Common Statistics Mistakes Students Make and How to Fix Them

The most common statistics mistakes students make are choosing a test that doesn't fit the data, misreading what a p-value means, treating "not significant" as "no effect," and claiming that a correlation proves cause and effect. Close behind are mechanical errors: using the population formula instead of the sample one, treating paired data as independent, rounding too early and running many tests without adjusting for them. None of these need advanced math to fix. They need a clear question, the right method for the data, and careful wording when you interpret the result.

This guide explains thirteen common errors with a short example and a fix for each. It also shares what more than 500 statistics help requests on our site show about where students most often get stuck. The mistakes themselves come from published reviews of statistical errors and from official guidance by the American Statistical Association, so you can check every one.

What Our Statistics Orders Show

We reviewed 529 orders placed on AceMyHomework and its sister site HomeworkDoer between 2019 and 2026 whose instructions mentioned statistical methods, software or terms. We grouped them by the topics their instructions named. Many requests named more than one topic, so the percentages add up to more than 100%, and 224 requests gave too little detail to classify.

Two patterns stand out. First, almost a third of requests involved a whole project with real data rather than a single question, which is exactly where choosing and justifying a method matters most. Second, hypothesis testing and regression account for most of the specific techniques students asked about. The mistakes below are concentrated in those same areas.

Our data has limits. Order instructions show what students needed help with, not how often a particular mistake occurred, and the topics were assigned by matching keywords in the instructions. Treat the table as a picture of demand, not a measure of error rates.

Mistakes in Choosing a Method

1. Using a Test That Doesn't Match the Data

Example: A student compares pass rates for students who did and didn't attend review sessions using a t-test.

Why it's wrong: A t-test compares means of a numerical variable. Passing is categorical (yes or no), so the right comparison is between proportions, using a chi-square test of independence or a two-proportion z-test.

Fix: Before choosing a test, write down your research question, whether each variable is categorical or numerical, how many groups you have and whether measurements are paired. Our guide on which statistical test to use walks through twelve scenarios.

2. Treating Paired Data as Independent

Example: Blood pressure is measured on the same 15 patients before and after a program, and the student runs an independent-samples t-test.

Why it's wrong: The before and after measurements come from the same people, so they're related. An independent test ignores that pairing and usually loses power, making a real change harder to detect.

Fix: Use a paired t-test, or the Wilcoxon signed-rank test if the differences are clearly non-normal. Ask yourself: is each value in one group matched to a specific value in the other?

3. Ignoring the Assumptions of a Test

Example: A student runs a standard two-sample t-test that assumes equal variances when one group's standard deviation is three times the other's.

Why it's wrong: Most tests assume something about the data, such as independent observations, roughly normal distributions or equal variances. When assumptions fail, p-values and confidence intervals can be misleading.

Fix: Check assumptions and say how you checked them. For two groups, Welch's t-test doesn't assume equal variances, and many statisticians recommend it as the default. For skewed data with small samples, consider a nonparametric alternative.

4. Counting Repeated Measurements as Separate People

Example: Ten students each complete five quizzes, and the analysis treats the 50 scores as 50 independent observations.

Why it's wrong: Scores from the same student are related, so the real sample size is closer to 10 than 50. Treating them as independent makes results look more certain than they are. Makin and Orban de Xivry list this "inflating the units of analysis" among the ten most common statistical mistakes in their review in eLife.

Fix: Analyze one value per student, such as their average, or use a method designed for repeated measures, such as repeated-measures ANOVA or a mixed model.

Mistakes in Calculation

5. Using the Population Formula Instead of the Sample Formula

Example: For the data 2, 4, 4, 4, 5, 5, 7, 9, a student divides the sum of squared deviations (32) by 8 and reports a standard deviation of 2.00.

Why it's wrong: When your data is a sample used to estimate a population, the sample standard deviation divides by n − 1, not n. Here that gives the square root of 32 ÷ 7, or 2.14.

Fix: Check which formula your course and software use. In Excel, STDEV.S is the sample version and STDEV.P the population version, and calculators often label them s and σ.

6. Rounding Too Early

Example: A student rounds the mean to one decimal place, then uses the rounded mean to calculate a standard deviation and a test statistic.

Why it's wrong: Small rounding errors compound through each step. The final answer can be far enough off to be marked wrong on an online homework system.

Fix: Keep full precision until the last step, then round the reported result to the precision your instructions ask for. Our guide to why Pearson Mastering marks answers wrong shows how early rounding pushes answers outside the grading tolerance.

7. Running Many Tests Without Adjusting

Example: A student compares 20 survey items between two groups and reports the one that came out significant at p < 0.05.

Why it's wrong: With 20 independent tests at the 0.05 level and no real effects, the chance of at least one false positive is 1 − 0.95²⁰, about 64%. One significant result among 20 is roughly what chance alone produces.

Fix: Decide on your main comparisons in advance, report every test you ran, and use an adjustment such as Bonferroni (divide 0.05 by the number of tests) or Holm when you make many comparisons.

Mistakes in Interpretation

8. Misreading What a P-Value Means

Example: "p = 0.03, so there is a 97% chance the treatment works."

Why it's wrong: The American Statistical Association's statement on p-values says they "do not measure the probability that the studied hypothesis is true, or the probability that the data were produced by random chance alone." A p-value of 0.03 means that if there were truly no effect, results at least this extreme would occur about 3% of the time.

Fix: Interpret p-values as a measure of how surprising the data would be under the null hypothesis, and report an effect size and confidence interval alongside them.

9. Treating "Not Significant" as "No Effect"

Example: A study of 12 students finds p = 0.20 and concludes that the tutoring program has no effect.

Why it's wrong: A non-significant result means the data didn't provide strong evidence of an effect. With a small sample, a real effect can easily go undetected. Absence of evidence is not evidence of absence.

Fix: Say "we did not find a statistically significant difference," report the confidence interval, and mention sample size as a limitation.

10. Comparing Two Effects by Their P-Values

Example: A program significantly improved scores for women (p = 0.01) but not for men (p = 0.12), so the student concludes it works better for women.

Why it's wrong: One significant result and one non-significant result don't show that the two effects differ. That requires testing the difference directly. A 2011 review in Nature Neuroscience found that among 157 neuroscience papers comparing two effects, 79 made exactly this error, so you're in good company, but it's still wrong.

Fix: Test the interaction, for example with a two-way ANOVA or a regression with an interaction term.

11. Confusing Correlation with Causation

Example: Students who use the library more have higher GPAs, so "using the library raises your GPA."

Why it's wrong: Without random assignment, a third factor such as motivation could explain both. The association could also run the other way.

Fix: Use language such as "is associated with" for observational data, and name plausible confounders. Only a well-designed experiment supports causal wording.

12. Missing a Confounder That Reverses the Result

Example: In a well-known 1975 study of graduate admissions at the University of California, Berkeley, men were admitted at a noticeably higher overall rate than women. When the researchers looked department by department, the bias largely disappeared: women had applied more often to departments that admitted a smaller share of all applicants.

Why it matters: This is Simpson's paradox. A trend in combined data can weaken or reverse when you account for a grouping variable.

Fix: Think about which variables could influence both your predictor and outcome, and analyze within groups or control for them in a regression.

13. Misinterpreting a Confidence Interval

Example: "There is a 95% probability that the true mean is between 48 and 56."

Why it's wrong: In the usual frequentist approach, the true mean is fixed. The 95% describes the method: if you repeated the study many times, about 95% of intervals built this way would contain the true mean.

Fix: Write "we are 95% confident that the true mean is between 48 and 56," and explain what the interval implies about the size of the effect.

A Checklist Before You Submit a Statistics Assignment

1. Is the research question written down, with each variable labeled categorical or numerical?
2. Does the test match the question, the variable types, the number of groups and whether data are paired?
3. Did you check the assumptions and say how?
4. Is each person or unit counted once, or does the method handle repeated measurements?
5. Did you use the sample formulas and keep full precision until the end?
6. If you ran several tests, did you report all of them and adjust if needed?
7. Does your interpretation avoid "proves," "no effect" and causal language that the design can't support?
8. Did you report an effect size and confidence interval, not only a p-value?
9. Are results reported in the format your course requires, such as APA style?

Why Common Statistics Mistakes Happen

Statistical mistakes are not just a student problem. Makin and Orban de Xivry wrote their eLife review because these errors appear regularly in published research, and a 2007 review of medical research by Strasak and colleagues catalogued similar pitfalls across study design, analysis, documentation, presentation and interpretation. The same root causes show up in coursework: choosing a method before thinking about the question, relying on software defaults, and wording conclusions more strongly than the design allows.

If you're working on a project with real data, it's worth asking someone to review your method before you run the analysis. Our statistics homework help connects you with tutors who can check your test choice, assumptions and interpretation, and our guide on how to choose a statistics tutor explains what good statistical explanations sound like. Use any outside help in line with your school's academic integrity policy.

About Our Data

The topic table comes from 529 orders placed on AceMyHomework and HomeworkDoer between November 2019 and October 2026 whose topic or instructions mentioned statistical methods, software or terms. We classified each request by matching keywords for each topic, so a request could count in several topics. The 224 requests with too little detail to classify are excluded from the topic counts but included in the total. The analysis used only the text of order requests, with no names or contact details, and no individual orders are described here. Order instructions tell us what students asked for, not how often they made a given mistake, so the list of mistakes in this guide is based on published reviews and official guidance rather than on our order data.

Frequently Asked Questions

What Are the Most Common Mistakes in Statistics?

Choosing the wrong test for the data, misinterpreting p-values, treating non-significant results as proof of no effect, confusing correlation with causation, ignoring assumptions, and running many tests without adjusting for multiple comparisons are among the most common.

How Can I Avoid Errors in Statistical Analysis?

Start with a clear question, match the method to your variable types and design, check assumptions, keep full precision until the end, and interpret results cautiously with effect sizes and confidence intervals.

What Is the Most Common Mistake with P-Values?

Treating the p-value as the probability that the null hypothesis is true. The American Statistical Association states explicitly that p-values don't measure that.

Why Is Correlation Not Causation?

Two variables can move together because a third factor affects both, because the relationship runs the other way, or by chance. Only a well-designed experiment with random assignment can support a causal claim.

What Is Simpson's Paradox?

It's when a trend that appears in combined data disappears or reverses once you separate the data into groups, usually because a confounding variable is unevenly distributed across groups.