Compare Means

Analyze → Compare Means. These procedures ask whether the mean of a scale variable differs — between groups, against a fixed value, or across paired measurements.

Means

When to use it. To get summary statistics for a scale variable broken down by the categories of one or more factors — a descriptive breakdown, not a test.

Dialog. A Dependent scale variable and one or more Independent (grouping) variables.

Output. A table of the dependent's mean, N and standard deviation within each group (and overall).

Example. Mean SystolicBP by StudyZone and by SmokingStatus.

T Tests

All three live under Compare Means and each can be run one- or two-tailed (set in the Options section).

One-Sample T Test

When. Compare a variable's mean against a known test value.

Dialog. The Test Variable(s) and the Test Value.

Output. The mean, the t statistic, degrees of freedom, the significance, and the confidence interval of the difference.

Example. Is mean BMI different from 25 (the overweight threshold)?

Independent-Samples T Test

When. Compare the means of two independent groups.

Dialog. A Test Variable and a Grouping Variable (define the two groups by their values).

Output. Group statistics, Levene's test for equal variances, and the t-test reported both ways (equal and unequal variances assumed) with the CI of the difference.

Example. Does mean FastingGlucose_mmolL differ between Diabetic = Yes and No?

Paired-Samples T Test

When. Compare two measurements on the same cases.

Dialog. One or more variable pairs.

Output. The paired differences' mean, the t statistic, df, significance and CI.

Example. SystolicBP vs DiastolicBP (illustrative paired comparison).

One-Way ANOVA

When to use it. Compare the means of a scale variable across three or more groups.

Dialog. A Dependent scale variable and a Factor (the grouping variable). The Options section adds:

• Levene's test of homogeneity of variances;
• the Welch robust test (for unequal variances);
• post-hoc comparisons — Bonferroni, Scheffé, Tukey HSD;
• a-priori contrasts (custom weighted comparisons).

Output. The ANOVA table (between/within sums of squares, F, significance), plus any homogeneity test, post-hoc table and contrast results you requested.

Example. Mean SystolicBP across the levels of EducationLevel, with Tukey HSD to see which education levels differ.

Bayesian t test

A Bayesian counterpart to the three t tests, under Analyze → Bayesian → t Test…. Where a classical t test gives a p-value — which can only ever fail to reject the null, never support it — a Bayesian t test reports a Bayes factor that grades the evidence in either direction.

When to use it. Whenever you would run a one-sample, paired or independent-samples t test but want to quantify evidence for the null as well as against it (e.g. to argue two groups are equivalent), or want a posterior on the effect size rather than a confidence interval.

Dialog. A One-Sample / Paired / Independent selector (the same three designs as the classical t tests), the test variables, and:

• Prior scale r — the width of the Cauchy prior on the standardized effect size δ; the default 0.707 (≈ 1/√2) is the standard "medium" scale.
• Credible % — the level for the posterior interval of δ (default 95).

Output. A Bayesian t Test table with, per variable/pair:

• BF₁₀ — the evidence for a difference, and BF₀₁ = 1/BF₁₀ — the evidence for the null. A BF₁₀ of 6 means the data are 6× more likely under a real effect; a BF₁₀ of 0.2 (BF₀₁ = 5) means they are 5× more likely under the null.
• Evidence — a verbal category for the Bayes factor (Anecdotal, Moderate, Strong, Very strong, Extreme), tagged with the favoured hypothesis.
• Median δ and its credible interval — the posterior for the standardized effect size.

Example. A paired Bayesian t test of Pre vs Post: a BF₁₀ of 0.3 ("Moderate (H0)") is positive evidence that the intervention made no difference — a conclusion a non-significant p-value could not have supported.

Bayesian correlation

Also under Analyze → Bayesian → Correlation…: the Bayesian counterpart to bivariate correlation. Pick two or more numeric variables; each pair is reported with its Pearson r, the BF₁₀ / BF₀₁ (evidence for / against a correlation) and evidence category, and the posterior median and credible interval of ρ.

• Prior width κ — the stretched-beta prior on ρ; the default 1 is a uniform prior on −1…1. (Smaller κ pulls the prior toward 0.)
• Credible % — the level for the posterior interval of ρ.

A BF₁₀ well above 1 is evidence the two variables are correlated; a BF₀₁ above 1 is evidence they are not — the latter being something a significance test on r cannot deliver.

Bayesian ANOVA

Under Analyze → Bayesian → ANOVA…: the Bayesian counterpart to the one-way ANOVA. Pick one or more numeric dependent variables and a factor; each is reported with its group count, η² (the variance explained), and the BF₁₀ / BF₀₁ for the group-means model against the no-effect null — i.e. whether the factor matters at all.

• Prior scale r — the Cauchy prior on the standardized group effects; the default 0.5 is the standard "medium" fixed-effect scale.

A BF₁₀ above 1 is evidence the groups differ; a BF₀₁ above 1 is evidence they do not — direct support for a null that an ANOVA F test cannot provide.

Bayesian linear regression

Under Analyze → Bayesian → Linear Regression…: the Bayesian counterpart to linear regression. Pick a dependent variable and one or more numeric predictors. It reports:

• Coefficients — each predictor's posterior mean (the OLS estimate under the diffuse prior) and its credible interval.
• Model summary — N, the predictor count, R², and the residual variance posterior (mean and credible interval).
• Bayes factor — BF₁₀ / BF₀₁ for the full model against the intercept-only null: whether the predictors collectively matter.

Controls: a Prior scale r (the g-prior on the effects; default √2/4 ≈ 0.354) and a Credible % for the intervals. A BF₁₀ above 1 favours the predictors; a BF₀₁ above 1 is evidence that an intercept-only model suffices.

Choosing among them

If a normality or variance assumption looks shaky (check it in Explore), consider the nonparametric equivalents.