All examples · Example 6 of 34

Strip PlotDistributionStatistical report

Strip Plot: qPCR ΔCt per Animal

ΔCt (target − GAPDH) for each animal in four treatment groups (n = 8 per group); lower ΔCt means higher target expression.

Key findings

One-way ANOVA F = 67.11, p = 6.7 × 10⁻¹³, ω² = 0.861: dose explains most of the variation in ΔCt.
With n = 8 animals per group the minimum detectable effect is d = 1.51 at 80% power; every observed contrast is larger than that.
6 of 6 pairwise contrasts survive Holm correction.

37 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
Vehicle	8	6.125	0.4818	0.1703	6.225	5.893 – 6.5	5.16 – 6.62	-1.18	1.34
Low dose	8	5.081	0.467	0.1651	5.085	4.86 – 5.418	4.3 – 5.67	-0.412	-0.493
Mid dose	8	4.026	0.2902	0.1026	4.03	3.947 – 4.105	3.51 – 4.53	-0.0705	1.75
High dose	8	3.318	0.43	0.152	3.305	3.11 – 3.643	2.69 – 3.85	-0.288	-1.1

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
Vehicle	8	0.8984	0.28	0.3637	0.34	0.1704	0.71	Consistent with normal
Low dose	8	0.9606	0.82	0.1876	0.86	0.1312	0.95	Consistent with normal
Mid dose	8	0.9491	0.70	0.3383	0.40	0.1901	0.54	Consistent with normal
High dose	8	0.931	0.53	0.2561	0.62	0.1603	0.79	Consistent with normal

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 'High dose' has n = 8; normality screening has very low power at this size, so a non-significant Shapiro–Wilk is weak evidence of normality.
Group 'Low dose' has n = 8; normality screening has very low power at this size, so a non-significant Shapiro–Wilk is weak evidence of normality.
Group 'Mid dose' has n = 8; normality screening has very low power at this size, so a non-significant Shapiro–Wilk is weak evidence of normality.
Group 'Vehicle' has n = 8; normality screening has very low power at this size, so a non-significant Shapiro–Wilk is weak evidence of normality.

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)	0.7357	0.54	2.76	Homogeneous
Bartlett	1.869	0.60	2.76	Homogeneous

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

Group 'High dose' has n = 8; normality screening has very low power at this size, so a non-significant Shapiro–Wilk is weak evidence of normality.
Group 'Low dose' has n = 8; normality screening has very low power at this size, so a non-significant Shapiro–Wilk is weak evidence of normality.
Group 'Mid dose' has n = 8; normality screening has very low power at this size, so a non-significant Shapiro–Wilk is weak evidence of normality.
Group 'Vehicle' has n = 8; normality screening has very low power at this size, so a non-significant Shapiro–Wilk is weak evidence of normality.
Non-significant. This test has low power on small samples, so treat this as 'no evidence against equal variances', not as evidence for them.
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	Vehicle	Low dose	Mid dose	High dose
Grubbs	none	none	none	none
Generalised ESD	none	none	none	none
Dixon's Q	none	none	none	none
Modified z (MAD)	none	none	none	none
IQR fences (1.5×)	none	none	2 (3.51, 4.53)	none

LabTools calls (5)

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 dixon-q

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.
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
Vehicle	8	6.125	[5.722, 6.528]
Low dose	8	5.081	[4.691, 5.472]
Mid dose	8	4.026	[3.784, 4.269]
High dose	8	3.318	[2.958, 3.677]

LabTools calls (2)

stats.ci

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

stats.ci

labtools stats ci --data @High_dose.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 = 67.11	3, 28	6.7 × 10⁻¹³	ω² = 0.861 · η² = 0.878 · Cohen's f = 2.68
Kruskal–Wallis H	H = 27.78	3	4.0 × 10⁻⁶	ε² = 0.896

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 'High dose' has n = 8; normality screening has very low power at this size, so a non-significant Shapiro–Wilk is weak evidence of normality.

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.

Comparison	Mean diff.	95% CI	Hedges' g	Welch p	Holm	BH	Mann–Whitney p	Holm	Cliff's δ
Vehicle vs Low dose	1.044	[0.5349, 1.553]	2.08	0.0006	0.001	0.0007	0.003	0.006	0.906
Vehicle vs Mid dose	2.099	[1.663, 2.534]	4.99	2.9 × 10⁻⁷	1.5 × 10⁻⁶	8.8 × 10⁻⁷	0.0009	0.006	1
Vehicle vs High dose	2.807	[2.317, 3.298]	5.81	7.9 × 10⁻⁹	4.7 × 10⁻⁸	4.7 × 10⁻⁸	0.0009	0.006	1
Low dose vs Mid dose	1.055	[0.6303, 1.48]	2.57	0.0002	0.0005	0.0003	0.001	0.006	0.969
Low dose vs High dose	1.764	[1.282, 2.245]	3.71	1.8 × 10⁻⁶	7.0 × 10⁻⁶	3.5 × 10⁻⁶	0.0009	0.006	1
Mid dose vs High dose	0.7088	[0.3101, 1.107]	1.83	0.002	0.002	0.002	0.003	0.006	0.891

LabTools calls (3)

stats.ttest

labtools stats ttest --a @Vehicle.json --b @Low_dose.json --test welch --no-assumption-checks

stats.mannwhitney

labtools stats mannwhitney --a @Vehicle.json --b @Low_dose.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 = 1.51

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

n = 8 vs 8

15.4%

Power to detect d = 0.5

32.0%

Power to detect d = 0.8

60.8%

Power to detect d = 1.2

LabTools calls (2)

stats.power

labtools stats power --n1 8 --n2 8 --mode mde --power 0.8

stats.power

labtools stats power --n1 8 --n2 8 --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.

Groups were compared by one-way ANOVA (F(3,28) = 67.1, p < 0.0001, ω² = 0.86); variances were homogeneous (Levene p = 0.54).

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.

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All examples · Example 6 of 34

Strip PlotDistributionStatistical report

Strip Plot: qPCR ΔCt per Animal

ΔCt (target − GAPDH) for each animal in four treatment groups (n = 8 per group); lower ΔCt means higher target expression.

Key findings

One-way ANOVA F = 67.11, p = 6.7 × 10⁻¹³, ω² = 0.861: dose explains most of the variation in ΔCt.
With n = 8 animals per group the minimum detectable effect is d = 1.51 at 80% power; every observed contrast is larger than that.
6 of 6 pairwise contrasts survive Holm correction.

37 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
Vehicle	8	6.125	0.4818	0.1703	6.225	5.893 – 6.5	5.16 – 6.62	-1.18	1.34
Low dose	8	5.081	0.467	0.1651	5.085	4.86 – 5.418	4.3 – 5.67	-0.412	-0.493
Mid dose	8	4.026	0.2902	0.1026	4.03	3.947 – 4.105	3.51 – 4.53	-0.0705	1.75
High dose	8	3.318	0.43	0.152	3.305	3.11 – 3.643	2.69 – 3.85	-0.288	-1.1

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
Vehicle	8	0.8984	0.28	0.3637	0.34	0.1704	0.71	Consistent with normal
Low dose	8	0.9606	0.82	0.1876	0.86	0.1312	0.95	Consistent with normal
Mid dose	8	0.9491	0.70	0.3383	0.40	0.1901	0.54	Consistent with normal
High dose	8	0.931	0.53	0.2561	0.62	0.1603	0.79	Consistent with normal

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 'High dose' has n = 8; normality screening has very low power at this size, so a non-significant Shapiro–Wilk is weak evidence of normality.
Group 'Low dose' has n = 8; normality screening has very low power at this size, so a non-significant Shapiro–Wilk is weak evidence of normality.
Group 'Mid dose' has n = 8; normality screening has very low power at this size, so a non-significant Shapiro–Wilk is weak evidence of normality.
Group 'Vehicle' has n = 8; normality screening has very low power at this size, so a non-significant Shapiro–Wilk is weak evidence of normality.

Equal variances

Test	Statistic	p	Largest / smallest variance	Verdict
Levene (Brown–Forsythe, median-centred)	0.7357	0.54	2.76	Homogeneous
Bartlett	1.869	0.60	2.76	Homogeneous

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

Group 'High dose' has n = 8; normality screening has very low power at this size, so a non-significant Shapiro–Wilk is weak evidence of normality.
Group 'Low dose' has n = 8; normality screening has very low power at this size, so a non-significant Shapiro–Wilk is weak evidence of normality.
Group 'Mid dose' has n = 8; normality screening has very low power at this size, so a non-significant Shapiro–Wilk is weak evidence of normality.
Group 'Vehicle' has n = 8; normality screening has very low power at this size, so a non-significant Shapiro–Wilk is weak evidence of normality.
Non-significant. This test has low power on small samples, so treat this as 'no evidence against equal variances', not as evidence for them.
Bartlett's test assumes normality and is badly inflated when that fails — confirm with stats.normality, or use method='levene'.

Outlier screen

Method	Vehicle	Low dose	Mid dose	High dose
Grubbs	none	none	none	none
Generalised ESD	none	none	none	none
Dixon's Q	none	none	none	none
Modified z (MAD)	none	none	none	none
IQR fences (1.5×)	none	none	2 (3.51, 4.53)	none

LabTools calls (5)

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 dixon-q

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.
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
Vehicle	8	6.125	[5.722, 6.528]
Low dose	8	5.081	[4.691, 5.472]
Mid dose	8	4.026	[3.784, 4.269]
High dose	8	3.318	[2.958, 3.677]

LabTools calls (2)

stats.ci

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

stats.ci

labtools stats ci --data @High_dose.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 = 67.11	3, 28	6.7 × 10⁻¹³	ω² = 0.861 · η² = 0.878 · Cohen's f = 2.68
Kruskal–Wallis H	H = 27.78	3	4.0 × 10⁻⁶	ε² = 0.896

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 'High dose' has n = 8; normality screening has very low power at this size, so a non-significant Shapiro–Wilk is weak evidence of normality.

Which groups differ? (pairwise, corrected)

Comparison	Mean diff.	95% CI	Hedges' g	Welch p	Holm	BH	Mann–Whitney p	Holm	Cliff's δ
Vehicle vs Low dose	1.044	[0.5349, 1.553]	2.08	0.0006	0.001	0.0007	0.003	0.006	0.906
Vehicle vs Mid dose	2.099	[1.663, 2.534]	4.99	2.9 × 10⁻⁷	1.5 × 10⁻⁶	8.8 × 10⁻⁷	0.0009	0.006	1
Vehicle vs High dose	2.807	[2.317, 3.298]	5.81	7.9 × 10⁻⁹	4.7 × 10⁻⁸	4.7 × 10⁻⁸	0.0009	0.006	1
Low dose vs Mid dose	1.055	[0.6303, 1.48]	2.57	0.0002	0.0005	0.0003	0.001	0.006	0.969
Low dose vs High dose	1.764	[1.282, 2.245]	3.71	1.8 × 10⁻⁶	7.0 × 10⁻⁶	3.5 × 10⁻⁶	0.0009	0.006	1
Mid dose vs High dose	0.7088	[0.3101, 1.107]	1.83	0.002	0.002	0.002	0.003	0.006	0.891

LabTools calls (3)

stats.ttest

labtools stats ttest --a @Vehicle.json --b @Low_dose.json --test welch --no-assumption-checks

stats.mannwhitney

labtools stats mannwhitney --a @Vehicle.json --b @Low_dose.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 = 1.51

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

n = 8 vs 8

15.4%

Power to detect d = 0.5

32.0%

Power to detect d = 0.8

60.8%

Power to detect d = 1.2

LabTools calls (2)

stats.power

labtools stats power --n1 8 --n2 8 --mode mde --power 0.8

stats.power

labtools stats power --n1 8 --n2 8 --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.

Groups were compared by one-way ANOVA (F(3,28) = 67.1, p < 0.0001, ω² = 0.86); variances were homogeneous (Levene p = 0.54).

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