute to the corrosion resistance of different aluminum alloys and could investigate the effects of other environmental factors on corrosion.

The lab report introduction provides your readers with background information on your experiment and its significance. It should be brief and to the point, so a few paragraphs is the maximum length recommended.

You can adopt either of two modes to write your introduction:

• Beginning with the research question and then adding context, ultimately closing with your purpose.
• Beginning with the broad topic and narrowing it down to your research question.

Follow these steps to write your lab report introduction:

• Begin with a brief overview of the broad research area and existing literature. 
• Include only essential background information and cite only highly relevant sources. 
• Clearly define any key terms or concepts that you’ll use in the report.
• State the specific purpose and objectives of your experiment.
• Mention the relevance and significance of your study.
• State a clear hypothesis and expected outcomes.
• Check with your instructor about adding the variables, results, and conclusions to the introduction.
• Refer to the university guidelines for instructions on labeling paragraphs in your introduction.
• Use the past tense when describing the purpose and other specifics of the experiment since it has already been carried out and is in the past. (“This experiment aimed to investigate the corrosion resistance of two different aluminum alloys.”)
• Use the present tense when describing the report, existing theories, and established facts. (“This information is important for industries that use aluminum alloys in environments prone to corrosion.”)

Make sure you use your own words rather than following a templatized format.

Lab report introduction example

Aluminum alloys are widely used in a variety of industrial applications due to their excellent strength-to-weight ratio, good corrosion resistance, and other desirable properties. However, the corrosion resistance of aluminum alloys can vary depending on their composition, and understanding the factors that contribute to corrosion resistance is crucial for their effective use in harsh environments. In this experiment, we aim to investigate the corrosion resistance of two different aluminum alloys: 6061-T6 and 7075-T6.

These alloys were selected because they are commonly used in industrial applications and have different compositions, with 6061-T6 containing magnesium and silicon, while 7075-T6 contains zinc and copper. By exposing samples of each alloy to a 3% NaCl solution and measuring the weight loss of the samples over time, we can determine which alloy is more corrosion-resistant and gain insight into the factors that contribute to their corrosion resistance. This information is important for industries that use aluminum alloys in harsh environments, such as marine and aerospace applications, and can contribute to the development of more effective corrosion-resistant materials.

The lab report methods section documents the methods, subjects, materials, and equipment you used to collect data. This is a record of the steps you followed and not the steps as they were prescribed.

Follow these tips to write a lab report method section:

• List all materials and equipment used in the experiment, including their material specifications such as weight or amount. (Ex: 5 ml of 3% NaCl solution)
• In the case of elaborate lists and sets of steps, you may include them in the appendix section and refer to them in the methods section. (Check this with your instructor!)
• Detail the procedures you used to carry out the experiment step-by-step, including apparatus setup, mixing of reagents, and other technical processes.
• Explain how you collected and recorded the data as well as the involved analytical methods and calculations.
• Use the past tense to write this section.
• Discuss the limitations and margins of error and how you tried to minimize them.
• Where relevant, mention the safety precautions and protective equipment used during the experiment.

Your methods section should be accurate enough for other researchers to follow the instructions and obtain results similar to yours.

Lab report method example

• Two aluminum alloy samples: 6061-T6 and 7075-T6
• 3% NaCl solution
• Two beakers
• Two stirring rods
• Digital scale
• Vernier caliper
• Cut four aluminum alloy samples, two from each type of alloy, each with dimensions of 1 cm x 1 cm x 0.2 cm.
• Clean the samples thoroughly using ethanol to remove any impurities or oils.
• Weigh each sample accurately using a digital scale and record the initial weight.
• Prepare a 3% NaCl solution by dissolving 30 g of NaCl in 1000 mL of deionized water.
• Pour 250 mL of the 3% NaCl solution into each beaker.
• Submerge two samples of each aluminum alloy in separate beakers containing the NaCl solution.
• Use the stirring rods to stir the solutions gently to ensure uniformity.
• Allow the samples to remain in the solutions for 72 hours at room temperature (25°C).
• After 72 hours, carefully remove each sample from the solution and rinse with deionized water to remove any remaining salt.
• Dry each sample using a lint-free cloth and measure its weight using the digital scale.
• Record the final weight of each sample.
• Calculate the weight loss of each sample by subtracting the final weight from the initial weight.
• Use a Vernier caliper to measure the thickness of each sample, and record these measurements.
• Calculate the corrosion rate for each sample by dividing the weight loss by the surface area of the sample and the time of immersion in the solution.

Data Collection:

Weight loss and thickness measurements were recorded for each sample after the 72-hour immersion period. Corrosion rates were calculated using the weight loss, surface area, and time of immersion.

The experiment was conducted in a well-ventilated area with appropriate personal protective equipment, including gloves and goggles. Care was taken when handling the NaCl solution to avoid contact with the skin or eyes.

Limitations:

The experiment was conducted under controlled conditions, which may not reflect real-world scenarios. The NaCl solution concentration used may not be representative of all environmental conditions that aluminum alloys may encounter in industrial applications. Further research could explore a wider range of environmental factors to more accurately predict the corrosion resistance of aluminum alloys.

The results section presents the findings of the experiment including the data you have collected and analyzed. In some cases, this section may be combined with the discussion section.

Put your findings into words and present relevant figures, tables, and graphs. You may also include the calculations you used to analyze the data.

Here are some guidelines on how to write a results section:

• Begin with a concise summary of your key findings in the form of a brief paragraph or bullet points.
• Present the data collected in the form of tables, graphs, or charts.
• Describe important data to highlight any patterns you have observed.
• Use descriptive statistics such as mean, median, and standard deviation, to summarize your data.

Add your raw data in the Appendices section and refer to it whenever required. Remember to use symbols and units of measurement correctly.

Lab report results example

The aluminum alloys tested have varying degrees of corrosion resistance. Table 1 shows the corrosion rates for each sample, calculated as the percentage weight loss over the duration of the experiment.

Table 1: Corrosion rates for aluminum alloy samples

Sample Corrosion rate (%)

As can be seen from Table 1, sample C had the lowest corrosion rate, indicating the highest resistance to corrosion among the four samples tested. Sample A had the highest corrosion rate, indicating the lowest corrosion resistance.

Figure 1 shows the corrosion morphology of the aluminum alloy samples after exposure to the saltwater solution for 7 days. The images were taken using scanning electron microscopy (SEM).

The SEM images show that sample C had the least amount of corrosion, with only small pits visible on the surface. Samples A and B showed more severe corrosion, with visible pitting and cracking. Sample D showed moderate corrosion, with some surface roughening and small pits.

In conclusion, the results of this experiment indicate that the corrosion resistance of aluminum alloys varies depending on the composition of the alloy. Sample C, which had the lowest corrosion rate and the least amount of corrosion morphology, showed the highest resistance to corrosion among the four samples tested. Further research could investigate the effect of different environmental conditions on the corrosion resistance of aluminum alloys.

The discussion section of a lab report is where you interpret and analyze the results of your experiment in the context of the research question or hypothesis. This is the most important part of the lab report because this is your contribution to your field of study.

Follow these guidelines to write your discussion section:

• Begin with a brief summary of the main findings of the experiment.
• Interpret the results and explain how they relate to your research question or hypothesis.
• Compare the results to previous research in the field and analyze how they support or oppose existing theories or models.
• Discuss any limitations or sources of error in the experiment and how they can be improved upon.
• If applicable, include any additional analysis such as post-hoc tests or follow-up experiments.

Your discussion section shouldn’t simply repeat the results but offer a critical interpretation and analysis of them. Furthermore, it should also reflect upon the methods and procedures undertaken and take stock of whether you applied processes most favorable for your subject.

Lab report discussion example

The investigation into the corrosion resistance of aluminum alloys has provided valuable insight into the behavior of these materials under various conditions. The results of the experiment indicated that the aluminum alloys tested had varying degrees of corrosion resistance depending on the specific alloy composition and environmental conditions.

Comparing the results to previous research in the field, the findings are consistent with the general understanding that aluminum alloys are susceptible to corrosion under certain circumstances. However, the exact mechanisms of corrosion and the specific factors that influence corrosion resistance are still subject to ongoing research.

One limitation of the experiment is the relatively short duration of exposure to the corrosive environment. Longer exposure times may have provided additional insights into the behavior of the aluminum alloys over time. Additionally, the use of only one type of corrosive environment may not accurately reflect the behavior of the materials in other environments.

The unexpected finding of pitting corrosion in Alloy B warrants further investigation to determine the underlying causes and potential solutions. Future research could also explore the effects of additional factors, such as temperature and humidity, on the corrosion resistance of aluminum alloys.

Overall, the results of this experiment demonstrate the importance of considering the specific composition and environmental conditions when evaluating the corrosion resistance of aluminum alloys. The findings have implications for the development of more durable and corrosion-resistant materials for various applications in industry and engineering.

The conclusion summarizes the experiment and its significance in your field of study. It’s usually one brief paragraph, and in some cases might be omitted altogether. Check with your instructor about whether or not you need to write a lab report conclusion.

Here’s how to write a lab report conclusion:

• State whether the experiment supported or opposed your hypothesis.
• Reflect upon the significance and implications of your study.
• Suggest avenues for future research.

Lab report conclusion example

The investigation into the corrosion resistance of aluminum alloys demonstrated that the aluminum alloys tested had varying degrees of corrosion resistance, depending on their specific composition and the nature of the corrosive environment. The results of the experiment are consistent with previous research in the field, and the findings support the notion that aluminum alloys are susceptible to corrosion under certain conditions.

The experiment also revealed some unexpected findings, such as the pitting corrosion observed in Alloy B. This finding warrants further investigation to determine the underlying causes and potential solutions.

The experiment was limited by the relatively short exposure time to the corrosive environment and the use of only one type of corrosive environment. Future research could explore the effects of longer exposure times and different corrosive environments on the corrosion resistance of aluminum alloys.

Overall, the results of this experiment provide important insights into the behavior of aluminum alloys and have implications for the development of more durable and corrosion-resistant materials for various applications in industry and engineering.

List all the sources you consulted while writing the lab report. Include the full bibliographic information in the appropriate format.

For lab reports in sciences and social sciences, the APA citation style is usually followed. Students of business, fine arts, and history will use Chicago style citations in their lab reports. In the rare event of a lab report under humanities, you’ll be expected to write your citations in MLA format .

Remember that failing to cite your sources is considered plagiarism and has serious consequences. Always give credit where credit is due!

Lab Report Example & Templates

A. basic lab report template, b. chemistry lab report example, c. example of good labeling.

The above examples accurately demonstrate the hallmarks of a good lab report. If you need help to perfect your lab report, you can consider taking our editing and proofreading services . Keep reading to perfect your writing skills! 

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Frequently Asked Questions

What is the primary purpose of writing a lab report, what should a lab report look like, how to write a lab report for biology, how long is a lab report, what is the longest part of a lab report.

Found this article helpful?

6 comments on “ How to Write a Lab Report: Examples from Academic Editors ”

Good info. Lucky me I came across your blog by chance. I’ve saved it for later!

Hi there, I don’t leave comments a lot but I must say, the lab report results part was quite well-written. Keep up the good work!

It’s quite well-written but you can improve the images maybe. Anyway, keep up writing.

You’ve explained each lab report section so easily! I appreciate the tips and example combination!

Honestly, the lab report examples could be better. But great work, super easy to read and informative

This information on lab report writing is so useful! Thanks for all the templates and examples, super helpful!

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How to Report the Shapiro-Wilk Test

The Shapiro-Wilk test is a statistical test used to check if a continuous variable follows a normal distribution. The null hypothesis (H 0 ) states that the variable is normally distributed, and the alternative hypothesis (H 1 ) states that the variable is NOT normally distributed. So after running this test:

• If p ≤ 0.05: then the null hypothesis can be rejected (i.e. the variable is NOT normally distributed).
• If p > 0.05: then the null hypothesis cannot be rejected (i.e. the variable MAY BE normally distributed).

Information that should be reported

When reporting the Shapiro-Wilk test, the following should be mentioned:

• The reason why the test was used.
• The results of the test: the value of the test statistic W and the p-value associated with it.
• The consequences/interpretation of these results.

Here are 2 examples:

Example 1: Reporting a Shapiro-Wilk test with p ≤ 0.05

Since we had a small sample size, determining the distribution of the variable X was important for choosing an appropriate statistical method. So a Shapiro-Wilk test was performed and showed that the distribution of X departed significantly from normality (W = 0.96, p-value < 0.01). Based on this outcome, a non-parametric test was used, and the median with the interquartile range were used to summarize the variable X.

Example 2: Reporting a Shapiro-Wilk test with p > 0.05

Since we had a small sample size, determining the distribution of the variable X was important for choosing an appropriate statistical method. So a Shapiro-Wilk test was performed and did not show evidence of non-normality (W = 0.92, p-value = 0.11). Based on this outcome, and after visual examination of the histogram of X and the QQ plot, we decided to use a parametric test. Also, the mean with the standard deviation were used to summarize the variable X.

Important notes for reporting a Shapiro-Wilk test

1. a p > 0.05 does not prove the alternative hypothesis:.

A Shapiro-Wilk test with a p > 0.05 does not mean that the variable is normally distributed , it only means that you cannot reject the null hypothesis which states that the variable is normally distributed.

This is why in the example above, where we reported a Shapiro-Wilk test with a p > 0.05, we used the words: “the Shapiro-Wilk test did not show evidence of non-normality “.

So be aware of incorrect interpretations like the following:

• “ The Shapiro-Wilk test indicates that the variable has a normal distribution “.
• “ The normality assumption was verified using the Shapiro-Wilk test “.
• “ Normality of the data was confirmed by a Shapiro-Wilk test “.
• “ The distribution of the variable was determined using the Shapiro-Wilk test “.

2. The probability of getting a p < 0.05 depends on the size of your sample

A large enough sample size will make the Shapiro-Wilk test detect the smallest deviation from normality, in this case the p-value will be < 0.05 even if the variable is, in fact, normally distributed. Conversely, a very small sample size will reduce the statistical power of the Shapiro-Wilk test to reject the null hypothesis, in this case the p-value will be ≥ 0.05 even if the data clearly do not come from a normal distribution.

For these reasons many data analysts prefer to assess normality visually and/or using common sense, as sometimes the shape of a distribution can be decided theoretically, especially if the variable has some natural boundaries. For instance, “age” and “bacterial count” cannot have values less than zero, however they may have a very high although improbable upper bound (i.e. a right tail). Therefore, these variables should be ruled as following non-normal distributions.

3. Reporting the results of Shapiro-Wilk tests on many variables

For reporting the results of Shapiro-Wilk tests on many variables, use 1 of the following templates:

The distributions were significantly non-normal for the variables X 1 (W = 0.93, p < 0.01), X 2 (W = 0.95, p < 0.01), and X 3 (W = 0.91, p < 0.01) according to Shapiro-Wilk tests.

Shapiro-Wilk tests showed that neither X 1 (W = 0.93, p < 0.01) nor X 2 (W = 0.95, p < 0.01) were normally distributed.

Further reading

• Which Variables to Include in a Regression Model
• Standardized vs Unstandardized Regression Coefficients
• Interpret Linear Regression Coefficients

Hypothesis Testing - Chi Squared Test

Lisa Sullivan, PhD

Professor of Biostatistics

Boston University School of Public Health

Introduction

This module will continue the discussion of hypothesis testing, where a specific statement or hypothesis is generated about a population parameter, and sample statistics are used to assess the likelihood that the hypothesis is true. The hypothesis is based on available information and the investigator's belief about the population parameters. The specific tests considered here are called chi-square tests and are appropriate when the outcome is discrete (dichotomous, ordinal or categorical). For example, in some clinical trials the outcome is a classification such as hypertensive, pre-hypertensive or normotensive. We could use the same classification in an observational study such as the Framingham Heart Study to compare men and women in terms of their blood pressure status - again using the classification of hypertensive, pre-hypertensive or normotensive status.  

The technique to analyze a discrete outcome uses what is called a chi-square test. Specifically, the test statistic follows a chi-square probability distribution. We will consider chi-square tests here with one, two and more than two independent comparison groups.

Learning Objectives

After completing this module, the student will be able to:

• Perform chi-square tests by hand
• Appropriately interpret results of chi-square tests
• Identify the appropriate hypothesis testing procedure based on type of outcome variable and number of samples

Tests with One Sample, Discrete Outcome

Here we consider hypothesis testing with a discrete outcome variable in a single population. Discrete variables are variables that take on more than two distinct responses or categories and the responses can be ordered or unordered (i.e., the outcome can be ordinal or categorical). The procedure we describe here can be used for dichotomous (exactly 2 response options), ordinal or categorical discrete outcomes and the objective is to compare the distribution of responses, or the proportions of participants in each response category, to a known distribution. The known distribution is derived from another study or report and it is again important in setting up the hypotheses that the comparator distribution specified in the null hypothesis is a fair comparison. The comparator is sometimes called an external or a historical control.   

In one sample tests for a discrete outcome, we set up our hypotheses against an appropriate comparator. We select a sample and compute descriptive statistics on the sample data. Specifically, we compute the sample size (n) and the proportions of participants in each response

Test Statistic for Testing H 0 : p 1 = p 10 , p 2 = p 20 , ..., p k = p k0

We find the critical value in a table of probabilities for the chi-square distribution with degrees of freedom (df) = k-1. In the test statistic, O = observed frequency and E=expected frequency in each of the response categories. The observed frequencies are those observed in the sample and the expected frequencies are computed as described below. χ 2 (chi-square) is another probability distribution and ranges from 0 to ∞. The test above statistic formula above is appropriate for large samples, defined as expected frequencies of at least 5 in each of the response categories.  

When we conduct a χ 2 test, we compare the observed frequencies in each response category to the frequencies we would expect if the null hypothesis were true. These expected frequencies are determined by allocating the sample to the response categories according to the distribution specified in H 0 . This is done by multiplying the observed sample size (n) by the proportions specified in the null hypothesis (p 10 , p 20 , ..., p k0 ). To ensure that the sample size is appropriate for the use of the test statistic above, we need to ensure that the following: min(np 10 , n p 20 , ..., n p k0 ) > 5.  

The test of hypothesis with a discrete outcome measured in a single sample, where the goal is to assess whether the distribution of responses follows a known distribution, is called the χ 2 goodness-of-fit test. As the name indicates, the idea is to assess whether the pattern or distribution of responses in the sample "fits" a specified population (external or historical) distribution. In the next example we illustrate the test. As we work through the example, we provide additional details related to the use of this new test statistic.  

A University conducted a survey of its recent graduates to collect demographic and health information for future planning purposes as well as to assess students' satisfaction with their undergraduate experiences. The survey revealed that a substantial proportion of students were not engaging in regular exercise, many felt their nutrition was poor and a substantial number were smoking. In response to a question on regular exercise, 60% of all graduates reported getting no regular exercise, 25% reported exercising sporadically and 15% reported exercising regularly as undergraduates. The next year the University launched a health promotion campaign on campus in an attempt to increase health behaviors among undergraduates. The program included modules on exercise, nutrition and smoking cessation. To evaluate the impact of the program, the University again surveyed graduates and asked the same questions. The survey was completed by 470 graduates and the following data were collected on the exercise question:

Based on the data, is there evidence of a shift in the distribution of responses to the exercise question following the implementation of the health promotion campaign on campus? Run the test at a 5% level of significance.

In this example, we have one sample and a discrete (ordinal) outcome variable (with three response options). We specifically want to compare the distribution of responses in the sample to the distribution reported the previous year (i.e., 60%, 25%, 15% reporting no, sporadic and regular exercise, respectively). We now run the test using the five-step approach.  

• Step 1. Set up hypotheses and determine level of significance.

The null hypothesis again represents the "no change" or "no difference" situation. If the health promotion campaign has no impact then we expect the distribution of responses to the exercise question to be the same as that measured prior to the implementation of the program.

H 0 : p 1 =0.60, p 2 =0.25, p 3 =0.15,  or equivalently H 0 : Distribution of responses is 0.60, 0.25, 0.15  

H 1 :   H 0 is false.          α =0.05

Notice that the research hypothesis is written in words rather than in symbols. The research hypothesis as stated captures any difference in the distribution of responses from that specified in the null hypothesis. We do not specify a specific alternative distribution, instead we are testing whether the sample data "fit" the distribution in H 0 or not. With the χ 2 goodness-of-fit test there is no upper or lower tailed version of the test.

• Step 2. Select the appropriate test statistic.  

The test statistic is:

We must first assess whether the sample size is adequate. Specifically, we need to check min(np 0 , np 1, ..., n p k ) > 5. The sample size here is n=470 and the proportions specified in the null hypothesis are 0.60, 0.25 and 0.15. Thus, min( 470(0.65), 470(0.25), 470(0.15))=min(282, 117.5, 70.5)=70.5. The sample size is more than adequate so the formula can be used.

• Step 3. Set up decision rule.  

The decision rule for the χ 2 test depends on the level of significance and the degrees of freedom, defined as degrees of freedom (df) = k-1 (where k is the number of response categories). If the null hypothesis is true, the observed and expected frequencies will be close in value and the χ 2 statistic will be close to zero. If the null hypothesis is false, then the χ 2 statistic will be large. Critical values can be found in a table of probabilities for the χ 2 distribution. Here we have df=k-1=3-1=2 and a 5% level of significance. The appropriate critical value is 5.99, and the decision rule is as follows: Reject H 0 if χ 2 > 5.99.

• Step 4. Compute the test statistic.  

We now compute the expected frequencies using the sample size and the proportions specified in the null hypothesis. We then substitute the sample data (observed frequencies) and the expected frequencies into the formula for the test statistic identified in Step 2. The computations can be organized as follows.

Notice that the expected frequencies are taken to one decimal place and that the sum of the observed frequencies is equal to the sum of the expected frequencies. The test statistic is computed as follows:

• Step 5. Conclusion.  

We reject H 0 because 8.46 > 5.99. We have statistically significant evidence at α=0.05 to show that H 0 is false, or that the distribution of responses is not 0.60, 0.25, 0.15.  The p-value is p < 0.005.  

In the χ 2 goodness-of-fit test, we conclude that either the distribution specified in H 0 is false (when we reject H 0 ) or that we do not have sufficient evidence to show that the distribution specified in H 0 is false (when we fail to reject H 0 ). Here, we reject H 0 and concluded that the distribution of responses to the exercise question following the implementation of the health promotion campaign was not the same as the distribution prior. The test itself does not provide details of how the distribution has shifted. A comparison of the observed and expected frequencies will provide some insight into the shift (when the null hypothesis is rejected). Does it appear that the health promotion campaign was effective?  

Consider the following: 

If the null hypothesis were true (i.e., no change from the prior year) we would have expected more students to fall in the "No Regular Exercise" category and fewer in the "Regular Exercise" categories. In the sample, 255/470 = 54% reported no regular exercise and 90/470=19% reported regular exercise. Thus, there is a shift toward more regular exercise following the implementation of the health promotion campaign. There is evidence of a statistical difference, is this a meaningful difference? Is there room for improvement?

The National Center for Health Statistics (NCHS) provided data on the distribution of weight (in categories) among Americans in 2002. The distribution was based on specific values of body mass index (BMI) computed as weight in kilograms over height in meters squared. Underweight was defined as BMI< 18.5, Normal weight as BMI between 18.5 and 24.9, overweight as BMI between 25 and 29.9 and obese as BMI of 30 or greater. Americans in 2002 were distributed as follows: 2% Underweight, 39% Normal Weight, 36% Overweight, and 23% Obese. Suppose we want to assess whether the distribution of BMI is different in the Framingham Offspring sample. Using data from the n=3,326 participants who attended the seventh examination of the Offspring in the Framingham Heart Study we created the BMI categories as defined and observed the following:

• Step 1.  Set up hypotheses and determine level of significance.

H 0 : p 1 =0.02, p 2 =0.39, p 3 =0.36, p 4 =0.23     or equivalently

H 0 : Distribution of responses is 0.02, 0.39, 0.36, 0.23

H 1 :   H 0 is false.        α=0.05

The formula for the test statistic is:

We must assess whether the sample size is adequate. Specifically, we need to check min(np 0 , np 1, ..., n p k ) > 5. The sample size here is n=3,326 and the proportions specified in the null hypothesis are 0.02, 0.39, 0.36 and 0.23. Thus, min( 3326(0.02), 3326(0.39), 3326(0.36), 3326(0.23))=min(66.5, 1297.1, 1197.4, 765.0)=66.5. The sample size is more than adequate, so the formula can be used.

Here we have df=k-1=4-1=3 and a 5% level of significance. The appropriate critical value is 7.81 and the decision rule is as follows: Reject H 0 if χ 2 > 7.81.

We now compute the expected frequencies using the sample size and the proportions specified in the null hypothesis. We then substitute the sample data (observed frequencies) into the formula for the test statistic identified in Step 2. We organize the computations in the following table.

The test statistic is computed as follows:

We reject H 0 because 233.53 > 7.81. We have statistically significant evidence at α=0.05 to show that H 0 is false or that the distribution of BMI in Framingham is different from the national data reported in 2002, p < 0.005.  

Again, the χ 2   goodness-of-fit test allows us to assess whether the distribution of responses "fits" a specified distribution. Here we show that the distribution of BMI in the Framingham Offspring Study is different from the national distribution. To understand the nature of the difference we can compare observed and expected frequencies or observed and expected proportions (or percentages). The frequencies are large because of the large sample size, the observed percentages of patients in the Framingham sample are as follows: 0.6% underweight, 28% normal weight, 41% overweight and 30% obese. In the Framingham Offspring sample there are higher percentages of overweight and obese persons (41% and 30% in Framingham as compared to 36% and 23% in the national data), and lower proportions of underweight and normal weight persons (0.6% and 28% in Framingham as compared to 2% and 39% in the national data). Are these meaningful differences?

In the module on hypothesis testing for means and proportions, we discussed hypothesis testing applications with a dichotomous outcome variable in a single population. We presented a test using a test statistic Z to test whether an observed (sample) proportion differed significantly from a historical or external comparator. The chi-square goodness-of-fit test can also be used with a dichotomous outcome and the results are mathematically equivalent.  

In the prior module, we considered the following example. Here we show the equivalence to the chi-square goodness-of-fit test.

The NCHS report indicated that in 2002, 75% of children aged 2 to 17 saw a dentist in the past year. An investigator wants to assess whether use of dental services is similar in children living in the city of Boston. A sample of 125 children aged 2 to 17 living in Boston are surveyed and 64 reported seeing a dentist over the past 12 months. Is there a significant difference in use of dental services between children living in Boston and the national data?

We presented the following approach to the test using a Z statistic. 

• Step 1. Set up hypotheses and determine level of significance

H 0 : p = 0.75

H 1 : p ≠ 0.75                               α=0.05

We must first check that the sample size is adequate. Specifically, we need to check min(np 0 , n(1-p 0 )) = min( 125(0.75), 125(1-0.75))=min(94, 31)=31. The sample size is more than adequate so the following formula can be used

This is a two-tailed test, using a Z statistic and a 5% level of significance. Reject H 0 if Z < -1.960 or if Z > 1.960.

We now substitute the sample data into the formula for the test statistic identified in Step 2. The sample proportion is:

We reject H 0 because -6.15 < -1.960. We have statistically significant evidence at a =0.05 to show that there is a statistically significant difference in the use of dental service by children living in Boston as compared to the national data. (p < 0.0001).  

We now conduct the same test using the chi-square goodness-of-fit test. First, we summarize our sample data as follows:

H 0 : p 1 =0.75, p 2 =0.25     or equivalently H 0 : Distribution of responses is 0.75, 0.25 

We must assess whether the sample size is adequate. Specifically, we need to check min(np 0 , np 1, ...,np k >) > 5. The sample size here is n=125 and the proportions specified in the null hypothesis are 0.75, 0.25. Thus, min( 125(0.75), 125(0.25))=min(93.75, 31.25)=31.25. The sample size is more than adequate so the formula can be used.

Here we have df=k-1=2-1=1 and a 5% level of significance. The appropriate critical value is 3.84, and the decision rule is as follows: Reject H 0 if χ 2 > 3.84. (Note that 1.96 2 = 3.84, where 1.96 was the critical value used in the Z test for proportions shown above.)

(Note that (-6.15) 2 = 37.8, where -6.15 was the value of the Z statistic in the test for proportions shown above.)

We reject H 0 because 37.8 > 3.84. We have statistically significant evidence at α=0.05 to show that there is a statistically significant difference in the use of dental service by children living in Boston as compared to the national data.  (p < 0.0001). This is the same conclusion we reached when we conducted the test using the Z test above. With a dichotomous outcome, Z 2 = χ 2 !   In statistics, there are often several approaches that can be used to test hypotheses. 

Tests for Two or More Independent Samples, Discrete Outcome

Here we extend that application of the chi-square test to the case with two or more independent comparison groups. Specifically, the outcome of interest is discrete with two or more responses and the responses can be ordered or unordered (i.e., the outcome can be dichotomous, ordinal or categorical). We now consider the situation where there are two or more independent comparison groups and the goal of the analysis is to compare the distribution of responses to the discrete outcome variable among several independent comparison groups.  

The test is called the χ 2 test of independence and the null hypothesis is that there is no difference in the distribution of responses to the outcome across comparison groups. This is often stated as follows: The outcome variable and the grouping variable (e.g., the comparison treatments or comparison groups) are independent (hence the name of the test). Independence here implies homogeneity in the distribution of the outcome among comparison groups.    

The null hypothesis in the χ 2 test of independence is often stated in words as: H 0 : The distribution of the outcome is independent of the groups. The alternative or research hypothesis is that there is a difference in the distribution of responses to the outcome variable among the comparison groups (i.e., that the distribution of responses "depends" on the group). In order to test the hypothesis, we measure the discrete outcome variable in each participant in each comparison group. The data of interest are the observed frequencies (or number of participants in each response category in each group). The formula for the test statistic for the χ 2 test of independence is given below.

Test Statistic for Testing H 0 : Distribution of outcome is independent of groups

and we find the critical value in a table of probabilities for the chi-square distribution with df=(r-1)*(c-1).

Here O = observed frequency, E=expected frequency in each of the response categories in each group, r = the number of rows in the two-way table and c = the number of columns in the two-way table.   r and c correspond to the number of comparison groups and the number of response options in the outcome (see below for more details). The observed frequencies are the sample data and the expected frequencies are computed as described below. The test statistic is appropriate for large samples, defined as expected frequencies of at least 5 in each of the response categories in each group.  

The data for the χ 2 test of independence are organized in a two-way table. The outcome and grouping variable are shown in the rows and columns of the table. The sample table below illustrates the data layout. The table entries (blank below) are the numbers of participants in each group responding to each response category of the outcome variable.

Table - Possible outcomes are are listed in the columns; The groups being compared are listed in rows.

In the table above, the grouping variable is shown in the rows of the table; r denotes the number of independent groups. The outcome variable is shown in the columns of the table; c denotes the number of response options in the outcome variable. Each combination of a row (group) and column (response) is called a cell of the table. The table has r*c cells and is sometimes called an r x c ("r by c") table. For example, if there are 4 groups and 5 categories in the outcome variable, the data are organized in a 4 X 5 table. The row and column totals are shown along the right-hand margin and the bottom of the table, respectively. The total sample size, N, can be computed by summing the row totals or the column totals. Similar to ANOVA, N does not refer to a population size here but rather to the total sample size in the analysis. The sample data can be organized into a table like the above. The numbers of participants within each group who select each response option are shown in the cells of the table and these are the observed frequencies used in the test statistic.

The test statistic for the χ 2 test of independence involves comparing observed (sample data) and expected frequencies in each cell of the table. The expected frequencies are computed assuming that the null hypothesis is true. The null hypothesis states that the two variables (the grouping variable and the outcome) are independent. The definition of independence is as follows:

 Two events, A and B, are independent if P(A|B) = P(A), or equivalently, if P(A and B) = P(A) P(B).

The second statement indicates that if two events, A and B, are independent then the probability of their intersection can be computed by multiplying the probability of each individual event. To conduct the χ 2 test of independence, we need to compute expected frequencies in each cell of the table. Expected frequencies are computed by assuming that the grouping variable and outcome are independent (i.e., under the null hypothesis). Thus, if the null hypothesis is true, using the definition of independence:

P(Group 1 and Response Option 1) = P(Group 1) P(Response Option 1).

 The above states that the probability that an individual is in Group 1 and their outcome is Response Option 1 is computed by multiplying the probability that person is in Group 1 by the probability that a person is in Response Option 1. To conduct the χ 2 test of independence, we need expected frequencies and not expected probabilities . To convert the above probability to a frequency, we multiply by N. Consider the following small example.

The data shown above are measured in a sample of size N=150. The frequencies in the cells of the table are the observed frequencies. If Group and Response are independent, then we can compute the probability that a person in the sample is in Group 1 and Response category 1 using:

P(Group 1 and Response 1) = P(Group 1) P(Response 1),

P(Group 1 and Response 1) = (25/150) (62/150) = 0.069.

Thus if Group and Response are independent we would expect 6.9% of the sample to be in the top left cell of the table (Group 1 and Response 1). The expected frequency is 150(0.069) = 10.4.   We could do the same for Group 2 and Response 1:

P(Group 2 and Response 1) = P(Group 2) P(Response 1),

P(Group 2 and Response 1) = (50/150) (62/150) = 0.138.

The expected frequency in Group 2 and Response 1 is 150(0.138) = 20.7.

Thus, the formula for determining the expected cell frequencies in the χ 2 test of independence is as follows:

Expected Cell Frequency = (Row Total * Column Total)/N.

The above computes the expected frequency in one step rather than computing the expected probability first and then converting to a frequency.  

In a prior example we evaluated data from a survey of university graduates which assessed, among other things, how frequently they exercised. The survey was completed by 470 graduates. In the prior example we used the χ 2 goodness-of-fit test to assess whether there was a shift in the distribution of responses to the exercise question following the implementation of a health promotion campaign on campus. We specifically considered one sample (all students) and compared the observed distribution to the distribution of responses the prior year (a historical control). Suppose we now wish to assess whether there is a relationship between exercise on campus and students' living arrangements. As part of the same survey, graduates were asked where they lived their senior year. The response options were dormitory, on-campus apartment, off-campus apartment, and at home (i.e., commuted to and from the university). The data are shown below.

Based on the data, is there a relationship between exercise and student's living arrangement? Do you think where a person lives affect their exercise status? Here we have four independent comparison groups (living arrangement) and a discrete (ordinal) outcome variable with three response options. We specifically want to test whether living arrangement and exercise are independent. We will run the test using the five-step approach.  

H 0 : Living arrangement and exercise are independent

H 1 : H 0 is false.                α=0.05

The null and research hypotheses are written in words rather than in symbols. The research hypothesis is that the grouping variable (living arrangement) and the outcome variable (exercise) are dependent or related.   

• Step 2.  Select the appropriate test statistic.  

The condition for appropriate use of the above test statistic is that each expected frequency is at least 5. In Step 4 we will compute the expected frequencies and we will ensure that the condition is met.

The decision rule depends on the level of significance and the degrees of freedom, defined as df = (r-1)(c-1), where r and c are the numbers of rows and columns in the two-way data table.   The row variable is the living arrangement and there are 4 arrangements considered, thus r=4. The column variable is exercise and 3 responses are considered, thus c=3. For this test, df=(4-1)(3-1)=3(2)=6. Again, with χ 2 tests there are no upper, lower or two-tailed tests. If the null hypothesis is true, the observed and expected frequencies will be close in value and the χ 2 statistic will be close to zero. If the null hypothesis is false, then the χ 2 statistic will be large. The rejection region for the χ 2 test of independence is always in the upper (right-hand) tail of the distribution. For df=6 and a 5% level of significance, the appropriate critical value is 12.59 and the decision rule is as follows: Reject H 0 if c 2 > 12.59.

We now compute the expected frequencies using the formula,

Expected Frequency = (Row Total * Column Total)/N.

The computations can be organized in a two-way table. The top number in each cell of the table is the observed frequency and the bottom number is the expected frequency.   The expected frequencies are shown in parentheses.

Notice that the expected frequencies are taken to one decimal place and that the sums of the observed frequencies are equal to the sums of the expected frequencies in each row and column of the table.  

Recall in Step 2 a condition for the appropriate use of the test statistic was that each expected frequency is at least 5. This is true for this sample (the smallest expected frequency is 9.6) and therefore it is appropriate to use the test statistic.

We reject H 0 because 60.5 > 12.59. We have statistically significant evidence at a =0.05 to show that H 0 is false or that living arrangement and exercise are not independent (i.e., they are dependent or related), p < 0.005.  

Again, the χ 2 test of independence is used to test whether the distribution of the outcome variable is similar across the comparison groups. Here we rejected H 0 and concluded that the distribution of exercise is not independent of living arrangement, or that there is a relationship between living arrangement and exercise. The test provides an overall assessment of statistical significance. When the null hypothesis is rejected, it is important to review the sample data to understand the nature of the relationship. Consider again the sample data. 

Because there are different numbers of students in each living situation, it makes the comparisons of exercise patterns difficult on the basis of the frequencies alone. The following table displays the percentages of students in each exercise category by living arrangement. The percentages sum to 100% in each row of the table. For comparison purposes, percentages are also shown for the total sample along the bottom row of the table.

From the above, it is clear that higher percentages of students living in dormitories and in on-campus apartments reported regular exercise (31% and 23%) as compared to students living in off-campus apartments and at home (10% each).  

Test Yourself

 Pancreaticoduodenectomy (PD) is a procedure that is associated with considerable morbidity. A study was recently conducted on 553 patients who had a successful PD between January 2000 and December 2010 to determine whether their Surgical Apgar Score (SAS) is related to 30-day perioperative morbidity and mortality. The table below gives the number of patients experiencing no, minor, or major morbidity by SAS category.  

Question: What would be an appropriate statistical test to examine whether there is an association between Surgical Apgar Score and patient outcome? Using 14.13 as the value of the test statistic for these data, carry out the appropriate test at a 5% level of significance. Show all parts of your test.

In the module on hypothesis testing for means and proportions, we discussed hypothesis testing applications with a dichotomous outcome variable and two independent comparison groups. We presented a test using a test statistic Z to test for equality of independent proportions. The chi-square test of independence can also be used with a dichotomous outcome and the results are mathematically equivalent.  

In the prior module, we considered the following example. Here we show the equivalence to the chi-square test of independence.

A randomized trial is designed to evaluate the effectiveness of a newly developed pain reliever designed to reduce pain in patients following joint replacement surgery. The trial compares the new pain reliever to the pain reliever currently in use (called the standard of care). A total of 100 patients undergoing joint replacement surgery agreed to participate in the trial. Patients were randomly assigned to receive either the new pain reliever or the standard pain reliever following surgery and were blind to the treatment assignment. Before receiving the assigned treatment, patients were asked to rate their pain on a scale of 0-10 with higher scores indicative of more pain. Each patient was then given the assigned treatment and after 30 minutes was again asked to rate their pain on the same scale. The primary outcome was a reduction in pain of 3 or more scale points (defined by clinicians as a clinically meaningful reduction). The following data were observed in the trial.

We tested whether there was a significant difference in the proportions of patients reporting a meaningful reduction (i.e., a reduction of 3 or more scale points) using a Z statistic, as follows. 

H 0 : p 1 = p 2    

H 1 : p 1 ≠ p 2                             α=0.05

Here the new or experimental pain reliever is group 1 and the standard pain reliever is group 2.

We must first check that the sample size is adequate. Specifically, we need to ensure that we have at least 5 successes and 5 failures in each comparison group or that:

In this example, we have

Therefore, the sample size is adequate, so the following formula can be used:

Reject H 0 if Z < -1.960 or if Z > 1.960.

We now substitute the sample data into the formula for the test statistic identified in Step 2. We first compute the overall proportion of successes:

We now substitute to compute the test statistic.

• Step 5.  Conclusion.  

We now conduct the same test using the chi-square test of independence.  

H 0 : Treatment and outcome (meaningful reduction in pain) are independent

H 1 :   H 0 is false.         α=0.05

The formula for the test statistic is:  

For this test, df=(2-1)(2-1)=1. At a 5% level of significance, the appropriate critical value is 3.84 and the decision rule is as follows: Reject H0 if χ 2 > 3.84. (Note that 1.96 2 = 3.84, where 1.96 was the critical value used in the Z test for proportions shown above.)

We now compute the expected frequencies using:

The computations can be organized in a two-way table. The top number in each cell of the table is the observed frequency and the bottom number is the expected frequency. The expected frequencies are shown in parentheses.

A condition for the appropriate use of the test statistic was that each expected frequency is at least 5. This is true for this sample (the smallest expected frequency is 22.0) and therefore it is appropriate to use the test statistic.

(Note that (2.53) 2 = 6.4, where 2.53 was the value of the Z statistic in the test for proportions shown above.)

Chi-Squared Tests in R

The video below by Mike Marin demonstrates how to perform chi-squared tests in the R programming language.

Answer to Problem on Pancreaticoduodenectomy and Surgical Apgar Scores

We have 3 independent comparison groups (Surgical Apgar Score) and a categorical outcome variable (morbidity/mortality). We can run a Chi-Squared test of independence.

H 0 : Apgar scores and patient outcome are independent of one another.

H A : Apgar scores and patient outcome are not independent.

Chi-squared = 14.3

Since 14.3 is greater than 9.49, we reject H 0.

There is an association between Apgar scores and patient outcome. The lowest Apgar score group (0 to 4) experienced the highest percentage of major morbidity or mortality (16 out of 57=28%) compared to the other Apgar score groups.

How to accept or reject a hypothesis?

A hypothesis is a proposed statement to explore a possible theory. Many studies in the fields of social sciences, sciences, and mathematics make use of hypothesis testing to prove a theory. Assumptions in a hypothesis help in making predictions. It is presented in the form of null and alternate hypotheses. When a hypothesis is presented negatively (for example, TV advertisements do not affect consumer behavior), it is called a null hypothesis. This article explains the conditions to accept or reject a hypothesis.

Why is it important to reject the null hypothesis?

A null hypothesis is a statement that describes that there is no difference in the assumed characteristics of the population. For example, in a study wherein the impact of the level of education on the efficiency of the employee need to be determined, null (Ho) and alternate (HA) hypothesis would be:

In the above-stated null hypothesis, there is very little chance of a relationship between both the variables (education and employee’s efficiency). When a null hypothesis is accepted, it shows that the study has a lack of evidence in showing any significant connection between the variables. This could be due to problems with the data such as:

• high variability,
• small sample size,
• inappropriate sample and,
• wrong data testing method.

Hence, for efficient, appropriate, and reliable results, it is suggested to reject the null hypothesis.

Conditions for rejecting a null hypothesis

Rejection of the null hypothesis provides sufficient evidence for supporting the perception of the researcher. Thus, a statistician always prefers to reject the null hypothesis. However, there are certain conditions which need to be fulfilled for the required results i.e.

Condition 1: Sample data should be reasonably random

A random sample is the one every person in the sample universe has an equal possibility of being selected for the analysis. Random sampling is necessary for deriving accurate results and rejecting the null hypothesis. This is because when a sample is randomly selected, characteristic traits of each participant in the study are the same, so there is no error in decision making. For example, in the sample hypothesis, instead of collecting data from all employees, the data was collected from only the board members of the company. This hypothesis testing would not provide good results as the sample does not represent all the employees of the company.

Condition 2: Distribution of the sample should be known

A dataset can be of two types: normally distributed or skewed. Normally distributed datasets require application of parametric tests i.e. Z-test, T-test, χ2-test, and F-distribution. On the other hand, skewed dataset uses non-parametric test i.e. Wilcoxon rank sum test, Wilcoxon signed rank test, and Kruskal Wallis test. For reliable hypothesis test result, it is essential that the distribution of the sample be tested.

Condition 3: Value of test statistic should not fall in the rejection region

Test statistic value is compared with critical value when the null hypothesis is true (critical value). If the test statistic is more extreme as compared to the critical value, then the null hypothesis would be rejected.

For example, in the sample hypothesis if the sample size is 50 and the significance level of the study is 5% then the critical value for the given two-tailed test would be 1.960. Hence, null hypothesis would be rejected if,

Condition 4: P-value should be less than the significance of the study

P-value represents the probability that the null hypothesis true. In order to reject the null hypothesis, it is essential that the p-value should be less that the significance or the precision level considered for the study. Hence,

• Reject null hypothesis (H0) if ‘p’ value  < statistical significance (0.01/0.05/0.10)
• Accept null hypothesis (H0) if ‘p’ value > statistical significance (0.01/0.05/0.10)

For example, in the sample hypothesis if the considered statistical significance level is 5% and the p-value of the model is 0.12. Hence, the hypothesis of having no significant impact would not be rejected as 0.12 > 0.05.

Important points to note

While making the final decision of the hypothesis, these points should be noted i.e.

• A large sample size i.e. at least greater than 30 should be considered. As per the Central Limit Theorem (CLT) large sample size i.e. at least greater than 30 is considered to be approximately normally distributed.
• For deriving the results either p-value approach or rejection approach could be used. However, the p-value is a more preferable approach.
• Statistical significance should be maintained at a minimum level.
• The choice of the rejection region should be appropriately made by verifying the direction of the alternative hypothesis.
• Priya Chetty

I am a management graduate with specialisation in Marketing and Finance. I have over 12 years' experience in research and analysis. This includes fundamental and applied research in the domains of management and social sciences. I am well versed with academic research principles. Over the years i have developed a mastery in different types of data analysis on different applications like SPSS, Amos, and NVIVO. My expertise lies in inferring the findings and creating actionable strategies based on them. 

Over the past decade I have also built a profile as a researcher on Project Guru's Knowledge Tank division. I have penned over 200 articles that have earned me 400+ citations so far. My Google Scholar profile can be accessed here . 

I now consult university faculty through Faculty Development Programs (FDPs) on the latest developments in the field of research. I also guide individual researchers on how they can commercialise their inventions or research findings. Other developments im actively involved in at Project Guru include strengthening the "Publish" division as a bridge between industry and academia by bringing together experienced research persons, learners, and practitioners to collaboratively work on a common goal. 

I am a Senior Analyst at Project Guru, a research and analytics firm based in Gurugram since 2012. I hold a master’s degree in economics from Amity University (2019). Over 4 years, I have worked on worked on various research projects using a range of research tools like SPSS, STATA, VOSViewer, Python, EVIEWS, and NVIVO. My core strength lies in data analysis related to Economics, Accounting, and Financial Management fields.

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Scientific Method: Step 3: HYPOTHESIS

• Step 1: QUESTION
• Step 2: RESEARCH
• Step 3: HYPOTHESIS
• Step 4: EXPERIMENT
• Step 5: DATA
• Step 6: CONCLUSION

Step 3: State your hypothesis

Now it's time to state your hypothesis . The hypothesis is an educated guess as to what will happen during your experiment. 

The hypothesis is often written using the words "IF" and "THEN." For example, " If I do not study, then I will fail the test." The "if' and "then" statements reflect your independent and dependent variables . 

The hypothesis should relate back to your original question and must be testable .

A word about variables...

Your experiment will include variables to measure and to explain any cause and effect. Below you will find some useful links describing the different types of variables.

• "What are independent and dependent variables" NCES
• [VIDEO] Biology: Independent vs. Dependent Variables (Nucleus Medical Media) Video explaining independent and dependent variables, with examples.

Resource Links

• What is and How to Write a Good Hypothesis in Research? (Elsevier)
• Hypothesis brochure from Penn State/Berks

• << Previous: Step 2: RESEARCH
• Next: Step 4: EXPERIMENT >>
• Last Updated: Aug 2, 2024 3:45 PM
• URL: https://harford.libguides.com/scientific_method

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Learn How to Write a Hypothesis in a Lab Report

Published 17 Jul 2023

Lab Report: What is the Purpose of a Lab Report in Scientific Experiments? 

In learning how to write a hypothesis for a lab report, it is crucial to understand the main purpose and aspects of the scientific lab report itself. In simple terms, we are dealing with a particular structure that must reflect its importance and relevance. It can be related to an experiment, an assumption, or a hypothesis being made. It means discussing the aims and providing a hypothesis based on a particular methodology. It has to explain why the practical work has been conducted and what tools or solutions have been chosen. The method part must also be added to show how the work has been conducted and what data processing methods have been used. All of it brings us to the explanation of a hypothesis. 

This way, a lab report hypothesis represents a special statement that makes a proposal or an assumption of a scientific idea. The main purpose is to explain a phenomenon or an argument that follows your objectives. It can also be related to an event. Most importantly, it has to be a testable statement that can be evaluated and include a prediction. 

Understand the Role of Hypothesis and Scientific Methods: Defining The Differences

A hypothesis definition can be summed up by making a scientific assumption based on certain evidence. It means that one should have an initial point to start an investigation. It may include your objectives and transition of ideas into research questions and predictions of the outcomes. The crucial components include variables, sample groups, geopolitical factors, population peculiarities, or other variables to make a hypothesis trustworthy. 

The key is to test things in advance using your research work for that! The lab report represents a perfect environment for a real-time experiment where variables are tested. Learning how to write a hypothesis in a lab report, you may turn to prior observations like noticing how racial prejudice has shaped student movements during the 1970s and how things have changed since then. You may ask yourself about the interconnection between these two events and explain how exactly! 

The key differences between a hypothesis, a theory, and a fact can be explained easily this way: 

• Fact: "When you drop an apple, it will hit the ground." 
• Theory: "There is a gravitational force that will affect an apple once it falls.”
• Hypothesis: "When an apple hits the ground, it happens because a certain force pulls it down." 

Summing up, we can safely state that a theory is the next step to a scientific fact. A hypothesis is a process that needs evidence to explain the scientific assumption. In creating a lab report hypothesis, leading your target audience to an explanation and justification of the outcomes is essential. 

Crucial Elements of a Good Hypothesis 

The structure plays a critical role in creating a strong hypothesis to help you proceed with the further elements of a scientific lab report. In most scenarios, you should provide the following: 

• An assumption you offer should not be a stated question because the main purpose is to assume something based on facts by keeping your target audience motivated. Offer a practical objective instead! 
• Your hypothesis lab report writing should be testable regarding empirical research, stating whether something is right or wrong. 
• Keep your statement specific and precise! 
• The key is to specify variables to help readers determine the relationship between what is being tested and the outcome (including methodology). 

Summing things up, we receive this: 

• The research question or a problem. 
• The independent variable. 
• The dependent variable. 
• A relationship between what is independent and dependent. 

The best way to compose a reliable hypothesis for a lab report is to first ask a question by formulating the problem and conducting preliminary research. Next, variables must be defined as the " IF X is so, then Y is that " pattern. Collect sufficient research data that will help to support your hypothesis. Finally, keep your tone confident as you develop an explanation and the conclusion part (basic summary) of your research lab report. 

Hypothesis vs. Null Hypothesis

Many students often feel confused when they have to learn the difference between working with a scientific hypothesis and a null hypothesis. To keep things simple and accessible, a hypothesis always stands for something that a person tries to prove as a researcher. Now, a null hypothesis is totally different because it is what you have to argue and disprove. Still, you can safely use both methods to research and evaluate your data.

When dealing with a classic hypothesis, you should speculate and brainstorm a particular theory. If your evidence is insufficient, it must be mentioned, as your lab report leads to even more testing, evaluation, and experiments. Learning how to write hypotheses in lab report limitations and using a null hypothesis will include the same set of variables with a major difference. It often states that there is no significance or strong relation between two variables that you have obtained. 

In terms of examples, a null hypothesis may state, "There is no difference in the number of autism cases between children who have gone through vaccination procedures and those who have not." It often speaks of the elimination of connections between this and that, unlike a hypothesis that would say, "Poor vaccination culture leads to autism risks among children." 

6 Steps to Take When Composing a Hypothesis in a Lab Report

While there are many ways to write a hypothesis statement, there are still universal ways to develop it for your lab report. Without a doubt, you must consult your academic advisor and check your grading rubric twice. Let's narrow things down a little bit to the following six steps: 

• Provide a research question . It means that you must start with a research question introduction you offer. It should be precise and clear. 
• Offer preliminary research work. Consider research theories and prior studies to support your methodology and an assumption. It is a step that should include lab analysis and evaluation aspects. 
• Narrow down your hypothesis statement . When you have an idea, create a detailed yet short hypothesis like, "Playing video games daily improves cognitive skills". 
• Refine your hypothesis with variables. It is where you must make your hypothesis possible to replicate and test as you offer a lab report. Talk about variables and specific sample groups, and add your predictions. 
• Work on "IF" and "THEN" elements. Talk about relationships, positive or negative effects, differences, and comparisons. 
• Compose a null hypothesis (If necessary). If something has no effect, state that "X has no effect on Y, as Z proves." 

The Most Popular Formats to Write a Hypothesis 

It's possible to choose various approaches to composing your hypothesis statement. Still, the best of them would be the classic method of the "If this happens under certain variables, then this is bound to happen" pattern. Taking things to practice, one can structure things by using a descriptive tone. The trick is to make an assumption and describe what will happen to the dependent variable in case you change the features of the independent variable. Other types of lab report hypothesis options may include but are not limited to the following: 

• Simple (classic) hypothesis;
• Complex hypothesis structure;
• Directional hypothesis format;
• Non-directional hypothesis method;
• Discussion in a lab report approach; 
• Null hypothesis;
• Associative and causal hypothesis combination.

Choosing one of the above will depend on your type of lab reporting, research subject, and the list of variables. Choosing an associative evidence method will be the best solution if you want to work in the cause-and-effect field. Likewise, if you are unsure about what method to choose, the typical “IF” and “THEN,” “BECAUSE” would be the most universal approach. 

Conclusion and Initial Section of Hypothesis 

The conclusion of your lab report must provide a summary with an analytical explanation. It should not become a repetition of the results but talk about your objectives and methodology mentioned in your conclusion. As you make a hypothesis, you always provide some evidence. Now, when you write your lab report , do not discuss the evidence and the facts but discuss the results achieved with limitations and challenges faced. If you are unsure how to structure the final part, consider whether your assumption has been made and what has been discovered. 

As a rule, your lab report conclusion should be about 15% of the total amount or even less. Do not introduce any new ideas or statistical data in this part because you should only summarize things and discuss the results by stating your hypothesis once again. Keep your tone and language simple in this part, and avoid using citations or references to prior research work. 

Eliminating the Most Common Mistakes 

As a way to receive the best grades for your hypothesis in a lab report, you must avoid the most common mistakes in addition to grammar and spelling issues: 

• Your hypothesis should not be a question. 
• Avoid placing a citation before and after your hypothesis statement. 
• Do not use colloquial language in a lab report.
• Avoid the first person in a lab report and hypothesis statement unless specified. 
• Do not state a hypothesis that is not narrowed down and unclear. 
• Do not use lengthy statistical data, as it is not a hypothesis but evidence that helps to support your assumption. 
• Avoid submitting your lab report without proofreading your content aloud. 
• Avoid using more than three citations per page (300 words).
• Never submit a hypothesis in a lab report without a Method part that is clearly outlined after your goals and statement of the problem.

Writing a Hypothesis in a Lab Report Checklist 

If all of this sounds like rocket science to you and you are about to give up on your Chemistry lab report or any other subject, try to do the following by checking this simple hypothesis in a lab report checklist: 

• Choose a particular problem that you would like to address. 
• Continue with the specific format of hypothesis writing. 
• Try predicting relationships between variables and the possible outcome. 
• Keep your writing simple without being wordy. 
• Make no assumptions about what your target audience knows or does not know. 
• Keep your results replicable and possible to test and/or observe. 
• Provide relevant examples to understand your method in a better way. 
• It must be possible to repeat and analyze your research work. 
• Proofread and edit things twice! 

Using Additional Helpful Resources 

When you are writing hypothesis for a lab report based on specific research, it is important to take your time and explore additional resources. These may include online libraries, academic journals, books in print, specific databases, or even paying a visit to the local library of your college or university. As you look at similar research works, you can find out why some problems are relevant and what methods work best or what approaches have not been taken. It will help you to narrow things down and make your research stand out from the rest. Here are some useful resources to help you explore your scientific subject: 

• JStor Database ;
• PubMed (good for healthcare and medical subjects);
• ScienceDirect ;
• Google Scholar ;
• Web of Science ;
• Semantic Scholar ;
• Purdue OWL Writing Lab (good for learning more about citation format styles).

If something is unclear, check your grading rubric twice and ask questions by turning to your academic advisor! 

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How to Write Hypothesis for Lab Report

• How to Write Hypothesis for…

What Is a Real Hypothesis?

A hypothesis is a tentative statement that proposes a possible explanation for some phenomenon or event. A useful hypothesis is a testable statement that may include a prediction.

When Are Hypotheses Used?

The keyword is testable. That is, you will perform a test of how two variables might be related. This is when you are doing a real experiment. You are testing variables. Usually, a hypothesis is based on some previous observations such as noticing that in November many trees undergo color changes in their leaves and the average daily temperatures are dropping. Are these two events connected? How?

Any laboratory procedure you follow without a hypothesis is really not an experiment. It is just an exercise or demonstration of what is already known.

How Are Hypotheses Written?

• Chocolate may cause pimples.
• Salt in soil may affect plant growth.
• Plant growth may be affected by the color of the light.
• Bacterial growth may be affected by temperature.
• Ultraviolet light may cause skin cancer.
• The temperature may cause leaves to change color.

All of these are examples of hypotheses because they use the tentative word “may.”. However, their form is not particularly useful. Using the word may do not suggest how you would go about proving it. If these statements had not been written carefully, they may not have even been hypotheses at all. For example, if we say “Trees will change color when it gets cold.” we are making a prediction. Or if we write, “Ultraviolet light causes skin cancer.” could be a conclusion. One way to prevent making such easy mistakes is to formalize the form of the hypothesis.

Formalized Hypotheses example: If the incidence of skin cancer is related to exposure levels of ultraviolet light , then people with a high exposure to uv light will have a higher frequency of skin cancer.

If leaf color change is related to temperature , then exposing plants to low temperatures will result in changes in leaf color .

Notice that these statements contain the words, if and then. They are necessary for a formalized hypothesis. But not all if-then statements are hypotheses. For example, “If I play the lottery, then I will get rich.” This is a simple prediction. In a formalized hypothesis, a tentative relationship is stated. For example, if the frequency of winning is related to the frequency of buying lottery tickets . “Then” is followed by a prediction of what will happen if you increase or decrease the frequency of buying lottery tickets. If you always ask yourself that if one thing is related to another, then you should be able to test it.

Formalized hypotheses contain two variables. One is “independent” and the other is “dependent.” The independent variable is the one you, the “scientist” control, and the dependent variable is the one that you observe and/or measure the results. In the statements above the dependent variable is underlined and the independent variable is underlined and italicized .

The ultimate value of a formalized hypothesis is it forces us to think about what results we should look for in an experiment.

For the “ If, Then, Because ” hypothesis…you would use: “ IF pigs and humans share the same nutritional behaviors, THEN their internal organs should look relatively the same BECAUSE of similar function and composure.” That is an example. For the “If, Then, Because” you should follow this guideline:

IF X and Y both do or share this, THEN this should be found/confirmed, BECAUSE of this fact or logical assumption.

Example Question : How does the type of liquid (water, milk, or orange juice) given to a plant affect how tall the plant will grow? Hypothesis : If the plant is given water then the plant will grow the tallest because water helps the plant absorb the nutrients that the plant needs to survive.

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16 Comments

How would I write a hypothesis about a flying pig lab?

your lab hypothesis should have been written before the experiment. The purpose of the hypothesis was to create a testable statement in which your experimental data would either support or reject. Having a hypothesis based on a logical assumption (regardless of whether your data supports it) is still correct. If there is a disagreement between your hypothesis and experimental data it should be addressed in the discussion.

So you can go ahead an choose a hypothesis for either increase or decrease of adipogenesis after the inducement of insulin and not be wrong….as long as it is correctly formatted (see examples above).

Hey, I am having trouble writing my hypothesis.. I am supposed to write a hypothesis about how much adipogenesis was produced after the inducement of insulin. However, after proceeding with the experiments the results were On/Off .. meaning it will increase, decrease, increase, etc.. so it wasnt a constant result. It was supposed to be increasing.

please help!!!

this is very helpful but i don’t know how i would structure my hypothesis. i’m supposed to come up with a hypothesis related to the topic ‘how does mass effect the stopping distance of a cart?’. Could you help?

Thank you so much, it really help alot.:)

This is a rather difficult usage of this construct. It would most likely follow

“If the empirical formula of (enter compound’s name) is (enter compound’s formula) then it would be expected that combustion of _________ would yield _________, because (enter your rationale)

Need more background info.

For the “If, then, because” hypothesis I am doing an experiment to determine the empirical formula by using combustion but I am unsure on how to formulate the hypothesis using this structure.

For the “If, Then, Because” hypothesis…you would use: “IF pigs and humans share the same nutritional behaviors, THEN their internal organs should look relatively the same BECAUSE of similar function and composure.” That is an example. For the “If, Then, Because” you should follow this guideline:

Thanks, really helpful. Just one question, what about the ‘because’ part? right after the ‘if’ and ‘then’ parts?

I really need help for onion skin lab hypothesis for class

@Lauren An if/and statement is not usually apart of the convention. What exactly do you need help with?

Is there such thing as a if/and statement? I am in 8th grade science an I need to know for my lab report due tomorrow.HELP!!!!

Would have been better if more examples were given

If the purpose of your lab is “To obtain dissecting skills in an observational lab,” you can’t really formulate a testable hypothesis for that. I’ll assume you are doing some kind of pig or frog dissection. Often teachers give general outlines of skills that students are meant to ascertain from an experiment which aren’t necessarily what the actual experiment is directly testing. Obviously to do the dissection lab you need to obtain dissection skills but testing that would be rather subjective unless the teacher provided you with standards or operationally defined “dissecting skills”. If I were you, I would obviously mention it in the introduction of your lab but I am not sure if your teacher wants you to actually format it as a hypothesis; you can ask your teacher for clarification. If making a hypothesis from each purpose was some arbitrary exercise assigned to you then, it could look like this:

“If a student has successful acquired dissection skills, then they will be able to complete this observational lab with satisfactory competence because they utilized these newly acquired skills.”

For the “If, Then, Because” hypothesis…you pretty much have it. You would modify what you posted: “IF pigs and humans share the same nutritional behaviors, THEN their internal organs should look relatively the same BECAUSE of similar function and composure.” That is an example. For the “If, Then, Because” you should follow this guideline:

Thanks for this, it proved to be helpful. However, I do have a few questions. Obviously different teachers or instructors have their own requirements for their classes. How would you write an appropriate Question to follow each purpose in your lab report? For example: If the purpose was, “To obtain dissecting skills in an observational lab,” what question could you formulate with the purpose? (which is answered in the hypothesis)

And if a teacher requires the hypothesis to be in the format “If, Then, Because” how should this be written? I can actively complete the if and then, but I’m unsure how to incorporate the “because’ statement. For example, “If pigs and humans share the same nutritional behaviors, then their internal organs should function comparably and look relatively the same.” (how do i incorporate because?)

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