Statistical Comparisons
Automatic test selection
AnnealIQ selects the appropriate statistical test based on your experimental design. The selection reasoning is displayed alongside every result so you can verify the choice.
Two-group comparisons
Welch’s t-test is used by default for two-group comparisons. It does not assume equal variance — the safer choice for biological data. If the normality assumption fails (Shapiro-Wilk test), AnnealIQ switches to the Mann-Whitney U non-parametric alternative and explains why.
Effect size is reported as Cohen’s d.
Multi-group comparisons
One-way ANOVA with Tukey HSD post-hoc is used for three or more groups. If normality fails, Kruskal-Wallis is used instead.
Effect size is reported as eta-squared (η²).
Two-way ANOVA with interaction
For experiments with two independent variables (e.g., treatment × genotype), AnnealIQ offers two-way factorial ANOVA. The AI detects factorial designs from group names like "WT_Control", "WT_Treated", "KO_Control", "KO_Treated".
A factor confirmation card shows detected factors, their levels, and cell sizes. If any cell has fewer than 4 biological replicates, a power warning appears. You can confirm, swap which variable is Factor A vs. Factor B, or reject to one-way ANOVA.
Results include: Type III sum of squares, F-statistics, p-values, and partial eta-squared for Factor A, Factor B, and the A:B interaction. Assumption tests (Shapiro-Wilk on residuals, Levene’s for variance homogeneity) are included.
An interaction plot renders with Factor A on the x-axis and Factor B levels as line colors. If the interaction is significant, Tukey HSD post-hoc comparisons auto-expand. The AI uses "depends on" language for interaction interpretation — never "causes".
If residuals fail the normality test, AnnealIQ falls back to the Scheirer-Ray-Hare non-parametric test and explains the practical difference.
Normality testing
For samples of n ≤ 50, AnnealIQ uses the true Shapiro-Wilk test with contextual attribution ("Shapiro-Wilk normality test, appropriate for n = N samples"). For n > 50, it falls back to the Jarque-Bera test.
P-value formatting
All p-values follow APA 7th edition formatting: no leading zero, asterisk notation (* < .05, < .01, * < .001). P-values below .001 are reported as "< .001".