Choosing the right statistical test is one of the most important decisions in any psychology research project, and also one of the decisions that generates the most uncertainty. Faced with a freshly collected dataset, many researchers wonder whether they should use a t-test or an ANOVA, whether their data allow for regression or require a nonparametric approach, or whether the Pearson correlation is appropriate or Spearman would be better. The answer always depends on the same factors: the type of research question, the nature of the variables involved, the study design, and the fulfillment of statistical assumptions. Once you understand how these factors interact, the choice ceases to be a mystery and becomes a logical and fairly straightforward process.
The first thing worth clarifying is that there is no hierarchy of tests where some are inherently better than others. A t-test is not inferior to a mixed ANOVA, nor is a Pearson correlation more rudimentary than a structural equation model. Each technique is designed to answer a type of question with a type of data. The error lies in applying a sophisticated tool when a simple one would suffice, or in using a simple test when the complexity of the data calls for something more elaborate. The key is the fit between the question, the data, and the analysis.
Which statistical test should I use? The 3 factors that decide it
To choose the right statistical test, you only need to answer three questions, in this order:
- The design and type of question: are you comparing groups, measuring the relationship between variables, or predicting one variable from others?
- The number of measurements or groups: one measurement, two groups/measures, or three or more? Are the samples independent or repeated measures?
- The measurement scale of the variables: nominal, ordinal, or interval/ratio? Are the assumptions (normality, homoscedasticity) required by parametric tests met?
With those three answers the test almost picks itself: comparing two independent groups on a continuous, normally distributed variable points to an independent-samples t-test; if the variable is ordinal or non-normal, to the Mann-Whitney U test. You can walk through this decision tree interactively, step by step, in the statistical test selector.
The starting point: your research question
Before thinking about statistical tests, you need to clearly formulate what you want to know. Research questions in psychology typically fall into three broad categories: comparing groups, exploring relationships between variables, or predicting one variable from others. Each category points toward a different family of techniques, and refining the question within each category helps to further narrow the choice.
When we want to compare groups, the key questions are how many groups are being compared and whether the measures are independent or repeated. If we are comparing two independent groups on a continuous variable, the independent samples Student's t-test is the classic option. If the same participants are measured at two time points (before and after an intervention, for example), we use the paired samples t-test. When there are three or more independent groups, one-way ANOVA takes over. And if we combine multiple between-subjects factors, or between- and within-subjects factors, we enter the domain of factorial and mixed ANOVAs.
When the interest lies in the relationship between variables, the relevant questions are how many variables are involved and what type of association is sought. For the linear relationship between two continuous variables, the Pearson correlation is the starting point. If we want to predict a continuous variable from one or several predictors, linear regression (simple or multiple) is the appropriate tool. When the variable we want to predict is categorical (for example, presence or absence of a diagnosis), we turn to logistic regression (whose results are interpreted through odds ratios). And if the relationships between variables are more complex, involving mediations, moderations, or latent variables, structural equation models provide the most flexible framework.
The nature of your variables matters
The level of measurement of the variables is a determining factor in the choice of test. Continuous variables (or interval/ratio variables), such as scores on a questionnaire with sufficient items or chronometric measures, allow the use of most parametric techniques. Ordinal variables (such as a single-item Likert scale or a ranking) and nominal variables (such as gender, diagnosis, or experimental condition) require different treatments.
When the dependent variable is continuous and the independent variables are categorical, we are in the territory of t-tests and ANOVAs. When both the dependent and independent variables are continuous, correlation and regression are the natural choices. When the dependent variable is categorical, we need chi-square (if the independent variables are also categorical) or logistic regression (if there are continuous or mixed predictors). And when the dependent variables are counts or times to an event, specific techniques exist such as Poisson regression or survival analysis.
An important nuance is the difference between the theoretical and practical measurement scale. A 7-point Likert scale from a single item is, strictly speaking, ordinal. But the sum of 20 Likert items produces a total score that many researchers treat as continuous, and empirical evidence suggests that parametric tests are reasonably robust with these variables as long as the distributions are not extremely skewed. The decision to treat a variable as continuous or ordinal is not purely statistical but involves substantive judgments about the nature of the construct being measured.
Statistical assumptions: verify before deciding
Each parametric technique comes with a set of assumptions that, ideally, must be met for the results to be reliable. The most common ones are normality of the distribution (or of the residuals, depending on the case), homogeneity of variances (homoscedasticity), and independence of observations. Verifying these assumptions before making a final test choice is good practice that can save problems later on.
Normality is assessed through tests such as Shapiro-Wilk or Kolmogorov-Smirnov, although visual inspection of histograms and Q-Q plots is usually more informative. Homogeneity of variances is tested with Levene's test. Independence of observations is not verified statistically but is ensured through the study design (each participant contributes data independently, without influence from other participants). When these assumptions are violated, there are three possible strategies: use the robust version of the parametric test (such as the Welch correction for the t-test when variances are unequal), transform the data to meet the assumptions, or resort to the corresponding nonparametric alternative.
The most common nonparametric alternatives are the Mann-Whitney U test (equivalent to the independent samples Student's t-test), the Wilcoxon signed-rank test (equivalent to the paired t-test), the Kruskal-Wallis H test (equivalent to one-way ANOVA), and Spearman's rho (equivalent to the Pearson correlation). These tests work with ranks rather than raw scores and do not assume normality, but they have lower statistical power when parametric assumptions are actually met. For this reason, it is not advisable to use nonparametric tests by default as a preventive strategy, but only when there is clear evidence that parametric assumptions are seriously compromised.
Beyond the basics
Current psychological research poses increasingly complex questions that require techniques beyond the classical repertoire of t-tests, ANOVA, and regression. Nested data (students within classrooms, patients within therapists) require multilevel models that account for the hierarchical structure. Longitudinal data with more than two measurements require growth curve models or repeated measures ANOVA with appropriate corrections. Questionnaires with multiple subscales are better analyzed with structural equation models than with isolated bivariate correlations. And when the interest lies in identifying homogeneous subgroups within a sample, techniques such as latent class analysis or latent profile analysis offer possibilities that classical clustering analyses do not provide.
The final recommendation, and perhaps the most practical one, is to always start with the simplest approach. If a t-test answers your question, do not use an ANOVA. If an ANOVA suffices, do not build a structural equation model. Analytical complexity should be justified by the complexity of the question and the data, not by the desire to impress reviewers. At the same time, it is not advisable to oversimplify when the question and data require a more sophisticated approach. The balance between parsimony and adequacy is what defines a good statistical analysis, and finding that balance is a skill developed through experience, methodological reading, and, above all, practice.
If you are stuck deciding which test to apply to your dissertation data, my statistical consulting for doctoral theses walks through the design with you and picks the right analysis before any software runs. Getting this decision right early saves weeks of re-analysis later.