Box Plot: Western Blot Quantification

Design: why n = 3, not 12

Each condition has 3 biological replicates, each run as 4 technical lanes. Technical lanes are not independent — they share a lysate — so testing all 12 lanes as if they were would be pseudoreplication and would inflate every p-value. The lanes are averaged within each biological replicate (a mean computed here, before the data reach LabTools) and the tests below run on those n = 3 means per condition.

All lanes (descriptive only)

Per-condition summary of all 12 lanes. Useful for spotting a bad lane; not the unit of analysis.

labtools stats describe --groups @groups.json

Lane-level 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 dixon-q

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

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

Biological-replicate means (the unit of analysis)

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

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

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)

6 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 @Treated.json --test welch --no-assumption-checks

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

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

labtools stats power --n1 3 --n2 3 --mode mde --power 0.8

labtools stats power --n1 3 --n2 3 --effect-size 0.5

Methods paragraph

Written to go straight into a manuscript.

To avoid pseudoreplication, technical replicates were averaged within each biological replicate and conditions compared by Welch’s t-test on the replicate means (n = 3); p-values were adjusted by Benjamini–Hochberg. Treatment increased band intensity 2.0-fold (p_adj = 0.005), and the inhibitor partially reversed it (p_adj = 0.025).