Statistics Tutorials: Step-by-Step Guides with APA7 Reporting

One guide for every analysis on StatFas. Each tutorial explains when to use the method, how to prepare your data, which assumptions to check, how to read the output and how to write the result in APA7 style, with a worked example and a practice dataset.

Which analysis do I need?

Descriptives and charts

Descriptive StatisticsDescriptive statistics summarise a variable with a few numbers: where its centre is, how spread out it is, and what shape it has.Frequency AnalysisA frequency analysis counts how often each category of a variable occurs and shows the counts as percentages.Bar PlotA bar plot shows one bar per category.Pie ChartA pie chart splits a circle into slices whose sizes show each category's share of the whole.Line GraphA line graph connects points across an ordered x-axis such as time, so you can see change and compare trajectories between groups.HeatmapA heatmap shows a table of numbers as coloured cells, so patterns in large matrices become visible at a glance.

Relationships and prediction

CorrelationA correlation measures how strongly and in which direction two variables move together, on a scale from −1 to +1.Pearson CorrelationPearson's r measures the strength and direction of a linear relationship between two continuous variables.Spearman's rank CorrelationSpearman's rank correlation (rs) is Pearson's correlation computed on the ranks of the scores.Regression AnalysisRegression models an outcome from one or more predictors.Linear RegressionLinear regression fits a straight-line (or plane) model that predicts a continuous outcome from one or more predictors.Logistic RegressionLogistic regression models the probability of a yes/no (binary) outcome from one or more predictors and reports effects as odds ratios.

Mediation, moderation and SEM

MediationMediation asks whether the effect of a predictor (X) on an outcome (Y) works through an intermediate variable, the mediator (M): X → M → Y.ModerationModeration asks whether the strength or direction of the relationship between X and Y depends on a third variable, the moderator (W).SEMStructural equation modeling tests a theory about relationships among observed and latent (unobserved) variables.CFAConfirmatory factor analysis tests whether a set of items measures the latent factors you expect, based on a structure you specify in advance.EFAExploratory factor analysis uncovers the underlying latent factors that explain why a set of items are correlated, without specifying the structure in advance.

Structure and networks

PCAPrincipal component analysis combines many correlated variables into a smaller number of uncorrelated components that capture as much of the variance as possible.Network AnalysisPsychological network analysis represents variables as nodes and their relationships as edges, usually regularised partial correlations, so you can see which variables are directly connected after accounting for all others.

Compare means

t-TestA t-test compares means.One sample t-TestThe one-sample t-test compares the mean of one group with a fixed, known or hypothesised value (μ0).Independent t-TestThe independent-samples t-test compares the means of two separate groups on a continuous outcome.Paired t-TestThe paired-samples t-test compares two measurements from the same people (or matched pairs) by testing whether the average difference is zero.ANOVAAnalysis of variance (ANOVA) tests whether the means of three or more groups or conditions differ, using one overall test instead of many t-tests.One-way ANOVAOne-way ANOVA tests whether the means of three or more independent groups differ on a continuous outcome.Two-way ANOVATwo-way ANOVA tests the effects of two categorical factors on a continuous outcome, including whether the two factors interact.One-way ANOVA with repeated measuresOne-way repeated-measures ANOVA tests whether the means of the same participants differ across three or more conditions or time points.Two-way ANOVA with repeated measuresTwo-way repeated-measures ANOVA tests two factors when at least one of them is a within-subject (repeated) factor, plus their interaction.

Non-parametric and categorical

Mann-Whitney U-testThe Mann–Whitney U test compares two independent groups using ranks instead of means, so it does not need normally distributed data.Wilcoxon TestThe Wilcoxon signed-rank test compares two related measurements using the ranks of the differences.Kruskal-Wallis TestThe Kruskal–Wallis H test compares three or more independent groups using ranks.Friedman TestThe Friedman test compares three or more related measurements using ranks within each participant.Binomial TestThe binomial test checks whether the proportion of "successes" in a sample differs from a proportion you expected in advance.Chi-squared TestThe chi-squared (χ2) test compares observed counts with expected counts.

How each tutorial is organised

• What it is and when to use it, with an example research question.
• Preparing your data, including a downloadable simulated dataset (CSV) you can upload to practise.
• Assumptions and checks to make before trusting the result.
• Key numbers to read and which effect size to report.
• APA7 reporting: a fill-in template and a worked example whose numbers are computed from the practice dataset.
• Mistakes, alternatives and FAQ.

Example datasets are simulated for teaching and are not real findings. Guides explain general practice; follow the requirements of your journal or institution.