Which test: t-test, ANOVA, chi-square, correlation and regression
Last reviewed September 2026 by Dr. Andrew Wichterman · Aligned to the current NCE blueprint. Valid for exams through June 30, 2027.
AI-narrated overview made with Google NotebookLM. The written lesson below is by Dr. Andrew Wichterman.
The exam describes a small study in two sentences and asks which statistical test fits. Three questions answer it every time: what kind of question, how many groups, what kind of data. This lesson walks the decision tree branch by branch with plain-language examples, assuming no statistics background.
Try to answer each from memory first, even if you have to guess. Guessing before reading makes the answer stick; reveal only after you have tried.
Start here: three questions choose the test
A recurring exam item describes a small study in two sentences and asks which statistical test fits. It looks intimidating, but the choice comes down to three questions you can answer from the description. What kind of question is being asked: are groups being compared, are categories being counted, or is a relationship being measured? How many groups: two, or three or more? What kind of numbers: real measurements (interval or ratio) or categories and ranks (nominal or ordinal)? Answer those three and the test names itself.
Branch 1: comparing group averages
If the study compares the average score of one group against another, and the score is a real measurement (an anxiety scale, a test score, minutes, dollars), you are in the t-test and ANOVA family.
Two groups: the t-test
A t-test compares the means of two groups and asks whether the gap is bigger than chance would produce. There are two versions, and the exam tests the difference. An independent-samples t-test is for two separate groups of people: treatment versus wait list, men versus women. A paired (dependent) t-test is for the same people measured twice, or matched pairs: each client's anxiety before and after treatment. The paired version is more powerful because it removes the differences between people; each person is their own control.
Three or more groups: ANOVA
With three or more groups you could run several t-tests, but every extra test adds another 5 percent chance of a false alarm. Analysis of variance (ANOVA) compares all the groups in one test. It produces an F ratio; a significant F tells you that at least one group differs from the others, but not which. To find out which, you follow up with post-hoc tests (Tukey, Scheffé, Bonferroni). A one-way ANOVA has one independent variable (say, three types of therapy). A two-way (factorial) ANOVA has two (therapy type and gender) and can also show an interaction, where the effect of one depends on the other.
| Situation | Test |
|---|---|
| Two separate groups, one measurement each | Independent-samples t-test |
| Same people measured twice (before/after) or matched pairs | Paired (dependent) t-test |
| Three or more groups, one independent variable | One-way ANOVA, then post-hoc tests |
| Two independent variables at once | Two-way (factorial) ANOVA; look for interaction |
| Same people measured three or more times | Repeated-measures ANOVA |
| ANOVA while statistically controlling for a nuisance variable (e.g., pretest score) | ANCOVA (analysis of covariance) |
| Several outcome variables at once | MANOVA (multivariate ANOVA) |
Branch 2: counting people in categories
Sometimes the outcome is not a score but a category: passed or failed, relapsed or did not, chose option A, B or C. You cannot average categories. Instead you count how many people landed in each box and compare the counts to what you would expect if nothing were going on. That test is chi-square (written χ²). Example: did more clients in the treatment group stay in therapy past six sessions than in the control group? Two categories (stayed / left) by two groups, and you compare the counts. Chi-square is the workhorse for nominal data and needs no assumptions about normal distributions.
Branch 3: measuring a relationship
When both variables are measured on the same people and nobody is assigned to anything, you are describing how the two move together. Lesson 8 introduced the correlation coefficient r. Pearson's r is for two interval or ratio variables (hours studied and exam score). Spearman's rho is the same idea for ranked (ordinal) data, or for interval data that is badly skewed. Both run from −1 to +1.
Regression goes one step further: instead of just describing the relationship, it builds an equation to predict one variable from the other. Simple regression uses one predictor (predict GPA from GRE). Multiple regression uses several predictors at once (predict GPA from GRE, undergraduate GPA and interview rating). The variable being predicted is still called the dependent variable; the predictors are independent variables. If an item uses the word "predict," think regression.
When the data are ranks or lopsided: nonparametric versions
The t-test, ANOVA and Pearson correlation assume roughly normal, interval-level data. When the data are ranks (ordinal), or the sample is small and badly skewed, you use a nonparametric substitute that works on ranks instead of raw scores. Each parametric test has a twin.
| Parametric test | Nonparametric twin | Both answer… |
|---|---|---|
| Independent-samples t-test | Mann-Whitney U | Do two separate groups differ? |
| Paired t-test | Wilcoxon signed-rank | Did the same people change? |
| One-way ANOVA | Kruskal-Wallis | Do three or more groups differ? |
| Pearson r | Spearman rho | How strongly are two variables related? |
| (none needed) | Chi-square | Do the category counts differ from expected? |
A few other names you should recognize
| Term | Plain meaning |
|---|---|
| Degrees of freedom (df) | A number, based on sample size and number of groups, that the test uses to find its cutoff. You will not compute it; just know it is reported alongside t, F and χ² |
| Factor analysis | A technique for finding which items on a test cluster together into underlying dimensions; how the Big Five and the 16PF were built |
| Meta-analysis | A study of studies: combining the effect sizes from many studies on the same question into one overall estimate |
| Standard error | How much a sample statistic (like a mean) would bounce around from sample to sample; smaller with bigger samples |
| Confidence interval | A range around a sample estimate that probably contains the population value ("95% CI: 3.2 to 6.8") |
How the exam asks about this
Read the two-sentence study and answer the three questions in order.
| The item says… | Question 1: kind? | Question 2: groups? | Question 3: data? | Test |
|---|---|---|---|---|
| "Compares GAD-7 scores of clients receiving CBT versus those on a wait list" | Comparing averages | Two, separate people | Interval | Independent t-test |
| "Measures each client's depression before and after eight sessions" | Comparing averages | Two, same people | Interval | Paired t-test |
| "Compares outcome scores across three counseling approaches" | Comparing averages | Three | Interval | One-way ANOVA |
| "Asks whether men and women differ in the proportion who complete treatment" | Counting categories | Two by two | Nominal | Chi-square |
| "Examines whether hours of supervision are related to trainee confidence ratings" | Relationship | — | Interval (or ranks → Spearman) | Pearson correlation |
| "Uses undergraduate GPA and GRE to predict success in a counseling program" | Predict | — | Interval | Multiple regression |
| "Compares rankings of three treatments by a small group of clients" | Comparing groups | Three | Ordinal | Kruskal-Wallis |
Without scrolling up, write everything you remember from this lesson. Then check yourself against the key terms. Recalling the whole lesson once, right after reading it, does more than reading it twice.
Ten more questions from the whole domain, with an explanation after each answer.
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