Which Statistical Test Should I Use? 12 Assignment Scenarios Explained

To know which statistical test to use, answer five questions in order. Are you looking for a difference between groups or a relationship between variables? Is your outcome variable numerical or categorical? How many groups are you comparing? Are the measurements independent or paired? And do the data meet the test's assumptions? For example, comparing the mean exam scores of two separate classes calls for an independent-samples t-test, the same students measured twice calls for a paired t-test, and three or more groups call for ANOVA. If both variables are categorical, such as passing or failing by attendance group, you need a chi-square test, not a t-test.

This guide gives you a decision table, then works through twelve assignment-style scenarios. For each one it explains which test fits, why the obvious alternatives don't, what to check, and how to report the result. Every result was calculated with SciPy, a widely used open-source statistics library, using small illustrative datasets you can rerun yourself.

Which Statistical Test to Use: The Decision Table

Five Questions That Pick the Right Test

1. What is the research question? "Do groups differ?" points to t-tests, ANOVA or chi-square. "Are these variables related?" points to correlation or regression.
2. What type is the outcome variable? Numerical outcomes, such as scores, times or weights, use t-tests, ANOVA and regression. Categorical outcomes, such as pass/fail or a chosen option, use chi-square, Fisher's exact test or logistic regression. Ordinal ratings, such as Likert scale items, often call for rank-based tests.
3. How many groups are there? Two groups point to a t-test or Mann-Whitney U. Three or more point to ANOVA or Kruskal-Wallis. Running several t-tests instead of one ANOVA inflates the chance of a false positive.
4. Are the observations independent or paired? The same people measured twice, or matched pairs, need a paired test.
5. Do the assumptions hold? Check approximate normality for small samples, similar variances, independence, and expected counts of at least about 5 for chi-square. When they fail, use the nonparametric or exact alternative in the table.

12 Assignment Scenarios Explained

Scenario 1: Is Average Study Time Different from 10 Hours? (One-Sample t-Test)

Assignment: A survey of 12 students recorded weekly study hours. Is the average different from the 10 hours the college recommends?

Why this test: One numerical variable is compared with a fixed value. A one-sample t-test compares the sample mean with that value when the population standard deviation is unknown.

Why not a z-test: A z-test requires a known population standard deviation, which assignments rarely give you.

Result: The mean was 9.25 hours (SD = 2.18). The difference from 10 hours was not significant, t(11) = −1.19, p = .258.

How to report it: "Students' weekly study time (M = 9.25, SD = 2.18) did not differ significantly from the recommended 10 hours, t(11) = −1.19, p = .258." Remember that a non-significant result with 12 students doesn't show the two are the same.

Scenario 2: Do Two Class Sections Score Differently? (Welch's t-Test)

Assignment: Exam scores for Section A (n = 10) and Section B (n = 12). Is there a difference?

Why this test: Two independent groups and a numerical outcome. Welch's t-test doesn't assume equal variances or equal group sizes, which is why many statisticians recommend it over the classic pooled t-test as the default.

Why not a paired t-test: Different students are in each section, so nothing links a score in one group to a score in the other.

Result: Section A averaged 78.4 (SD = 7.85) and Section B 86.58 (SD = 5.35). The difference was significant, t(15.43) = −2.80, p = .013, with a large effect (Cohen's d = 1.24). The fractional degrees of freedom are normal for Welch's test.

How to report it: "Section B scored higher than Section A, Welch's t(15.43) = −2.80, p = .013, d = 1.24."

Scenario 3: Did a Workshop Reduce Test Anxiety? (Paired t-Test)

Assignment: Ten students rated their test anxiety before and after a workshop on a scale scored from 10 to 50.

Why this test: The same students were measured twice, so the data are paired. The test looks at each student's change score.

Why not an independent t-test: It would ignore the pairing and treat natural differences between students as noise, which makes a real change harder to detect.

Check: The differences should be roughly normal. Here a Shapiro-Wilk test on the differences gave p = .261, so there's no evidence against normality.

Result: Anxiety fell from 43.0 to 37.5 on average, a mean reduction of 5.5 points (SD = 2.22), t(9) = 7.82, p < .001.

How to report it: "Test anxiety was lower after the workshop (M = 37.5) than before (M = 43.0), t(9) = 7.82, p < .001."

Scenario 4: Which of Three Teaching Methods Works Best? (One-Way ANOVA)

Assignment: Eighteen students were randomly assigned to lecture, flipped classroom or project-based teaching, six per group, and took the same final test.

Why this test: Three independent groups and a numerical outcome. One-way ANOVA tests whether any group mean differs in a single test.

Why not three t-tests: Each extra test adds another chance of a false positive. ANOVA controls that, and post hoc tests then show which groups differ.

Check: Levene's test for equal variances gave p = .901, so the equal-variance assumption looks reasonable.

Result: Mean scores were 79.5 for lecture, 70.3 for flipped and 85.3 for project-based teaching, F(2, 15) = 28.88, p < .001, η² = .79. Tukey's post hoc test showed that all three pairs differed significantly, with p-values from .026 to below .001.

How to report it: "Teaching method had a significant effect on test scores, F(2, 15) = 28.88, p < .001, η² = .79. Tukey's HSD tests showed that all three methods differed from one another."

Scenario 5: Is Passing Related to Attending Review Sessions? (Chi-Square Test of Independence)

Assignment: Of 80 students who attended review sessions, 48 passed. Of 80 who didn't, 27 passed.

Why this test: Both variables are categorical (attended or not, passed or not), arranged in a 2×2 table. The chi-square test of independence checks whether pass rates differ between groups.

Why not a t-test: There's no numerical outcome to average, only counts in categories.

Check: The smallest expected count was 37.5, well above 5.

Result: The pass rate was 60% among attendees and 34% among non-attendees, χ²(1, N = 160) = 11.07, p < .001, φ = .26.

Interpretation: Attendance and passing are associated, but students chose whether to attend, so motivation could explain both. This design doesn't show that review sessions caused the higher pass rate, a question of internal validity.

Scenario 6: Are Course Choices Evenly Spread? (Chi-Square Goodness-of-Fit Test)

Assignment: 160 students chose among four elective courses: 28, 41, 35 and 56 chose each one. Is demand equal across courses?

Why this test: One categorical variable compared with expected proportions, here 25% each, or 40 students per course.

Result: Choices were not evenly spread, χ²(3, N = 160) = 10.65, p = .014. The fourth course was chosen by 56 students against an expected 40.

Scenario 7: Is Sleep Related to GPA? (Pearson Correlation)

Assignment: Fifteen students reported average nightly sleep and their GPA.

Why this test: Two numerical variables measured on the same students, with the question of how strongly they move together. A scatterplot should look roughly linear, without extreme outliers.

Result: Sleep and GPA were strongly positively correlated, r(13) = .96, p < .001.

Interpretation: This shows an association only. Students with more sleep may differ in other ways, such as workload or health, that also affect GPA. Real survey data usually shows a much weaker correlation than this illustrative example.

Scenario 8: How Much Does Advertising Predict Sales? (Simple Linear Regression)

Assignment: A small business recorded monthly advertising spend (in thousands of dollars) and sales (in thousands of dollars) for 10 months, and wants to predict sales from spend.

Why this test: The goal is prediction, and the answer needs to be in units: how much sales change per extra $1,000 of advertising. Regression gives a slope, an intercept and a test of whether the slope differs from zero.

Result: The fitted line was sales = 9.18 + 2.94 × advertising, R² = .99, and the slope was significant, t(8) = 31.56, p < .001. Each additional $1,000 of advertising was associated with about $2,940 more in sales.

Check: Plot the residuals to confirm there's no curve or funnel shape, and avoid predicting outside the range of spend in the data.

Scenario 9: Do Two Clinics Have Different Waiting Times? (Mann-Whitney U Test)

Assignment: Waiting times in minutes for 10 patients at each of two clinics. Both samples include a few very long waits.

Why this test: Two independent groups with small, strongly skewed samples. Shapiro-Wilk tests rejected normality for both clinics (p < .001). The Mann-Whitney U test compares the groups using ranks, so a few extreme values can't dominate the result.

Why not a t-test: The outliers pull the means up. Clinic A's mean was 9.5 minutes but its median only 5.5.

Result: Clinic A had shorter waits (median 5.5 minutes) than Clinic B (median 11.5), U = 18, p = .017.

Scenario 10: Did Ratings Improve After a Redesign? (Wilcoxon Signed-Rank Test)

Assignment: Twelve users rated a website from 1 to 5 before and after a redesign.

Why this test: The ratings are paired, because the same users rated both versions, and they are ordinal. A single 1 to 5 rating isn't really an interval scale, and there are only five possible values.

Why not a paired t-test: It assumes roughly normal, interval-level differences. The Wilcoxon signed-rank test uses the ranks of the differences instead.

Result: The median rating rose from 2.5 to 4.0. Eleven of the 12 users rated the redesign higher and one gave the same rating, W = 0, p = .001.

Scenario 11: Do Two Judges Rank Entries Similarly? (Spearman Rank Correlation)

Assignment: Two judges ranked the same 10 science fair projects from 1 to 10. Do their rankings agree?

Why this test: The data are ranks, not measurements, so Spearman's rank correlation fits. It measures any consistent increasing or decreasing relationship, not only a straight line.

Result: The judges' rankings agreed strongly, rₛ = .90, p < .001.

Scenario 12: Did a Treatment Work in a Very Small Study? (Fisher's Exact Test)

Assignment: In a pilot study, 9 of 10 patients improved with a new treatment, compared with 4 of 10 with standard care.

Why this test: Two categorical variables in a 2×2 table, but the sample is tiny. Two expected counts are only 3.5, below the usual threshold of 5 for a chi-square test.

Why it matters here: An uncorrected chi-square test on these data gives p = .019, which looks significant. Fisher's exact test, which calculates the probability directly, gives p = .057. Choosing the wrong test would change your conclusion.

Result: The odds ratio was 13.5, but the difference was not statistically significant, Fisher's exact p = .057. With samples this small, the honest conclusion is that a larger study is needed.

Quick Comparisons Students Ask About

Chi-Square Test vs. t-Test

Use a t-test when your outcome is numerical and you're comparing means of two groups. Use a chi-square test when both variables are categorical and you're comparing counts or proportions. "Average score by section" is a t-test. "Pass rate by section" is a chi-square test.

ANOVA vs. t-Test

A t-test compares two groups. ANOVA compares three or more. With exactly two groups, a one-way ANOVA and a pooled t-test give the same p-value, because F equals t². With three or more groups, use ANOVA and then post hoc tests rather than repeated t-tests.

t-Test vs. Mann-Whitney U Test

Use a t-test when the data are roughly normal or the samples are large enough for the central limit theorem to help. Use Mann-Whitney U for ordinal data, or for small samples with strong skew or outliers. The Mann-Whitney test compares the overall distributions using ranks, which is often described as comparing medians.

Correlation vs. Regression

Correlation measures how strongly two variables move together, on a scale from −1 to 1. Regression estimates how much the outcome changes per unit of the predictor, and it can include several predictors at once.

How to Check the Assumptions

• Independence: Each observation should come from a different person or unit, unless you're using a paired or repeated-measures test. This comes from the study design, not from a test.
• Normality: For small samples, inspect a histogram or Q-Q plot, and use a Shapiro-Wilk test if your course asks for one. For t-tests, check the differences in paired designs and each group in independent designs.
• Equal variances: Levene's test checks this for t-tests and ANOVA. Our guide to variability in statistics explains variance and standard deviation if you need a refresher. Welch's t-test avoids the assumption altogether.
• Expected counts: For chi-square tests, expected counts should be at least about 5. If not, use Fisher's exact test.
• Linearity: For correlation and regression, make a scatterplot and a residual plot.

The NIST/SEMATECH e-Handbook of Statistical Methods is a free, authoritative reference for these checks and for how each test works.

How to Report a Statistical Test

Most courses use APA style, which reports the test statistic, degrees of freedom, p-value and an effect size. The pattern is test(df) = value, p = value, effect size. APA's guide to numbers and statistics shows the formatting rules, such as italicizing statistical symbols, reporting exact p-values to two or three decimals, and writing p < .001 for very small values.

If you're unsure which test fits your own assignment, or your results don't make sense, our statistics homework help connects you with tutors who can check your choice and explain the output. Use any outside help in line with your school's academic integrity policy.

Frequently Asked Questions

How Do I Know Which Statistical Test to Use?

Identify your research question, the type of outcome variable, the number of groups, and whether measurements are independent or paired. Then check the test's assumptions. The decision table at the top of this guide maps those answers to a test.

When Should I Use a Chi-Square Test Instead of a t-Test?

Use a chi-square test when both variables are categorical, such as pass/fail by group. Use a t-test when the outcome is numerical, such as test scores, and you're comparing two group means.

When Should I Use ANOVA Instead of a t-Test?

Use ANOVA when you compare three or more groups. Running several t-tests instead increases the chance of a false positive.

What Test Should I Use to Compare Two Groups?

For a numerical outcome and independent groups, use Welch's t-test, or Mann-Whitney U if the data are skewed with small samples. For the same people measured twice, use a paired t-test or the Wilcoxon signed-rank test. For a categorical outcome, use a chi-square test, or Fisher's exact test with small counts.

What Is the Difference Between Parametric and Nonparametric Tests?

Parametric tests, such as t-tests and ANOVA, assume a particular distribution, usually normal, and compare means. Nonparametric tests, such as Mann-Whitney U and Kruskal-Wallis, use ranks and make fewer assumptions, which makes them suitable for ordinal data, small skewed samples and outliers.

Can I Use a t-Test with a Small Sample?

Yes, if the data, or the paired differences, are roughly normal without extreme outliers. With very small and clearly skewed samples, a nonparametric test is safer.