Which statistical test should I use? A free selector for psychology dissertations

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Every test the Selector can recommend

The Selector walks you to one of these 17 tests in five questions. They are all set out below too — when each one applies, the assumptions it makes, what to do when those assumptions fail, the exact SPSS and jamovi menu path, and an APA 7 sentence you can adapt.

Parametric

Paired Samples t-Test

Track changes in the same participants over time

Because the same people were measured twice, every participant acts as their own control. The test works on each person's change score (Time 2 minus Time 1) and asks whether the average change is bigger than chance alone would produce. Comparing people to themselves strips out stable individual differences, some people just score high, others low, which gives you noticeably more statistical power than comparing two separate groups.

Assumptions
  • Continuous DV
  • Same participants at both time points
  • Difference scores approximately normal
  • No significant outliers in differences
If those fail
Use the Wilcoxon Signed-Rank Test when differences are non-normal.
Example
PHQ-9 depression scores before vs. after a 12-week mindfulness programme.
Effect size
Cohen's d from difference scores
APA 7 write-up

A paired-samples t-test revealed that [DV] [significantly/did not significantly] [increase/decrease] from [Time 1] (M=___, SD=___) to [Time 2] (M=___, SD=___), t(df)=___, p=.___, d=___.

[DV] [significantly changed / did not significantly change] from [Time 1] to [Time 2].

In SPSS
Analyze → Compare Means → Paired-Samples T Test
In jamovi
T-Tests → Paired Samples T-Test
In G*Power
t-tests → Means: Difference between two dependent means (matched pairs)
How to plot it
Paired line plot; histogram of difference scores
What it can’t tell you
Cannot establish causation, only that scores changed between time points.
Your supervisor may ask
Report t, df, p, and Cohen's d.
Parametric

Pearson Correlation (r)

Measure linear relationship between two continuous variables

Pearson's r puts a single number on how tightly two continuous variables move together in a straight line: from −1 (perfect negative relationship) through 0 (no linear relationship) to +1 (perfect positive). Your variables are both continuous and roughly normal, which is exactly when r is at its best. One caution: always look at the scatter plot too, r can completely miss a curved relationship.

Assumptions
  • Both variables continuous
  • Both approximately normally distributed
  • Linear relationship, verify with scatter plot
  • No significant outliers
If those fail
Use the Spearman's Rank Correlation (ρ) when either variable is non-normal or ordinal.
Example
Correlating weekly exercise hours with WEMWBS wellbeing scores.
Effect size
r itself, small≥0.10, medium≥0.30, large≥0.50
APA 7 write-up

A Pearson correlation indicated a [significant/non-significant] [positive/negative] relationship between [Var 1] and [Var 2], r(N−2)=.___, p=.___.

There was [a significant/no significant] linear relationship between [Var 1] and [Var 2].

In SPSS
Analyze → Correlate → Bivariate → select Pearson
In jamovi
Regression → Correlation Matrix → select Pearson's r
In G*Power
Exact → Correlation: Bivariate normal model
How to plot it
Scatter plot with regression line and 95% confidence band
What it can’t tell you
Cannot establish causation. Cannot describe non-linear relationships.
Your supervisor may ask
Check both variables for normality and inspect the scatter plot.
Parametric

Welch's Independent t-Test

Compare two independent groups, robust to unequal variances

You have two separate groups of people and want to know whether their average scores genuinely differ, or whether the gap you see could just be chance. Welch's t-test compares the two means while allowing the groups to have different spreads (variances) and even different sizes, which is why it has replaced the classic Student's t-test as the modern default (Field, 2018). If your scores are roughly bell-shaped within each group, this is the strongest, most defensible choice.

Assumptions
  • Continuous DV
  • Approximately normal per group (or n>30 by CLT)
  • Independent observations
  • No assumption of equal variances required
If those fail
Use the Mann-Whitney U Test when normality is violated.
Example
Comparing mean anxiety (GAD-7) between a CBT group and a waitlist control.
Effect size
Cohen's d, small≥0.20, medium≥0.50, large≥0.80
APA 7 write-up

A Welch's independent-samples t-test indicated that [DV] [significantly/did not significantly] differ between [Group 1] (M=___, SD=___) and [Group 2] (M=___, SD=___), t(df)=___, p=.___, d=___.

[Group 1] scored [significantly] [higher/lower] than [Group 2] on [DV].

In SPSS
Analyze → Compare Means → Independent-Samples T Test → use 'Equal variances not assumed' row
In jamovi
T-Tests → Independent Samples T-Test (Welch's is the default in jamovi)
In G*Power
t-tests → Means: Two independent groups
How to plot it
Side-by-side box plots; bar chart with mean ± 95% CI
What it can’t tell you
Cannot tell you which variable caused the difference.
Your supervisor may ask
Supervisors may ask: 'Why Welch's not Student's t?' Answer: Welch's is the modern recommended default.
Parametric

Binary Logistic Regression

Predict the probability of a binary outcome

Your outcome has exactly two possibilities (pass/fail, yes/no, dropout/stay), so an ordinary straight-line model won't work, predictions must stay between 0% and 100%. Logistic regression models the probability of the outcome instead, and expresses each predictor's influence as an odds ratio: how many times the odds of the outcome multiply for each one-unit increase in that predictor. It happily mixes continuous and categorical predictors in the same model.

Assumptions
  • Binary DV
  • Log-odds linearity with continuous predictors
  • No multicollinearity
  • ≥20 events per predictor
  • Independent observations
If those fail
Use the Probit regression for alternative probability modelling.
Example
Predicting pass/fail from attendance rate, study hours, and prior GPA.
Effect size
Nagelkerke R²; Odds Ratios (OR); AUC-ROC
APA 7 write-up

Binary logistic regression indicated a [significant/non-significant] model, χ²(df)=___, p=.___, Nagelkerke R²=___. [Predictor] [significantly/did not significantly] predict [DV] (OR=___, 95% CI [___,___], p=___).

[Predictor] [significantly/did not significantly] predict the likelihood of [DV].

In SPSS
Analyze → Regression → Binary Logistic
In jamovi
Regression → Logistic Regression → Binomial
In G*Power
z-tests → Logistic regression
How to plot it
ROC curve; forest plot of odds ratios
What it can’t tell you
Odds Ratios ≠ probabilities.
Parametric

Multiple Linear Regression

Predict a continuous outcome from multiple predictors

Real outcomes rarely have a single cause, and multiple regression embraces that: it weighs all your predictors at once and reports each one's unique contribution, what it adds over and above everything else in the model. That word 'unique' is the key insight: a predictor can correlate strongly with the outcome on its own, yet add almost nothing once the other predictors are accounted for.

Assumptions
  • Linear relationships
  • Normal residuals
  • Homoscedasticity
  • No multicollinearity (VIF<10)
  • Independent observations
If those fail
Use the Ridge or Lasso regression when multicollinearity is severe.
Example
Predicting wellbeing from age, social support, and perceived stress.
Effect size
R² (overall); standardised β per predictor; ΔR² per block
APA 7 write-up

Multiple regression indicated the model [significantly/did not significantly] predict [DV], F(df₁,df₂)=___, p=.___, R²=___. [Predictor 1] (β=.___, p=___) [was/was not] a significant predictor.

The predictors [accounted / did not account] for a significant proportion of variance in [DV].

In SPSS
Analyze → Regression → Linear (all IVs in 'Independents')
In jamovi
Regression → Linear Regression
In G*Power
F-tests → Linear Multiple Regression: Fixed model, R² increase
How to plot it
Coefficient plot; residuals vs. fitted
What it can’t tell you
Use adjusted R² for honest comparison. Cannot prove causation.
Parametric

One-Way ANOVA

Compare three or more independent groups

With three or more groups, running several t-tests would quietly inflate your chance of a false positive, every extra comparison is another roll of the dice. One-way ANOVA solves this by asking a single overall question first: is there at least one real difference somewhere among the group means? Only if the answer is yes do you follow up with post-hoc tests to pinpoint exactly which groups differ, keeping the overall error rate under control.

Assumptions
  • Continuous DV
  • Normality within each group
  • Homogeneity of variance (Levene's test)
  • Independent observations
If those fail
Use the Kruskal-Wallis Test when normality or equal variances are violated.
Example
Comparing wellbeing across lecture, flipped, and problem-based learning groups.
Effect size
Eta-squared η², small≥0.01, medium≥0.06, large≥0.14
APA 7 write-up

A one-way ANOVA indicated a [significant/non-significant] effect of [IV] on [DV], F(df₁,df₂)=___, p=.___, η²=___. Post-hoc comparisons (Tukey HSD) [showed/showed no significant differences].

There was a [significant/non-significant] difference in [DV] across the groups.

In SPSS
Analyze → Compare Means → One-Way ANOVA → Post Hoc
In jamovi
ANOVA → One-Way ANOVA
In G*Power
F-tests → ANOVA: Fixed effects, omnibus, one-way
How to plot it
Box plots per group; means plot with 95% CI
What it can’t tell you
Post-hoc tests are required to identify which specific groups differ.
Your supervisor may ask
Always report the omnibus F, η², and post-hoc results.
Parametric

Repeated Measures ANOVA

Track the same participants across 3+ time points

The same participants were measured at three or more time points (or under three or more conditions), so their scores are related, and that's actually an advantage. Repeated measures ANOVA uses each person as their own baseline, separating genuine change across conditions from stable differences between people. That makes it far more sensitive than testing separate groups at each time point would be.

Assumptions
  • Continuous DV
  • Sphericity, check Mauchly's test
  • Approximately normal residuals
If those fail
Use the Friedman Test when sphericity or normality is violated.
Example
Wellbeing at baseline, 3, 6, and 12 months post-intervention.
Effect size
Partial η²p
APA 7 write-up

A one-way repeated measures ANOVA indicated a [significant/non-significant] effect of [time/condition] on [DV], F(df₁,df₂)=___, p=.___, η²p=___.

[DV] [significantly changed / did not significantly change] across the time points.

In SPSS
Analyze → General Linear Model → Repeated Measures
In jamovi
ANOVA → Repeated Measures ANOVA
In G*Power
F-tests → ANOVA: Repeated measures, within factors
How to plot it
Line chart of means over time with SE bars
What it can’t tell you
Cannot establish causation from time alone.
Your supervisor may ask
Report Mauchly's test result and the correction applied.
Parametric

Simple Linear Regression

Predict a continuous outcome from one predictor

Correlation tells you two variables are related; regression goes one step further and gives you a prediction equation, a line of best fit through your data. It tells you how much the outcome is expected to change for every one-unit increase in your predictor, and R² tells you what percentage of the outcome's variation your predictor actually explains. That's a much more useful sentence for your results chapter than 'they're correlated'.

Assumptions
  • Linear relationship
  • Normal residuals, check Q-Q plot after running model
  • Homoscedasticity
  • Independent observations
If those fail
Use the Spearman or non-linear regression when linearity or residual normality is violated.
Example
Predicting exam performance (%) from total study hours.
Effect size
R²; Cohen's f², small≥0.02, medium≥0.15, large≥0.35
APA 7 write-up

[Predictor] [significantly/did not significantly] predict [DV], β=.___, t(df)=___, p=.___, R²=.___.

[Predictor] [significantly/did not significantly] predict [DV], accounting for ___% of its variance.

In SPSS
Analyze → Regression → Linear (1 IV in 'Independents')
In jamovi
Regression → Linear Regression
In G*Power
F-tests → Linear Multiple Regression: Fixed model, R² increase
How to plot it
Scatter with regression line; residual-vs-fitted plot
What it can’t tell you
Cannot prove causation. Normality applies to residuals, not the raw DV.
Non-Parametric

Chi-Square Test (χ²)

Test association between two categorical variables

Both of your variables are categories, so there are no means to compare, only counts of people in each combination. Chi-square compares the counts you actually observed against the counts you would expect if the two variables had nothing to do with each other. A big enough gap between observed and expected tells you the variables are associated, for example, that therapy preference really does differ by gender.

Assumptions
  • Both variables categorical
  • Independent observations
  • Expected cell frequencies ≥5 in ALL cells
If those fail
Use the Fisher's Exact Test when any expected cell frequency is < 5.
Example
Gender × preference for face-to-face vs. online therapy.
Effect size
Cramér's V, small≥0.10, medium≥0.30, large≥0.50
APA 7 write-up

A chi-square test of independence indicated a [significant/non-significant] association between [Var 1] and [Var 2], χ²(df)=___, p=.___, N=___, V=___.

There was [a significant/no significant] association between [Var 1] and [Var 2].

In SPSS
Analyze → Descriptive Statistics → Crosstabs → Statistics → Chi-square
In jamovi
Frequencies → Contingency Tables
In G*Power
χ²-tests → Goodness-of-fit tests: Contingency tables
How to plot it
Stacked bar chart; mosaic plot
What it can’t tell you
Shows that an association exists, not its direction.
Your supervisor may ask
Always verify expected cell frequencies. Report χ², df, p, N, and Cramér's V.
Non-Parametric

Fisher's Exact Test

Test association when expected cell counts are small

Chi-square relies on an approximation that breaks down when any expected cell count drops below 5, which happens all the time in small samples and pilot studies. Fisher's exact test sidesteps the approximation entirely: it calculates the exact probability of getting a table like yours by chance. That means the p-value stays trustworthy no matter how small your sample is.

Assumptions
  • Both variables categorical (typically 2×2)
  • At least one expected cell frequency <5
  • Independent observations
If those fail
Use the Chi-Square Test (χ²) when all expected cell frequencies are ≥5.
Example
Treatment type (CBT vs. waitlist) predicting dropout in a small pilot study (n=24).
Effect size
Odds Ratio (OR); phi coefficient φ
APA 7 write-up

Fisher's exact test indicated a [significant/non-significant] association between [Var 1] and [Var 2], p=.___ (exact), OR=___, 95% CI [___,___].

There was [a significant/no significant] association between [Var 1] and [Var 2].

In SPSS
Analyze → Descriptive Statistics → Crosstabs (Fisher's appears automatically for 2×2)
In jamovi
Frequencies → Contingency Tables → Statistics → Fisher's exact test
In G*Power
χ²-tests → Contingency tables (use chi-square as approximation)
How to plot it
2×2 contingency table with exact p-value
What it can’t tell you
Standard Fisher's is designed for 2×2 tables.
Non-Parametric

Kendall's Tau-b (τ-b)

Correlation for ordinal data with many tied ranks

Like Spearman's, Kendall's tau works on ranks rather than raw scores, but it handles tied ranks much more gracefully. Ties happen whenever many participants give the same answer, which is very common with ordinal measures like education level or single Likert items. With lots of ties or a small sample, tau-b gives a more accurate, more conservative picture of the association than Spearman's ρ would.

Assumptions
  • Both variables ordinal or ranked
  • Monotonic relationship
  • Handles tied ranks well
If those fail
Use the Spearman's Rank Correlation (ρ) when few ties exist and n is large.
Example
Correlating education level (1=GCSE…5=PhD) with symptom severity rating.
Effect size
τ-b itself, small≥0.10, medium≥0.30, large≥0.50
APA 7 write-up

A Kendall's tau-b correlation indicated a [significant/non-significant] relationship between [Var 1] and [Var 2], τ-b=.___, z=___, p=.___.

There was [a significant/no significant] association between [Var 1] and [Var 2].

In SPSS
Analyze → Correlate → Bivariate → select Kendall's tau-b
In jamovi
Regression → Correlation Matrix → select Kendall's tau-b
In G*Power
Exact → Correlation: Bivariate normal model (add ~15%)
How to plot it
Scatter plot of ranks
What it can’t tell you
τ-b and Spearman's ρ cannot be compared directly.
Non-Parametric

Kruskal-Wallis Test

Compare 3+ independent groups without normality

Think of this as the non-parametric version of one-way ANOVA. All scores from every group are ranked together in one list, and the test asks whether some groups consistently hold higher ranks than others, more than chance shuffling would produce. It's the safe choice when scores are skewed, ordinal, or contain outliers: no bell curve required, and your conclusion stays defensible.

Assumptions
  • Ordinal or continuous DV
  • Independent observations
  • Similar distribution shapes
If those fail
Use the One-Way ANOVA when normality and equal variances are met.
Example
Self-reported stress across five different occupational groups.
Effect size
ε² or η² from the H statistic
APA 7 write-up

A Kruskal-Wallis test revealed a [significant/non-significant] difference in [DV] across groups, H(df)=___, p=.___, ε²=___.

There was [a significant/no significant] difference in [DV] across the groups.

In SPSS
Analyze → Nonparametric Tests → Legacy Dialogs → K Independent Samples
In jamovi
ANOVA → One-Way ANOVA → check Kruskal-Wallis
In G*Power
F-tests → ANOVA: Fixed effects, omnibus, one-way (add ~15% to N)
How to plot it
Box plots per group; violin plots
What it can’t tell you
Post-hoc tests are required to identify which specific groups differ.
Non-Parametric

Mann-Whitney U Test

Compare two groups without assuming normality

Your data don't meet the bell-curve assumption, so comparing means could mislead you. Mann-Whitney takes every score from both groups, puts them in one big ordered list, and checks whether one group's scores consistently sit higher in the ranking than the other's. Because it works on ranks rather than raw numbers, skewed data and extreme outliers can't distort the result. It's the safe, defensible choice here.

Assumptions
  • Ordinal or continuous DV
  • Independent observations
  • Similar distribution shapes
If those fail
Use the Welch's Independent t-Test when normality and approximately equal variances are met.
Example
Comparing Likert-scale job satisfaction (1–7) between two departments.
Effect size
Rank-biserial r, small≥0.10, medium≥0.30, large≥0.50
APA 7 write-up

A Mann-Whitney U test indicated that [DV] [significantly/did not significantly] differ between [Group 1] (Mdn=___) and [Group 2] (Mdn=___), U=___, z=___, p=.___, r=___.

There was [a significant/no significant] difference between groups on [DV].

In SPSS
Analyze → Nonparametric Tests → Legacy Dialogs → 2 Independent Samples
In jamovi
T-Tests → Independent Samples T-Test → check Mann-Whitney U
In G*Power
t-tests → Means: Two independent groups (add ~15% to N)
How to plot it
Box plots with median highlighted; violin plots
What it can’t tell you
Report medians, not means.
Non-Parametric

Spearman's Rank Correlation (ρ)

Robust correlation for non-normal or ordinal data

Spearman's ρ measures whether two variables rise and fall together, without assuming the relationship is a straight line or that the data are bell-shaped. It converts each variable to ranks first, so a few extreme values can't drag the result around the way they can with Pearson's r. That makes it ideal for ordinal scales, skewed scores, and small samples with outliers.

Assumptions
  • Ordinal or continuous variables
  • Monotonic relationship, check scatter plot
  • No normality required
If those fail
Use the Pearson Correlation (r) when both variables are normally distributed and linearly related.
Example
Correlating Likert attachment anxiety scores with relationship satisfaction.
Effect size
ρ itself, same benchmarks as Pearson r
APA 7 write-up

A Spearman's rank-order correlation indicated a [significant/non-significant] [positive/negative] relationship between [Var 1] and [Var 2], ρ(N−2)=.___, p=.___.

There was [a significant/no significant] monotonic relationship between [Var 1] and [Var 2].

In SPSS
Analyze → Correlate → Bivariate → select Spearman
In jamovi
Regression → Correlation Matrix → select Spearman's rho
In G*Power
Exact → Correlation: Bivariate normal model (add ~15% to N)
How to plot it
Scatter plot with Loess smoother
What it can’t tell you
Captures monotonic relationships only.
Non-Parametric

Wilcoxon Signed-Rank Test

Paired comparison without normality assumption

This is the rank-based cousin of the paired t-test, for when your difference scores aren't normally distributed. It ranks each participant's change from Time 1 to Time 2 by size and asks whether changes in one direction (say, improvements) consistently outweigh changes in the other. Because only the ranks matter, a couple of extreme changes can't dominate the result the way they would in a t-test.

Assumptions
  • Paired observations
  • Ordinal or continuous DV
  • Differences can be meaningfully ranked
If those fail
Use the Paired Samples t-Test when differences are normally distributed.
Example
Anxiety ratings (1–10) before and after a relaxation training workshop.
Effect size
Matched-pairs rank-biserial r
APA 7 write-up

A Wilcoxon signed-rank test indicated that [DV] [significantly/did not significantly] [change] from [Time 1] (Mdn=___) to [Time 2] (Mdn=___), z=___, p=.___, r=___.

[DV] [significantly changed / did not significantly change] from [Time 1] to [Time 2].

In SPSS
Analyze → Nonparametric Tests → Legacy Dialogs → 2 Related Samples
In jamovi
T-Tests → Paired Samples T-Test → check Wilcoxon signed rank
In G*Power
t-tests → Means: Difference between two dependent means (add ~15%)
How to plot it
Pre/post median bar chart; dot plot of individual changes
What it can’t tell you
Reports whether the typical change is zero, not the magnitude in original units.
Non-Parametric

Friedman Test

Repeated measures without parametric assumptions

When the same participants are measured across three or more conditions but the data don't meet parametric assumptions, the Friedman test steps in. It ranks each participant's own scores across the conditions (their personal 1st, 2nd, 3rd…) and then checks whether one condition consistently outranks the others across people. No normality, no sphericity, just a clean within-person comparison.

Assumptions
  • Same participants across all conditions
  • Ordinal or continuous DV
  • 3+ conditions
If those fail
Use the Repeated Measures ANOVA when sphericity and normality are met.
Example
Therapists rating CBT, DBT, and ACT effectiveness for shared clients.
Effect size
Kendall's W (0=no agreement, 1=perfect)
APA 7 write-up

A Friedman test indicated a [significant/non-significant] difference in [DV] across conditions, χ²(df)=___, p=.___, W=___.

[DV] [significantly differed / did not significantly differ] across the conditions.

In SPSS
Analyze → Nonparametric Tests → Legacy Dialogs → K Related Samples
In jamovi
ANOVA → Repeated Measures ANOVA → check Friedman
In G*Power
F-tests → ANOVA: Repeated measures (add ~15% to N)
How to plot it
Median rank line chart
What it can’t tell you
Shows whether conditions differ in rank order, not the size of change in original units.
Advanced

Mediation / Moderation Analysis

Unpack how and when relationships occur

These analyses unpack a relationship rather than just confirm one exists. Mediation asks how: does X influence Y through some in-between mechanism M (X→M→Y)? Moderation asks when: does the strength of the X→Y link change depending on a third variable? One crucial caveat, your causal ordering must come from theory, not from the data. The analysis cannot tell you which direction the arrows point; your literature review has to.

Assumptions
  • Causal ordering grounded in theory
  • Bootstrapping recommended (n≥200)
  • Measurement reliability across all variables
If those fail
Use the Structural Equation Modelling (SEM) for complex mediation chains or latent variables.
Example
Self-efficacy mediating social support → academic performance (Hayes, 2022).
Effect size
Mediation: indirect effect (a×b path); Moderation: interaction β₃
APA 7 write-up

A mediation analysis using bootstrapping (5,000 samples; Hayes, 2022) indicated a [significant/non-significant] indirect effect of [X] on [Y] through [M], b=.___, 95% CI [___,___].

[M] [significantly / did not significantly] mediate the relationship between [X] and [Y].

In SPSS
PROCESS v4 → Model 4 (mediation) or Model 1 (moderation)
In jamovi
Install jAMM or PROCESS module from jamovi library
In G*Power
F-tests → Linear Multiple Regression (for direct paths only)
How to plot it
Path diagram; interaction plot
What it can’t tell you
Mediation in correlational data cannot prove causation.
Your supervisor may ask
Examiners will ask: what is your theoretical justification for the causal ordering?

Test choice follows standard psychology practice (Field, 2018) and APA 7 reporting conventions. The Selector applies the same rules to your answers so you get one recommendation instead of eighteen.