Statistical Tests in Research: When to Use Which Test

Introduction

Few moments in a researcher’s training are as quietly paralysing as the moment they finish collecting data and realise they have no idea which statistical test to run. The data sits in SPSS or R, looking innocent. The research questions are written. The supervisor says “just run the analysis.” But which analysis? A t-test? An ANOVA? A chi-square? A regression? Pick the wrong one and the results are either meaningless or, worse, misleadingly significant. Pick the right one and the chapter practically writes itself.

The truth is that choosing statistical tests in research is not a matter of memorising a long list. It is a matter of asking three structured questions about your data and your research question, then walking down a decision tree to the test that fits. Once you internalise those three questions, you can choose correctly in under a minute for 90% of graduate-research scenarios.

This guide walks you through the decision framework, the major families of tests, the assumptions you must check before running each one, and the APA-style template for reporting results. If you would like a specialist to handle the analysis for you, our data analysis service pairs you with a PhD-qualified statistician. For the hands-on workflow, see our SPSS guide and our SPSS output interpretation walkthrough.

The Three Questions That Determine Your Test

Every statistical test answers one of three questions. Identify which question your research is asking, and the field of candidate tests collapses to a handful.

1. Is there a difference between groups? — Does Group A differ from Group B on some outcome? This is the territory of t-tests, ANOVA, and their non-parametric cousins.
2. Is there a relationship between variables? — Do two variables move together? This is the territory of correlation and chi-square tests.
3. Can I predict one variable from others? — Given some predictors, what value of the outcome do we expect? This is the territory of regression.

Once you know which question you are asking, two further pieces of information finish the decision: the level of measurement of your variables (nominal, ordinal, interval, ratio) and the number of groups or variables involved. With those three pieces, the test is essentially determined.

Levels of Measurement: A Quick Refresher

The choice of test depends first on the level of measurement of your variables, so a quick refresher is essential. The four levels, in increasing strength, are:

• Nominal: categories with no order — gender, religion, marital status. Permits frequencies and chi-square.
• Ordinal: ordered categories with unequal spacing — Likert items, education level, cancer stage. Permits medians, Mann-Whitney, Spearman.
• Interval: ordered, equal spacing, no true zero — Celsius temperature, IQ. Permits means, t-tests, Pearson.
• Ratio: interval with a true zero — age, height, income, reaction time. All statistics are permissible.

A common pragmatic decision is whether to treat a 5-point Likert item as ordinal or interval. Strictly, it is ordinal; practically, multi-item Likert scales with 5 or more points and approximately normal distribution are often treated as interval. Document your choice in your methodology chapter. For the deeper discussion, see our SPSS data analysis guide.

Tests for Comparing Groups

When your research question is about whether groups differ on some outcome, the test family is determined by the number of groups, whether the groups are independent or related, and the level of measurement of the outcome.

Two Independent Groups

For comparing two separate groups (e.g., male vs female exam scores, treatment vs control), use the independent-samples t-test if the outcome is continuous and approximately normal. The test compares the mean of Group A to the mean of Group B and asks whether the difference is larger than what chance would produce. Report the t-statistic, degrees of freedom, p-value, and Cohen’s d (effect size: 0.2 = small, 0.5 = medium, 0.8 = large).

If normality is violated or the outcome is ordinal, use the Mann-Whitney U test, the non-parametric equivalent. It compares rank sums rather than means and makes no distributional assumption. Report the U statistic, p-value, and rank-biserial correlation as effect size.

Two Related Groups

For comparing the same participants at two time points (pre-test vs post-test) or matched pairs, use the paired-samples t-test if normal; the Wilcoxon signed-rank test if not. Both test whether the average change from Time 1 to Time 2 is significantly different from zero.

Three or More Groups

For three or more independent groups (e.g., exam scores across three teaching methods), use one-way ANOVA. ANOVA tests whether any group mean differs from the others; it does not tell you which pair differs. Always follow a significant ANOVA with a post-hoc test (Tukey’s HSD or Bonferroni) to identify the specific group differences. Report the F-statistic, degrees of freedom (between and within), p-value, and eta-squared or partial eta-squared (0.01 = small, 0.06 = medium, 0.14 = large).

If ANOVA assumptions are violated, use the Kruskal-Wallis test, the non-parametric equivalent. For two or more factors (e.g., teaching method and gender), use factorial ANOVA, which also tests for interaction effects. For repeated measures across three or more time points, use repeated-measures ANOVA or its non-parametric cousin, the Friedman test.

Tests for Relationships

When your research question is about whether two variables are associated — not whether one causes the other, but whether they move together — the test depends on the level of measurement of both variables.

Two Continuous Variables

For two interval or ratio variables (e.g., hours of study and exam score), use Pearson’s correlation coefficient (r). Pearson measures the strength and direction of a linear relationship, ranging from −1 (perfect negative) through 0 (no linear relationship) to +1 (perfect positive). Report r, degrees of freedom (n − 2), and p-value. Effect-size conventions: 0.1 = small, 0.3 = medium, 0.5 = large.

If either variable is ordinal or the relationship is monotonic but non-linear, use Spearman’s rho, the rank-based non-parametric alternative. If you want to test whether one variable can predict another, graduate to simple linear regression, which generalises Pearson by fitting a line of best fit and quantifying the explained variance (R²).

Two Categorical Variables

For two nominal variables (e.g., gender and voting preference), use the chi-square test of independence. The test compares the observed cell frequencies in a contingency table to the frequencies expected if the variables were independent. Report the chi-square statistic, degrees of freedom ((rows − 1) × (columns − 1)), p-value, and an effect size (Cramér’s V for tables larger than 2×2; phi for 2×2 tables). Expected cell frequencies should be at least 5; if not, use Fisher’s exact test instead.

For paired nominal data (e.g., the same participants classified before and after an intervention), use McNemar’s test. For three or more paired measurements, use Cochran’s Q.

Tests for Predicting Outcomes

When your research question is about prediction — given some predictors, what outcome do we expect? — the test family is regression. The choice depends on the level of measurement of the outcome variable.

Continuous Outcome: Linear Regression

For a continuous outcome predicted by one or more independent variables, use multiple linear regression. The model produces an R² (proportion of variance explained), an F-test of overall significance, and a coefficient (B, beta, p-value) for each predictor. Check four assumptions: linearity, independence of residuals, homoscedasticity, and normality of residuals. For multiple predictors, also check multicollinearity (VIF < 5, tolerance > 0.20) and report adjusted R² rather than raw R².

Categorical Outcome: Logistic Regression

For a binary outcome (e.g., pass/fail, disease/no disease) predicted by one or more independent variables, use binary logistic regression. The model produces a chi-square test of model fit, a Nagelkerke R² (pseudo-R²), and an odds ratio (Exp(B)) for each predictor. Report the odds ratio, 95% confidence interval, and p-value for each predictor. For outcomes with three or more unordered categories, use multinomial logistic regression; for ordered categories, use ordinal logistic regression.

Assumption Checks Before You Run Anything

The single biggest error in statistical tests in research is running a parametric test without checking its assumptions. Every parametric test rests on three assumptions: normality of the outcome (or residuals), homogeneity of variance across groups, and independence of observations. Violate any of them silently and your p-values are untrustworthy.

• Normality: Shapiro-Wilk for n < 50; Kolmogorov-Smirnov (with Lilliefors correction) for larger samples. Visual inspection of Q-Q plots is also expected.
• Homogeneity of variance: Levene’s test (produced automatically by SPSS t-test and ANOVA procedures). If significant (p < 0.05), use Welch’s t-test or Welch’s ANOVA instead of the standard versions.
• Independence of observations: This is a design issue, not a test. If your data has repeated measures or clustered structure, use the appropriate model (paired t-test, repeated-measures ANOVA, multilevel model).

When assumptions are violated, switch to the non-parametric equivalent. The mapping is straightforward: independent-samples t-test → Mann-Whitney U; paired-samples t-test → Wilcoxon signed-rank; one-way ANOVA → Kruskal-Wallis; repeated-measures ANOVA → Friedman; Pearson → Spearman. Document the assumption check and the switch in your methodology chapter; reviewers increasingly reject papers that skip this step.

A Decision Tree for Choosing Tests

If you remember nothing else, remember this compact decision tree. Walk down it for every analysis and you will choose the correct test in under a minute.

1. One continuous outcome, two independent groups, normal: independent-samples t-test.
2. One continuous outcome, two independent groups, non-normal: Mann-Whitney U.
3. One continuous outcome, same participants twice, normal: paired-samples t-test.
4. One continuous outcome, same participants twice, non-normal: Wilcoxon signed-rank.
5. One continuous outcome, three or more independent groups, normal: one-way ANOVA + post-hoc.
6. One continuous outcome, three or more independent groups, non-normal: Kruskal-Wallis + post-hoc.
7. Two continuous variables, linear relationship: Pearson r.
8. Two variables, at least one ordinal or non-linear: Spearman rho.
9. Two categorical variables: chi-square (Fisher’s exact if expected cell count < 5).
10. One continuous outcome predicted by ≥ 1 variables: multiple linear regression.
11. One binary outcome predicted by ≥ 1 variables: binary logistic regression.

This tree covers roughly 90% of graduate-research scenarios. Advanced designs (ANCOVA, MANOVA, mixed-effects models, structural equation modelling, survival analysis) require specialist guidance — our data analysis team handles these regularly.

Reporting Test Results in APA Style

Choosing the right test is half the job; reporting it correctly is the other half. APA 7th edition specifies a compact format that combines the test statistic, degrees of freedom, p-value, and effect size in a single sentence. Templates for the four most common tests:

• t-test: “An independent-samples t-test showed that students in the flipped condition (M = 78.4, SD = 6.2) scored significantly higher than those in the traditional condition (M = 72.1, SD = 7.5), t(118) = 4.82, p < .001, d = 0.88.”
• ANOVA: “A one-way ANOVA showed a significant effect of teaching method on exam score, F(2, 117) = 8.43, p < .001, η² = 0.126. Tukey post-hoc tests indicated that the flipped condition significantly outperformed both the traditional and hybrid conditions.”
• Chi-square: “A chi-square test of independence showed a significant association between gender and voting preference, χ²(1, N = 412) = 9.87, p = .002, φ = 0.155.”
• Regression: “A multiple linear regression predicted exam score from hours of study and prior GPA, F(2, 197) = 64.2, p < .001, adjusted R² = 0.39. Both predictors were significant: study hours (B = 2.14, β = 0.48, p < .001) and prior GPA (B = 8.92, β = 0.31, p < .001).”

Reporting only p-values is no longer acceptable in most journals. Effect sizes are now expected for every test, and confidence intervals are increasingly required. The APA 7th edition manual treats effect-size reporting as a default, not an option.

Conclusion

Choosing the right statistical tests in research comes down to three structured questions — difference, relationship, or prediction? — combined with the level of measurement and the number of groups or variables. Walk the decision tree, check the assumptions, switch to a non-parametric equivalent if assumptions fail, and report each result in APA style with effect sizes and confidence intervals. The framework above covers the overwhelming majority of graduate-research scenarios; advanced designs deserve specialist input. If you would like an expert to run your analysis, our data analysis service covers everything from test selection to results write-up. Pair this guide with our SPSS walkthrough, SPSS output interpretation guide, and data analysis chapter template, and reach us through our contact page for a free consultation.

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