All examples · Example 7 of 34

Ridgeline PlotDistributionStatistical report

Ridgeline Plot: Cell Size over Time

Distribution of cell area (µm²) at eight time points after stimulation (n = 300 cells per time point).

Key findings

Mean cell area grows from 108.7 µm² at 0 h to 184.2 µm² at 48 h (Kruskal–Wallis p = 2.0 × 10⁻¹⁰⁸).
Every time point is right-skewed (skewness 0.37–1.1), which is why ridgelines — whole distributions — are the right display.
Against baseline, the first time point to differ after Holm correction is 2 h.

42 LabTools stats calls

11 of 15 stats methods

LabTools 0.14.3

600 dpi PNG Data (CSV) Raw LabTools output

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.

Group	n	Mean	SD	SEM	Median	Q1 – Q3	Min – Max	Skewness	Excess kurtosis
0 h	300	108.7	37.19	2.147	102.9	83.5 – 128	38.2 – 257.5	1.06	1.67
2 h	300	118.6	38.26	2.209	112.3	92.08 – 141.6	38 – 258.9	0.654	0.505
4 h	300	124.2	39.53	2.282	118.4	96.17 – 149.6	40.3 – 282.5	0.675	0.716
8 h	300	135.6	43.87	2.533	133.7	103.9 – 160.2	34.6 – 288.7	0.575	0.39
12 h	300	146.2	47.16	2.723	141.3	112.8 – 175.7	57.2 – 295.4	0.615	0.119
24 h	300	153.8	54.39	3.14	149.8	113.7 – 179.6	56 – 350.3	0.803	0.903
36 h	300	171.4	54.07	3.122	166.4	130.4 – 203.9	64.8 – 351.1	0.539	0.0485
48 h	300	184.2	54.7	3.158	181	144.8 – 221.1	46.5 – 404.4	0.365	0.0987

LabTools call

stats.describe

labtools stats describe --groups @groups.json

The same method is available as an MCP tool (stats_describe) and from the desktop app's statistics panel.

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.

Group	n	Shapiro–Wilk W	p	Anderson–Darling A²	p	K–S D	p	Verdict
0 h	300	0.9412	1.5 × 10⁻⁹	4	5.6 × 10⁻¹⁰	0.097	3.5 × 10⁻⁷	Normality rejected
2 h	300	0.9739	2.8 × 10⁻⁵	1.859	9.3 × 10⁻⁵	0.06977	0.001	Normality rejected
4 h	300	0.973	2.0 × 10⁻⁵	1.445	0.0010	0.06278	0.006	Normality rejected
8 h	300	0.9764	7.4 × 10⁻⁵	1.526	0.0006	0.04687	0.11	Normality rejected
12 h	300	0.9721	1.5 × 10⁻⁵	2.003	4.1 × 10⁻⁵	0.06554	0.003	Normality rejected
24 h	300	0.9595	2.1 × 10⁻⁷	2.545	1.9 × 10⁻⁶	0.07703	0.0002	Normality rejected
36 h	300	0.9781	0.0002	1.598	0.0004	0.05998	0.011	Normality rejected
48 h	300	0.9869	0.008	0.8862	0.023	0.05834	0.015	Normality rejected

LabTools calls (3)

stats.normality

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

stats.normality

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

stats.normality

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

The same method is available as an MCP tool (stats_normality) and from the desktop app's statistics panel.

LabTools notes

Group '0 h' rejects normality (p = 0.0000); prefer a rank-based test.
Group '12 h' rejects normality (p = 0.0000); prefer a rank-based test.
Group '2 h' rejects normality (p = 0.0000); prefer a rank-based test.
Group '24 h' rejects normality (p = 0.0000); prefer a rank-based test.
Group '36 h' rejects normality (p = 0.0002); prefer a rank-based test.
Group '4 h' rejects normality (p = 0.0000); prefer a rank-based test.
Group '48 h' rejects normality (p = 0.0078); prefer a rank-based test.
Group '8 h' rejects normality (p = 0.0001); prefer a rank-based test.
Group '2 h' rejects normality (p = 0.0001); prefer a rank-based test.
Group '36 h' rejects normality (p = 0.0004); prefer a rank-based test.
Group '4 h' rejects normality (p = 0.0010); prefer a rank-based test.
Group '48 h' rejects normality (p = 0.0232); prefer a rank-based test.
Group '8 h' rejects normality (p = 0.0006); prefer a rank-based test.
Group '12 h' rejects normality (p = 0.0034); prefer a rank-based test.
Group '2 h' rejects normality (p = 0.0013); prefer a rank-based test.
Group '24 h' rejects normality (p = 0.0002); prefer a rank-based test.
Group '36 h' rejects normality (p = 0.0112); prefer a rank-based test.
Group '4 h' rejects normality (p = 0.0062); prefer a rank-based test.
Group '48 h' rejects normality (p = 0.0154); prefer a rank-based test.

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.

Test	Statistic	p	Largest / smallest variance	Verdict
Levene (Brown–Forsythe, median-centred)	14.26	3.0 × 10⁻¹⁸	2.16	Variances differ
Bartlett	111	5.6 × 10⁻²¹	2.16	Variances differ

LabTools calls (2)

stats.levene

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

stats.levene

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

The same method is available as an MCP tool (stats_levene) and from the desktop app's statistics panel.

LabTools notes

Variances differ: use Welch's t-test (stats.ttest default) or stats.kruskal rather than the pooled-variance alternatives.
Bartlett's test assumes normality and is badly inflated when that fails — confirm with stats.normality, or use method='levene'.

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.

Method	0 h	2 h	4 h	8 h	12 h	24 h	36 h	48 h
Grubbs	1 (257.5)	none	1 (282.5)	none	none	none	none	1 (404.4)
Generalised ESD	2 (257.5, 248.4)	none	1 (282.5)	none	none	none	none	1 (404.4)
Modified z (MAD)	5 (257.5, 228.2, 218.3, 238.6 …)	2 (254.8, 258.9)	1 (282.5)	1 (288.7)	none	3 (322.8, 350.3, 343.2)	none	1 (404.4)
IQR fences (1.5×)	11 (257.5, 228.2, 207, 195.7 …)	5 (219, 254.8, 223.5, 218.3 …)	5 (282.5, 234.6, 235.8, 242.4 …)	5 (258.3, 288.7, 252.9, 269.1 …)	4 (282.4, 280.7, 294.6, 295.4)	11 (285.8, 304.4, 283.5, 279.8 …)	3 (351.1, 315.4, 341.1)	1 (404.4)

LabTools calls (4)

stats.outliers

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

stats.outliers

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

stats.outliers

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

stats.outliers

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

The same method is available as an MCP tool (stats_outliers) and from the desktop app's statistics panel.

LabTools notes

Flagged points are candidates, not verdicts, and nothing has been removed. Look for a physical cause before excluding anything; if there is none, keep the point and use a robust test instead. Any exclusion must be reported.
Grubbs tests only the single most extreme point, so a second outlier can mask the first. On larger samples use method='generalized_esd'.
The IQR rule is descriptive — it has no p-value and flags roughly 0.7% of a perfectly normal sample by construction.

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.

Group	n	Mean	95% CI
0 h	300	108.7	[104.5, 112.9]
2 h	300	118.6	[114.3, 122.9]
4 h	300	124.2	[119.8, 128.7]
8 h	300	135.6	[130.6, 140.6]
12 h	300	146.2	[140.8, 151.5]
24 h	300	153.8	[147.6, 160]
36 h	300	171.4	[165.3, 177.6]
48 h	300	184.2	[178, 190.4]

LabTools calls (2)

stats.ci

labtools stats ci --data @0_h.json --conf-level 0.95

stats.ci

labtools stats ci --data @48_h.json --conf-level 0.95

The same method is available as an MCP tool (stats_ci) and from the desktop app's statistics panel.

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.

Test	Statistic	df	p	Effect size
One-way ANOVA	F = 94.6	7, 2,392	3.7 × 10⁻¹²²	ω² = 0.214 · η² = 0.217 · Cohen's f = 0.526
Kruskal–Wallis H	H = 521.4	7	2.0 × 10⁻¹⁰⁸	ε² = 0.217

LabTools calls (2)

stats.anova

labtools stats anova --groups @groups.json

stats.kruskal

labtools stats kruskal --groups @groups.json

The same method is available as an MCP tool (stats_anova) and from the desktop app's statistics panel.

LabTools notes

Group '0 h' departs from normality (Shapiro–Wilk W = 0.9412, p = 0.0000 < 0.05). Consider stats.kruskal.
Group '12 h' departs from normality (Shapiro–Wilk W = 0.9721, p = 0.0000 < 0.05). Consider stats.kruskal.
Group '2 h' departs from normality (Shapiro–Wilk W = 0.9739, p = 0.0000 < 0.05). Consider stats.kruskal.
Group '24 h' departs from normality (Shapiro–Wilk W = 0.9595, p = 0.0000 < 0.05). Consider stats.kruskal.
Group '36 h' departs from normality (Shapiro–Wilk W = 0.9781, p = 0.0002 < 0.05). Consider stats.kruskal.
Group '4 h' departs from normality (Shapiro–Wilk W = 0.9730, p = 0.0000 < 0.05). Consider stats.kruskal.
Group '48 h' departs from normality (Shapiro–Wilk W = 0.9869, p = 0.0078 < 0.05). Consider stats.kruskal.
Group '8 h' departs from normality (Shapiro–Wilk W = 0.9764, p = 0.0001 < 0.05). Consider stats.kruskal.
Group variances are unequal (Levene W = 14.2577, p = 0.0000 < 0.05); the equal-variance assumption of this test is violated. Use the Welch variant instead.

Which groups differ? (pairwise, corrected)

7 comparisons (each group against 0 h), 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.

Comparison	Mean diff.	95% CI	Hedges' g	Welch p	Holm	BH	Mann–Whitney p	Holm	Cliff's δ
0 h vs 2 h	-9.905	[-15.95, -3.855]	-0.262	0.001	0.001	0.001	0.0004	0.0004	-0.167
0 h vs 4 h	-15.55	[-21.7, -9.397]	-0.405	9.1 × 10⁻⁷	1.8 × 10⁻⁶	1.1 × 10⁻⁶	1.5 × 10⁻⁷	3.0 × 10⁻⁷	-0.248
0 h vs 8 h	-26.89	[-33.41, -20.36]	-0.66	3.3 × 10⁻¹⁵	1.0 × 10⁻¹⁴	4.6 × 10⁻¹⁵	6.9 × 10⁻¹⁶	2.1 × 10⁻¹⁵	-0.381
0 h vs 12 h	-37.46	[-44.27, -30.65]	-0.881	7.3 × 10⁻²⁵	2.9 × 10⁻²⁴	1.3 × 10⁻²⁴	1.8 × 10⁻²⁴	7.1 × 10⁻²⁴	-0.482
0 h vs 24 h	-45.07	[-52.55, -37.6]	-0.966	6.9 × 10⁻²⁹	3.5 × 10⁻²⁸	1.6 × 10⁻²⁸	9.3 × 10⁻²⁹	4.7 × 10⁻²⁸	-0.525
0 h vs 36 h	-62.73	[-70.17, -55.29]	-1.35	6.2 × 10⁻⁵⁰	3.7 × 10⁻⁴⁹	2.2 × 10⁻⁴⁹	4.4 × 10⁻⁴⁷	2.7 × 10⁻⁴⁶	-0.68
0 h vs 48 h	-75.5	[-83, -68]	-1.61	1.7 × 10⁻⁶⁵	1.2 × 10⁻⁶⁴	1.2 × 10⁻⁶⁴	2.9 × 10⁻⁵⁸	2.0 × 10⁻⁵⁷	-0.759

LabTools calls (3)

stats.ttest

labtools stats ttest --a @0_h.json --b @2_h.json --test welch --no-assumption-checks

stats.mannwhitney

labtools stats mannwhitney --a @0_h.json --b @2_h.json

stats.adjust

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

The same method is available as an MCP tool (stats_ttest) and from the desktop app's statistics panel.

Design sensitivity

d = 0.229

Minimum detectable effect (80% power, α = 0.05)

n = 300 vs 300

100.0%

Power to detect d = 0.5

100.0%

Power to detect d = 0.8

100.0%

Power to detect d = 1.2

LabTools calls (2)

stats.power

labtools stats power --n1 300 --n2 300 --mode mde --power 0.8

stats.power

labtools stats power --n1 300 --n2 300 --effect-size 0.5

The same method is available as an MCP tool (stats_power) and from the desktop app's statistics panel.

Methods paragraph

Written to go straight into a manuscript.

Descriptive statistics per time point: median cell area rose from 102.9 µm² (0 h) to 181.0 µm² (48 h), with right-skewed distributions throughout.

Every number on this page was computed by the LabTools statistics engine (version 0.14.3) from the example's CSV on 2026-09-23. Where a value was derived before the data reached LabTools (replicate means, paired differences, log odds ratios), the text says so. The data are simulated from a fixed random seed.

Get started

Run the same analysis on your data

Every test on this page is built into LabTools — from the statistics panel, the command line, or an AI assistant through MCP.

Download free More examples

LabToolsThe Research Infrastructure

Download

All examples · Example 7 of 34

Ridgeline PlotDistributionStatistical report

Ridgeline Plot: Cell Size over Time

Distribution of cell area (µm²) at eight time points after stimulation (n = 300 cells per time point).

Key findings

Mean cell area grows from 108.7 µm² at 0 h to 184.2 µm² at 48 h (Kruskal–Wallis p = 2.0 × 10⁻¹⁰⁸).
Every time point is right-skewed (skewness 0.37–1.1), which is why ridgelines — whole distributions — are the right display.
Against baseline, the first time point to differ after Holm correction is 2 h.

42 LabTools stats calls

11 of 15 stats methods

LabTools 0.14.3

600 dpi PNG Data (CSV) Raw LabTools output

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.

Group	n	Mean	SD	SEM	Median	Q1 – Q3	Min – Max	Skewness	Excess kurtosis
0 h	300	108.7	37.19	2.147	102.9	83.5 – 128	38.2 – 257.5	1.06	1.67
2 h	300	118.6	38.26	2.209	112.3	92.08 – 141.6	38 – 258.9	0.654	0.505
4 h	300	124.2	39.53	2.282	118.4	96.17 – 149.6	40.3 – 282.5	0.675	0.716
8 h	300	135.6	43.87	2.533	133.7	103.9 – 160.2	34.6 – 288.7	0.575	0.39
12 h	300	146.2	47.16	2.723	141.3	112.8 – 175.7	57.2 – 295.4	0.615	0.119
24 h	300	153.8	54.39	3.14	149.8	113.7 – 179.6	56 – 350.3	0.803	0.903
36 h	300	171.4	54.07	3.122	166.4	130.4 – 203.9	64.8 – 351.1	0.539	0.0485
48 h	300	184.2	54.7	3.158	181	144.8 – 221.1	46.5 – 404.4	0.365	0.0987

LabTools call

stats.describe

labtools stats describe --groups @groups.json

The same method is available as an MCP tool (stats_describe) and from the desktop app's statistics panel.

Normality

Group	n	Shapiro–Wilk W	p	Anderson–Darling A²	p	K–S D	p	Verdict
0 h	300	0.9412	1.5 × 10⁻⁹	4	5.6 × 10⁻¹⁰	0.097	3.5 × 10⁻⁷	Normality rejected
2 h	300	0.9739	2.8 × 10⁻⁵	1.859	9.3 × 10⁻⁵	0.06977	0.001	Normality rejected
4 h	300	0.973	2.0 × 10⁻⁵	1.445	0.0010	0.06278	0.006	Normality rejected
8 h	300	0.9764	7.4 × 10⁻⁵	1.526	0.0006	0.04687	0.11	Normality rejected
12 h	300	0.9721	1.5 × 10⁻⁵	2.003	4.1 × 10⁻⁵	0.06554	0.003	Normality rejected
24 h	300	0.9595	2.1 × 10⁻⁷	2.545	1.9 × 10⁻⁶	0.07703	0.0002	Normality rejected
36 h	300	0.9781	0.0002	1.598	0.0004	0.05998	0.011	Normality rejected
48 h	300	0.9869	0.008	0.8862	0.023	0.05834	0.015	Normality rejected

LabTools calls (3)

stats.normality

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

stats.normality

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

stats.normality

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

The same method is available as an MCP tool (stats_normality) and from the desktop app's statistics panel.

LabTools notes

Group '0 h' rejects normality (p = 0.0000); prefer a rank-based test.
Group '12 h' rejects normality (p = 0.0000); prefer a rank-based test.
Group '2 h' rejects normality (p = 0.0000); prefer a rank-based test.
Group '24 h' rejects normality (p = 0.0000); prefer a rank-based test.
Group '36 h' rejects normality (p = 0.0002); prefer a rank-based test.
Group '4 h' rejects normality (p = 0.0000); prefer a rank-based test.
Group '48 h' rejects normality (p = 0.0078); prefer a rank-based test.
Group '8 h' rejects normality (p = 0.0001); prefer a rank-based test.
Group '2 h' rejects normality (p = 0.0001); prefer a rank-based test.
Group '36 h' rejects normality (p = 0.0004); prefer a rank-based test.
Group '4 h' rejects normality (p = 0.0010); prefer a rank-based test.
Group '48 h' rejects normality (p = 0.0232); prefer a rank-based test.
Group '8 h' rejects normality (p = 0.0006); prefer a rank-based test.
Group '12 h' rejects normality (p = 0.0034); prefer a rank-based test.
Group '2 h' rejects normality (p = 0.0013); prefer a rank-based test.
Group '24 h' rejects normality (p = 0.0002); prefer a rank-based test.
Group '36 h' rejects normality (p = 0.0112); prefer a rank-based test.
Group '4 h' rejects normality (p = 0.0062); prefer a rank-based test.
Group '48 h' rejects normality (p = 0.0154); prefer a rank-based test.

Equal variances

Test	Statistic	p	Largest / smallest variance	Verdict
Levene (Brown–Forsythe, median-centred)	14.26	3.0 × 10⁻¹⁸	2.16	Variances differ
Bartlett	111	5.6 × 10⁻²¹	2.16	Variances differ

LabTools calls (2)

stats.levene

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

stats.levene

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

The same method is available as an MCP tool (stats_levene) and from the desktop app's statistics panel.

LabTools notes

Variances differ: use Welch's t-test (stats.ttest default) or stats.kruskal rather than the pooled-variance alternatives.
Bartlett's test assumes normality and is badly inflated when that fails — confirm with stats.normality, or use method='levene'.

Outlier screen

Method	0 h	2 h	4 h	8 h	12 h	24 h	36 h	48 h
Grubbs	1 (257.5)	none	1 (282.5)	none	none	none	none	1 (404.4)
Generalised ESD	2 (257.5, 248.4)	none	1 (282.5)	none	none	none	none	1 (404.4)
Modified z (MAD)	5 (257.5, 228.2, 218.3, 238.6 …)	2 (254.8, 258.9)	1 (282.5)	1 (288.7)	none	3 (322.8, 350.3, 343.2)	none	1 (404.4)
IQR fences (1.5×)	11 (257.5, 228.2, 207, 195.7 …)	5 (219, 254.8, 223.5, 218.3 …)	5 (282.5, 234.6, 235.8, 242.4 …)	5 (258.3, 288.7, 252.9, 269.1 …)	4 (282.4, 280.7, 294.6, 295.4)	11 (285.8, 304.4, 283.5, 279.8 …)	3 (351.1, 315.4, 341.1)	1 (404.4)

LabTools calls (4)

stats.outliers

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

stats.outliers

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

stats.outliers

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

stats.outliers

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

The same method is available as an MCP tool (stats_outliers) and from the desktop app's statistics panel.

LabTools notes

Flagged points are candidates, not verdicts, and nothing has been removed. Look for a physical cause before excluding anything; if there is none, keep the point and use a robust test instead. Any exclusion must be reported.
Grubbs tests only the single most extreme point, so a second outlier can mask the first. On larger samples use method='generalized_esd'.
The IQR rule is descriptive — it has no p-value and flags roughly 0.7% of a perfectly normal sample by construction.

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.

Group	n	Mean	95% CI
0 h	300	108.7	[104.5, 112.9]
2 h	300	118.6	[114.3, 122.9]
4 h	300	124.2	[119.8, 128.7]
8 h	300	135.6	[130.6, 140.6]
12 h	300	146.2	[140.8, 151.5]
24 h	300	153.8	[147.6, 160]
36 h	300	171.4	[165.3, 177.6]
48 h	300	184.2	[178, 190.4]

LabTools calls (2)

stats.ci

labtools stats ci --data @0_h.json --conf-level 0.95

stats.ci

labtools stats ci --data @48_h.json --conf-level 0.95

The same method is available as an MCP tool (stats_ci) and from the desktop app's statistics panel.

Do the groups differ? (omnibus tests)

Test	Statistic	df	p	Effect size
One-way ANOVA	F = 94.6	7, 2,392	3.7 × 10⁻¹²²	ω² = 0.214 · η² = 0.217 · Cohen's f = 0.526
Kruskal–Wallis H	H = 521.4	7	2.0 × 10⁻¹⁰⁸	ε² = 0.217

LabTools calls (2)

stats.anova

labtools stats anova --groups @groups.json

stats.kruskal

labtools stats kruskal --groups @groups.json

The same method is available as an MCP tool (stats_anova) and from the desktop app's statistics panel.

LabTools notes

Group '0 h' departs from normality (Shapiro–Wilk W = 0.9412, p = 0.0000 < 0.05). Consider stats.kruskal.
Group '12 h' departs from normality (Shapiro–Wilk W = 0.9721, p = 0.0000 < 0.05). Consider stats.kruskal.
Group '2 h' departs from normality (Shapiro–Wilk W = 0.9739, p = 0.0000 < 0.05). Consider stats.kruskal.
Group '24 h' departs from normality (Shapiro–Wilk W = 0.9595, p = 0.0000 < 0.05). Consider stats.kruskal.
Group '36 h' departs from normality (Shapiro–Wilk W = 0.9781, p = 0.0002 < 0.05). Consider stats.kruskal.
Group '4 h' departs from normality (Shapiro–Wilk W = 0.9730, p = 0.0000 < 0.05). Consider stats.kruskal.
Group '48 h' departs from normality (Shapiro–Wilk W = 0.9869, p = 0.0078 < 0.05). Consider stats.kruskal.
Group '8 h' departs from normality (Shapiro–Wilk W = 0.9764, p = 0.0001 < 0.05). Consider stats.kruskal.
Group variances are unequal (Levene W = 14.2577, p = 0.0000 < 0.05); the equal-variance assumption of this test is violated. Use the Welch variant instead.

Which groups differ? (pairwise, corrected)

Comparison	Mean diff.	95% CI	Hedges' g	Welch p	Holm	BH	Mann–Whitney p	Holm	Cliff's δ
0 h vs 2 h	-9.905	[-15.95, -3.855]	-0.262	0.001	0.001	0.001	0.0004	0.0004	-0.167
0 h vs 4 h	-15.55	[-21.7, -9.397]	-0.405	9.1 × 10⁻⁷	1.8 × 10⁻⁶	1.1 × 10⁻⁶	1.5 × 10⁻⁷	3.0 × 10⁻⁷	-0.248
0 h vs 8 h	-26.89	[-33.41, -20.36]	-0.66	3.3 × 10⁻¹⁵	1.0 × 10⁻¹⁴	4.6 × 10⁻¹⁵	6.9 × 10⁻¹⁶	2.1 × 10⁻¹⁵	-0.381
0 h vs 12 h	-37.46	[-44.27, -30.65]	-0.881	7.3 × 10⁻²⁵	2.9 × 10⁻²⁴	1.3 × 10⁻²⁴	1.8 × 10⁻²⁴	7.1 × 10⁻²⁴	-0.482
0 h vs 24 h	-45.07	[-52.55, -37.6]	-0.966	6.9 × 10⁻²⁹	3.5 × 10⁻²⁸	1.6 × 10⁻²⁸	9.3 × 10⁻²⁹	4.7 × 10⁻²⁸	-0.525
0 h vs 36 h	-62.73	[-70.17, -55.29]	-1.35	6.2 × 10⁻⁵⁰	3.7 × 10⁻⁴⁹	2.2 × 10⁻⁴⁹	4.4 × 10⁻⁴⁷	2.7 × 10⁻⁴⁶	-0.68
0 h vs 48 h	-75.5	[-83, -68]	-1.61	1.7 × 10⁻⁶⁵	1.2 × 10⁻⁶⁴	1.2 × 10⁻⁶⁴	2.9 × 10⁻⁵⁸	2.0 × 10⁻⁵⁷	-0.759

LabTools calls (3)

stats.ttest

labtools stats ttest --a @0_h.json --b @2_h.json --test welch --no-assumption-checks

stats.mannwhitney

labtools stats mannwhitney --a @0_h.json --b @2_h.json

stats.adjust

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

The same method is available as an MCP tool (stats_ttest) and from the desktop app's statistics panel.

Design sensitivity

d = 0.229

Minimum detectable effect (80% power, α = 0.05)

n = 300 vs 300

100.0%

Power to detect d = 0.5

100.0%

Power to detect d = 0.8

100.0%

Power to detect d = 1.2

LabTools calls (2)

stats.power

labtools stats power --n1 300 --n2 300 --mode mde --power 0.8

stats.power

labtools stats power --n1 300 --n2 300 --effect-size 0.5

The same method is available as an MCP tool (stats_power) and from the desktop app's statistics panel.

Methods paragraph

Written to go straight into a manuscript.

Descriptive statistics per time point: median cell area rose from 102.9 µm² (0 h) to 181.0 µm² (48 h), with right-skewed distributions throughout.

Get started

Run the same analysis on your data

Every test on this page is built into LabTools — from the statistics panel, the command line, or an AI assistant through MCP.

Download free More examples