Best Examples of Chi-Square Test Lab Report Examples for Students

Examples of Chi-Square Test Lab Report Examples You Can Model

Before talking about formulas or theory, it helps to see how students actually use the chi-square test in lab reports. Below are several realistic examples of chi-square test lab report examples written in a style that would fit a college statistics or research methods course.

Each example of a chi-square test lab report follows the same basic structure:

• Research question and hypothesis
• Description of variables and data
• Statistical test and assumptions
• Results with chi-square statistic, degrees of freedom, and p-value
• Interpretation in plain language

Example 1: Chi-Square Goodness-of-Fit – M&M Color Distribution

Scenario
A student group wants to test whether the color distribution in a bag of chocolate candies matches the company’s advertised percentages.

Lab report excerpt (results and interpretation section):

We conducted a chi-square goodness-of-fit test to compare the observed frequencies of candy colors to the manufacturer’s claimed distribution (Brown 13%, Red 13%, Yellow 14%, Green 16%, Orange 20%, Blue 24%). We sampled 300 candies from multiple bags and recorded the color of each.

The chi-square test was significant, \(\chi^2(5, N = 300) = 12.47, p = 0.029\). Observed counts differed from expected counts most noticeably for blue (observed 56 vs. expected 72) and orange (observed 74 vs. expected 60).

These results suggest that the sample of candies in our lab did not follow the advertised color distribution. However, this may reflect batch-level variation rather than systematic mislabeling. A larger, multi-batch sample would be needed to draw stronger conclusions.

Why this works as one of the best examples of chi-square test lab report examples:

• States the theoretical distribution clearly
• Reports \(\chi^2\), df, N, and p-value
• Connects statistical result back to the real-world claim

If you need an example of a short, focused chi-square section, this candy-color write-up is a solid template.

Example 2: Chi-Square Test of Independence – Smoking Status and Exercise

Scenario
Students in an introductory biostatistics class collect survey data on campus to see whether smoking status is associated with exercise frequency.

Variables:

• Smoking status: Non-smoker, Occasional smoker, Daily smoker
• Exercise: Low (0–1 days/week), Moderate (2–3 days/week), High (4+ days/week)

Lab report excerpt (methods and results):

We used a chi-square test of independence to examine the association between smoking status and exercise frequency among college students. A total of 210 participants completed the survey. Both variables were categorical and all expected cell counts exceeded 5, supporting use of the chi-square approximation.

The association between smoking status and exercise frequency was statistically significant, \(\chi^2(4, N = 210) = 14.62, p = 0.006\). Non-smokers were more likely to report high exercise levels (48%) compared with daily smokers (19%). Daily smokers were overrepresented in the low exercise category.

These findings are consistent with national data from the CDC, which show that smoking often clusters with other health risk behaviors. In our sample, smoking status and exercise frequency were not independent.

This is one of the clearer examples of chi-square test lab report examples for health-related topics, especially if your instructor wants you to connect classroom data to public health datasets.

Example 3: Education – Homework Completion and Test Performance

Scenario
An education statistics class uses anonymized data from a middle school to see whether homework completion categories are associated with passing a math benchmark exam.

Variables:

• Homework completion: Low (0–50%), Medium (51–80%), High (81–100%)
• Test result: Pass, Fail

Lab report excerpt (results and discussion):

A chi-square test of independence was used to evaluate whether homework completion category was associated with passing the district math benchmark. The sample included 180 students.

The chi-square test was significant, \(\chi^2(2, N = 180) = 21.03, p < 0.001\). Among students with high homework completion, 82% passed the exam, compared with 54% in the medium group and 37% in the low group.

These results indicate that homework completion and benchmark performance are not independent in this dataset. While this does not prove that homework causes higher scores, the pattern aligns with prior research from the Institute of Education Sciences showing that consistent practice supports math achievement. Future lab reports could extend this example of chi-square analysis by adjusting for prior achievement or socioeconomic status.

Examples include education settings like this because they are easy to simulate in class and connect directly to policy discussions.

Example 4: Psychology – Preference for Study Environment

Scenario
In a psychology research methods course, students test whether introverts and extroverts differ in their preferred study environment.

Variables:

• Personality group (based on a validated scale): Introvert, Ambivert, Extrovert
• Preferred study environment: Silent library, Coffee shop, At home

Lab report excerpt (results):

We ran a chi-square test of independence to examine whether personality type was associated with preferred study environment. The sample included 132 undergraduates.

The test was significant, \(\chi^2(4, N = 132) = 9.98, p = 0.041\). Introverts were more likely to prefer the silent library (61%) compared with extroverts (29%). Extroverts more often preferred the coffee shop setting (46%) than introverts (18%). Ambiverts were relatively evenly distributed across the three options.

This example of a chi-square test lab report shows how categorical personality measures can be linked to behavior without needing correlation or regression. The association is modest but meaningful for designing study spaces on campus.

If you’re looking for examples of chi-square test lab report examples in psychology, this one illustrates how to describe categories that are more conceptual than physical (unlike candy colors or exercise levels).

Example 5: Public Health – Vaccination Status and COVID-19 Concern (2024 Data)

Scenario
In a 2024 public health statistics lab, students use a de-identified dataset based on recent survey trends to examine whether vaccination status is associated with level of concern about COVID-19.

Variables:

• Vaccination status: Unvaccinated, Partially vaccinated, Fully vaccinated, Boosted
• Concern level: Low, Moderate, High

Lab report excerpt (results and interpretation):

A chi-square test of independence was used to test whether COVID-19 vaccination status was associated with self-reported level of concern about COVID-19. The dataset included 520 adults from a 2024 online survey.

The chi-square test was highly significant, \(\chi^2(6, N = 520) = 38.71, p < 0.001\). Among boosted individuals, 63% reported high concern, whereas only 27% of unvaccinated respondents reported high concern. Unvaccinated participants were more likely to report low concern (41%) compared with boosted participants (12%).

These results mirror national survey patterns reported by the KFF COVID-19 Vaccine Monitor, where attitudes toward COVID-19 risk are strongly associated with vaccination behavior. This is one of the best examples of chi-square test lab report examples for connecting classroom analysis to current public health data.

This public health example shows how to bring 2024–2025 trends into your lab report while keeping the chi-square structure simple.

Example 6: Marketing – Ad Format and Click-Through Behavior

Scenario
A business analytics class partners with a campus marketing office to test whether ad format is associated with click behavior on a student event promotion.

Variables:

• Ad format: Static image, Short video, Text-only
• Click behavior: Clicked, Did not click

Lab report excerpt (methods and results):

We analyzed 4,200 impressions from an A/B/C test of three digital ad formats for a campus event. A chi-square test of independence was used to assess whether click behavior differed by ad format.

The chi-square test was significant, \(\chi^2(2, N = 4,200) = 31.55, p < 0.001\). Short video ads had the highest click-through rate (7.8%), followed by static image ads (5.1%) and text-only ads (3.4%). Standardized residuals indicated that video ads generated more clicks than expected under independence, while text-only ads generated fewer.

This example of a chi-square test lab report demonstrates how categorical marketing outcomes can be evaluated without modeling individual-level covariates. The results support prioritizing short video content in future campaigns.

If you’re in a business or data analytics track, examples include marketing experiments like this because they mirror what real digital teams do every day.

Example 7: Genetics – Mendelian Ratios in Fruit Flies

Scenario
In an undergraduate genetics lab, students test whether offspring phenotypes follow expected Mendelian ratios.

Variables:

• Phenotype categories: Wild type, Vestigial wings, White eyes, Double mutant

Lab report excerpt (results):

We tested whether the observed distribution of phenotypes in the F2 generation matched the expected 9:3:3:1 Mendelian ratio using a chi-square goodness-of-fit test. A total of 320 offspring were scored.

The chi-square test was not significant, \(\chi^2(3, N = 320) = 3.27, p = 0.35\), indicating that the observed distribution did not differ significantly from the expected Mendelian ratio. Minor deviations in the white-eye category (observed 68 vs. expected 60) were within sampling variability.

This stands as one of the classic examples of chi-square test lab report examples in biology. It shows how the same statistical test used for candy colors can also support genetic theory.

How to Structure Your Own Chi-Square Test Lab Report

Looking across these examples of chi-square test lab report examples, a clear pattern emerges. Strong reports do three things well:

They define the variables clearly.
Every example of chi-square test lab report above starts by labeling categories in a way a reader can picture. Instead of just saying “X and Y,” the report spells out smoking levels, homework bands, or ad formats.

They justify using chi-square.
Each report makes it clear that:

• Both variables are categorical, and
• Expected counts are large enough for the chi-square approximation (usually at least 5 per cell, though some instructors accept slightly smaller values in student projects).

For a quick refresher on the test’s foundations, many instructors point students to university stats pages like UCLA’s Institute for Digital Research and Education or Penn State’s STAT program, which explain chi-square assumptions in accessible language.

They separate statistical result from interpretation.
Notice how each lab report first states the numbers (\(\chi^2\), df, p, N) and only then explains what that means in plain English. That separation is one reason these are some of the best examples of chi-square test lab report examples you can copy structurally.

Common Mistakes Students Make (and How These Examples Avoid Them)

When instructors grade chi-square reports, the same errors show up repeatedly. The real examples above show you how to dodge them.

1. Treating chi-square like a correlation
Students often write, “There is a strong positive relationship,” as if chi-square gave a correlation coefficient. Instead, talk about association or independence, and focus on which categories are over- or under-represented.

2. Forgetting to report degrees of freedom
In every example of chi-square test lab report above, df is reported alongside the statistic. For a test of independence, df is:

[
(df) = (\text{rows} - 1) \times (\text{columns} - 1)
]

Your instructor expects to see it.

3. Ignoring expected counts
Good lab reports mention that expected counts were checked. Some instructors even require a short sentence like:

All expected cell frequencies were greater than 5, supporting validity of the chi-square approximation.

4. Overstating causality
The smoking–exercise and homework–test-score examples are careful not to claim cause and effect. They talk about association and consistency with prior research instead of saying “X causes Y.”

Adapting These Real Examples to Your Assignment

If your instructor wants you to “include real examples” or “find the best examples of chi-square test lab report examples,” here’s a practical way to use what you’ve just read.

Pick the example that matches your field:

• Biology or genetics lab: use the fruit fly Mendelian ratio structure.
• Psychology or social science: mirror the study environment or smoking example.
• Education or teaching methods: copy the homework vs. test performance layout.
• Public health or nursing: follow the vaccination and concern example.
• Business or marketing analytics: adapt the ad format and clicks write-up.

Then, keep the structure but swap in your own variables, your own sample size, and your own numbers. The goal is not to copy the wording; it’s to copy the logic:

1. Clear research question in one sentence.
2. Description of your categorical variables and sample.
3. Statement of the chi-square test used and assumptions checked.
4. Reporting of \(\chi^2\), df, N, and p.
5. Brief, non-causal interpretation tied back to your question.

When you treat these as working patterns—rather than scripts—you end up with a lab report that sounds like you, but reads like the best example of a chi-square test lab report your TA will see all semester.

FAQ: Chi-Square Test Lab Report Examples

Q1. Where can I find more examples of chi-square test lab report examples online?
University stats and methods courses often publish sample reports. Try searching within sites like site:.edu "chi-square" "lab report". Pages from departments at major universities (for example, Harvard’s statistics teaching resources) often include worked examples.

Q2. What is a good example of a chi-square test of independence in psychology?
A strong example of a chi-square test lab report in psychology is the personality–study-environment scenario above. Another common setup is testing the association between therapy type (CBT vs. medication vs. combined) and treatment outcome category (improved, unchanged, worsened) using anonymized clinical or simulated data.

Q3. Do I always need to report the full chi-square table in my lab report?
Not always. For short assignments, it’s usually enough to report the main chi-square statistic, degrees of freedom, p-value, and a short description of which categories drove the effect. For longer reports or theses, your instructor may expect a full contingency table of observed and expected counts in an appendix.

Q4. Can I use chi-square tests with large survey datasets from sources like CDC or NIH?
Yes, as long as your variables are categorical and you respect the survey design. Many instructors encourage students to pull public data from sources like CDC WONDER or NIH’s data resources and then run chi-square tests on variables such as gender by screening status, or region by health behavior.

Q5. How many categories are too many for a chi-square test?
Technically, you can have many rows and columns, but interpretation gets messy. Most of the best examples of chi-square test lab report examples in undergraduate courses keep tables modest—often 2×2, 3×2, or 3×3. If you find yourself with 7 or 8 categories per variable, consider combining rare categories or reframing your research question.