Raincloud Plot: Gene Expression

Descriptive statistics

Location, spread and shape for every group — the first thing to read before choosing a test. Skewness near 0 and excess kurtosis near 0 are what a normal distribution looks like.

labtools stats describe --groups @groups.json

Normality

Three tests of the same question — could these values come from a normal distribution? Shapiro–Wilk has the best power at bench sample sizes, Anderson–Darling is more sensitive in the tails, and Kolmogorov–Smirnov (Lilliefors-corrected) is included for comparability with older papers. A significant p means normality is rejected.

labtools stats normality --groups @groups.json --method shapiro-wilk

labtools stats normality --groups @groups.json --method anderson-darling

labtools stats normality --groups @groups.json --method kolmogorov-smirnov

Equal variances

Student's t and one-way ANOVA assume every group has the same spread. LabTools' Levene test uses deviations from the group median (the Brown–Forsythe form), which stays reliable on skewed data; Bartlett's test is more powerful but only trustworthy when the data are normal. A significant p means the equal-variance assumption fails — prefer Welch's t-test or a rank-based test.

labtools stats levene --groups @groups.json --method levene

labtools stats levene --groups @groups.json --method bartlett

Outlier screen

Five detectors with different assumptions. Grubbs tests the single most extreme point, generalised ESD looks for up to several (immune to masking), Dixon's Q is the small-sample chemistry test, modified-z uses the median and MAD so needs no normality, and the IQR rule is Tukey's boxplot fence. LabTools flags points; it never deletes them.

labtools stats outliers --groups @groups.json --method grubbs

labtools stats outliers --groups @groups.json --method generalized-esd --max-outliers 5

labtools stats outliers --groups @groups.json --method modified-z

labtools stats outliers --groups @groups.json --method iqr

Confidence intervals for the mean

t-based intervals: the range of population means these data are consistent with. Report them alongside p-values — an interval shows the size of an effect, a p-value does not.

labtools stats ci --data @Control.json --conf-level 0.95

labtools stats ci --data @Drug_B.json --conf-level 0.95

Do the groups differ? (omnibus tests)

One-way ANOVA compares means and assumes normal residuals with equal variances; Kruskal–Wallis compares ranks and assumes neither. Both only say the groups differ somewhere — the pairwise table below says where.

labtools stats anova --groups @groups.json

labtools stats kruskal --groups @groups.json

Which groups differ? (pairwise, corrected)

3 comparisons (every pair), each run as a Welch t-test and a Mann–Whitney test. Testing many pairs inflates false positives, so every p-value is corrected with Holm (family-wise) and Benjamini–Hochberg (false-discovery rate) through stats.adjust.

labtools stats ttest --a @Control.json --b @Drug_A.json --test welch --no-assumption-checks

labtools stats mannwhitney --a @Control.json --b @Drug_A.json

labtools stats adjust --p-values @p_values.json --labels @labels.json --method holm

labtools stats power --n1 40 --n2 40 --mode mde --power 0.8

labtools stats power --n1 40 --n2 40 --effect-size 0.5

Methods paragraph

Written to go straight into a manuscript.

Groups were compared by Kruskal–Wallis (H = 47.6, df = 2, p < 0.0001, ε² = 0.40), followed by pairwise Mann–Whitney U tests with Holm correction; all pairs differed (adjusted p ≤ 0.007).