Differential analysis & tests / Box plot with group tests
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Each group is drawn as a box (or violin, raincloud or bean): the box spans the interquartile range, the line is the median and whiskers reach the most extreme values within 1.5 × IQR; points are the raw data.
With more than two groups an overall test checks whether any group differs; pairwise P values are then adjusted for multiple testing with the method you choose, and the figure shows adjusted P (stars: * < 0.05, ** < 0.01, *** < 0.001, **** < 0.0001, ns = not significant).
Compact letters: groups sharing a letter do not differ significantly; groups with no letter in common do. Letters follow group medians (rank-sum test) or means (t-tests) from highest to lowest, so “a” marks the highest group.
Use the rank-sum test for skewed data or small samples; t-tests suit roughly normal data (Welch’s version does not assume equal variances). “Each group vs a reference” makes fewer comparisons, so the correction is milder.
Kruskal & Wallis (1952) J Am Stat Assoc 47:583; Mann & Whitney (1947) Ann Math Stat 18:50; Welch (1947) Biometrika 34:28; compact letters: Piepho (2004) J Comput Graph Stat 13:456. Statistics match scipy.stats (kruskal, f_oneway, mannwhitneyu, ttest_ind); adjustment matches R p.adjust.
Up to 100,000 rows; the number of pairwise comparisons grows with the square of the number of groups.
Send us your data and research question and you will receive a written plan within 1 working day: analysis steps, parameter rationale, deliverables and timeline. Quoted per project.