StatSphere: Your Data Compass
An educational hub to choose, run, interpret, and report statistical tests in R and SPSS.

Mean Comparisons & ANOVA (R)

Independent-samples t-test
  • When to use: DV numeric, one between-subjects IV with two groups.
  • Assumptions: independence; ~normal DV within each group; variance homogeneity (Levene). If variances unequal, use Welch.
  • R code: 
    # Welch t-test (default in t.test when var.equal = FALSE)
t.test(y ~ group, data = d, var.equal = FALSE)

# Check assumptions
car::leveneTest(y ~ group, data = d)      # homogeneity
shapiro.test(d$y[d$group=="A"])          # normality by group
  • Report: t(df) = value, p = value, Cohen's d, 95% CI.
  • Alternatives: Mann–Whitney U if non-normal/outliers and ordinal/continuous DV.
One-way ANOVA
  • When to use: DV numeric, one between-subjects IV with ≥3 groups.
  • Assumptions: independence; normality; homogeneity (Levene). Use Welch ANOVA if variances unequal.
  • R code: 
    aov1 <- aov(y ~ group, data=d)
summary(aov1)
car::leveneTest(y ~ group, data=d)
# Welch ANOVA
oneway.test(y ~ group, data=d, var.equal=FALSE)
# Post-hoc (Tukey for homoscedastic)
TukeyHSD(aov1)
# Games-Howell for heteroscedastic
userfriendlyscience::oneway(as.factor(group), y, posthoc = "games-howell", data=d)
  • Report: F(df1, df2) = value, p, η2 or partial η2, post-hoc MD with CI.
  • Alternatives: Kruskal–Wallis for nonparametric.
Repeated-measures ANOVA
  • When to use: DV numeric measured on the same subjects across ≥2 levels (within-subjects factor).
  • Assumptions: sphericity (Mauchly); normality of differences.
  • R code: 
    # Using afex + emmeans
aov_rm <- afex::aov_ez(id = "id", dv = "y", within = "time", data=d)
summary(aov_rm)
# Sphericity correction is provided; follow-ups
aemm <- emmeans::emmeans(aov_rm, ~ time)
emmeans::pairs(aemm, adjust="bonferroni")
  • Report: Greenhouse–Geisser-corrected F, p, partial η2, post-hocs with adjustment.
  • Alternatives: Friedman test (nonparametric).

Associations & Regression (R)

Pearson & Spearman Correlation
  • When to use: two numeric variables (Pearson); monotonic but non-normal or ordinal (Spearman).
  • Assumptions: linearity, normality (Pearson); monotonicity (Spearman).
  • R code: 
    cor.test(d$x, d$y, method = "pearson")
cor.test(d$x, d$y, method = "spearman")
# Diagnostic
car::qqPlot(d$y); graphics::pairs(d[c("x","y")])
  • Report: r(df) = value, p, 95% CI.
Linear Regression
  • When to use: DV numeric, IVs numeric/categorical.
  • Assumptions: linearity, independence, homoscedasticity, normal residuals, no multicollinearity.
  • R code: 
    m <- lm(y ~ x1 + x2 + factor(group), data=d)
summary(m)
car::vif(m) # multicollinearity
plot(m)     # residual diagnostics
  • Report: F, R2, coefficients (β, SE, t, p), CI.
Logistic Regression
  • When to use: DV binary; IVs numeric/categorical.
  • Assumptions: independent observations; linearity of logit for numeric IVs; no severe multicollinearity.
  • R code: 
    glm1 <- glm(y_bin ~ x1 + x2 + factor(group), data=d, family=binomial)
summary(glm1)
# Odds ratios
exp(cbind(OR = coef(glm1), confint(glm1)))
  • Report: OR with 95% CI, Wald z, p, model fit (AIC), pseudo-R2.

Nonparametric & Categorical (R)

Mann–Whitney U (Wilcoxon rank-sum)
  • When to use: DV ordinal/continuous non-normal; two independent groups.
  • R code: 
    wilcox.test(y ~ group, data=d, exact=FALSE)
# Effect size r
effsize::rank_biserial(y ~ group, data=d)
Wilcoxon Signed-Rank
  • When to use: two related measurements.
  • R code: 
    wilcox.test(d$y1, d$y2, paired=TRUE, exact=FALSE)
Chi-square Tests
  • When to use: association between two categorical variables; goodness-of-fit to expected counts.
  • R code: 
    tab <- table(d$x_cat, d$y_cat)
chisq.test(tab)           # independence
fisher.test(tab)          # small expected counts
  • Report: χ²(df) = value, p, effect size (Cramér's V).

Mean Comparisons & ANOVA (SPSS)

Independent-samples t-test
  • When to use: DV scale, one between-subjects IV with two groups.
  • Run: Analyze → Compare Means → Independent-Samples T Test. Set DV; set grouping variable and define groups.
  • Check: Analyze → Descriptive Statistics → Explore (normality, plots). Levene's Test in t-test output.
  • Read: “Independent Samples Test” table → Levene's Test row, then the appropriate t row (Equal variances assumed/not assumed).
  • Report: t(df) = value, p, Cohen's d, 95% CI.
  • Alternative: Mann–Whitney U: Analyze → Nonparametric Tests → Legacy Dialogs → 2 Independent Samples.
One-way ANOVA
  • Run: Analyze → Compare Means → One-Way ANOVA; Options → Homogeneity of variance; Post Hoc → Tukey (equal variances) or Games–Howell (unequal).
  • Read: “Test of Homogeneity of Variances”; “ANOVA”; “Multiple Comparisons”.
  • Report: F(df1, df2), p, effect size (η2/partial η2), post-hoc MD & CI.
Repeated-measures ANOVA
  • Run: Analyze → General Linear Model → Repeated Measures; define within-factor; Add; Specify; Options → Estimates of effect size, Mauchly's test; EM Means → pairwise comparisons.
  • Read: “Mauchly's Test of Sphericity”; “Tests of Within-Subjects Effects”; “Pairwise Comparisons”.
  • Report: GG-corrected F, p, partial η2, adjusted pairwise comparisons.

Associations & Regression (SPSS)

Pearson & Spearman Correlation
  • Run: Analyze → Correlate → Bivariate; select Pearson or Spearman.
  • Read: “Correlations” table: correlation coefficient, p, N.
Linear Regression
  • Run: Analyze → Regression → Linear; Statistics → Estimates, Confidence intervals, Collinearity diagnostics.
  • Read: “Model Summary” (R2), “ANOVA”, “Coefficients”.
Binary Logistic Regression
  • Run: Analyze → Regression → Binary Logistic.
  • Read: “Variables in the Equation” (B, Wald, Exp(B), CI), “Model Summary”.

Nonparametric & Categorical (SPSS)

Mann–Whitney U
  • Run: Analyze → Nonparametric Tests → Legacy Dialogs → 2 Independent Samples → Mann–Whitney U.
  • Read: “Test Statistics”.
Wilcoxon Signed-Rank
  • Run: Analyze → Nonparametric Tests → Legacy Dialogs → 2 Related Samples → Wilcoxon.
Chi-square (Independence)
  • Run: Analyze → Descriptive Statistics → Crosstabs → Statistics → Chi-square; Cells → expected counts.
  • Read: “Chi-Square Tests”; “Symmetric Measures” for Cramér's V.