All examples · Example 29 of 34

ROC CurveClinicalStatistical report

ROC Curve: Diagnostic Biomarker

Receiver operating characteristic curve for a biomarker score distinguishing 123 cases from 177 controls; dashed line is chance.

Key findings

AUC = 0.846, computed from the Mann–Whitney U statistic (123 cases, 177 controls), p = 1.9 × 10⁻²⁴ against chance (AUC = 0.5).
Hedges' g = 1.44: the case and control score distributions still overlap substantially, which is why a single cut-off trades sensitivity against specificity.

17 LabTools stats calls

7 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
Cases	123	1.303	0.9663	0.08712	1.318	0.649 – 1.943	-0.992 – 3.561	0.0718	-0.373
Controls	177	-0.0657	0.9338	0.07019	-0.085	-0.582 – 0.574	-2.918 – 2.69	-0.184	0.539

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
Cases	123	0.9918	0.69	0.1989	0.88	0.04325	0.83	Consistent with normal
Controls	177	0.9913	0.36	0.353	0.46	0.04979	0.35	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.

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)	0.657	0.42	1.07	Homogeneous
Bartlett	0.1685	0.68	1.07	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

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'.

Cases vs controls

The same comparison three ways. Welch's t-test (the LabTools default) does not assume equal variances; Student's pools them; Mann–Whitney compares ranks and needs no normality. When they agree the conclusion is robust to the choice.

Test	Statistic	df	p	Mean difference (Cases − Controls)	95% CI of difference
Welch t-test	t = 12.23	256.8	2.0 × 10⁻²⁷	1.369	[1.148, 1.589]
Student t-test	t = 12.31	298	2.0 × 10⁻²⁸	1.369	[1.15, 1.587]
Mann–Whitney U	U = 18,425	—	1.9 × 10⁻²⁴	—	—

LabTools calls (3)

stats.ttest

labtools stats ttest --a @Cases.json --b @Controls.json --test welch

stats.ttest

labtools stats ttest --a @Cases.json --b @Controls.json --test student

stats.mannwhitney

labtools stats mannwhitney --a @Cases.json --b @Controls.json

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

Effect sizes — how big, not just whether

Measure	Estimate	95% CI	Magnitude
Hedges' g (bias-corrected)	1.44	[1.183, 1.697]	very large
Cohen's d	1.44	—	very large
Glass's Δ (scaled by the Cases SD)	1.42	—	very large
Cliff's δ (non-parametric)	0.693	—	large

LabTools calls (4)

stats.effectsize

labtools stats effectsize --a @Cases.json --b @Controls.json --measure hedges-g

stats.effectsize

labtools stats effectsize --a @Cases.json --b @Controls.json --measure cohens-d

stats.effectsize

labtools stats effectsize --a @Controls.json --b @Cases.json --measure glass-delta

stats.effectsize

labtools stats effectsize --a @Cases.json --b @Controls.json --measure cliffs-delta

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

Design sensitivity

d = 0.33

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

n = 123 vs 177

98.9%

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 123 --n2 177 --mode mde --power 0.8

stats.power

labtools stats power --n1 123 --n2 177 --effect-size 0.5

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

The ROC curve is a Mann–Whitney test

The area under the ROC curve equals the probability that a randomly chosen case scores higher than a randomly chosen control — which is exactly what the Mann–Whitney U statistic counts. AUC = U / (n_cases × n_controls), and Cliff's δ = 2·AUC − 1. So the AUC comes with a p-value for free.

0.846

AUC from Mann–Whitney U

U = 18,425 of 21,771 pairs

0.846

AUC from Cliff's δ

δ = 0.693

1.9 × 10⁻²⁴

p (H0: AUC = 0.5)

Mann–Whitney, two-sided

Methods paragraph

Written to go straight into a manuscript.

The biomarker discriminated cases from controls with AUC = 0.846 (Mann–Whitney U = 18,425, p < 0.0001).

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

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All examples · Example 29 of 34

ROC CurveClinicalStatistical report

ROC Curve: Diagnostic Biomarker

Receiver operating characteristic curve for a biomarker score distinguishing 123 cases from 177 controls; dashed line is chance.

Key findings

AUC = 0.846, computed from the Mann–Whitney U statistic (123 cases, 177 controls), p = 1.9 × 10⁻²⁴ against chance (AUC = 0.5).
Hedges' g = 1.44: the case and control score distributions still overlap substantially, which is why a single cut-off trades sensitivity against specificity.

17 LabTools stats calls

7 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
Cases	123	1.303	0.9663	0.08712	1.318	0.649 – 1.943	-0.992 – 3.561	0.0718	-0.373
Controls	177	-0.0657	0.9338	0.07019	-0.085	-0.582 – 0.574	-2.918 – 2.69	-0.184	0.539

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
Cases	123	0.9918	0.69	0.1989	0.88	0.04325	0.83	Consistent with normal
Controls	177	0.9913	0.36	0.353	0.46	0.04979	0.35	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.

Equal variances

Test	Statistic	p	Largest / smallest variance	Verdict
Levene (Brown–Forsythe, median-centred)	0.657	0.42	1.07	Homogeneous
Bartlett	0.1685	0.68	1.07	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

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'.

Cases vs controls

Test	Statistic	df	p	Mean difference (Cases − Controls)	95% CI of difference
Welch t-test	t = 12.23	256.8	2.0 × 10⁻²⁷	1.369	[1.148, 1.589]
Student t-test	t = 12.31	298	2.0 × 10⁻²⁸	1.369	[1.15, 1.587]
Mann–Whitney U	U = 18,425	—	1.9 × 10⁻²⁴	—	—

LabTools calls (3)

stats.ttest

labtools stats ttest --a @Cases.json --b @Controls.json --test welch

stats.ttest

labtools stats ttest --a @Cases.json --b @Controls.json --test student

stats.mannwhitney

labtools stats mannwhitney --a @Cases.json --b @Controls.json

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

Effect sizes — how big, not just whether

Measure	Estimate	95% CI	Magnitude
Hedges' g (bias-corrected)	1.44	[1.183, 1.697]	very large
Cohen's d	1.44	—	very large
Glass's Δ (scaled by the Cases SD)	1.42	—	very large
Cliff's δ (non-parametric)	0.693	—	large

LabTools calls (4)

stats.effectsize

labtools stats effectsize --a @Cases.json --b @Controls.json --measure hedges-g

stats.effectsize

labtools stats effectsize --a @Cases.json --b @Controls.json --measure cohens-d

stats.effectsize

labtools stats effectsize --a @Controls.json --b @Cases.json --measure glass-delta

stats.effectsize

labtools stats effectsize --a @Cases.json --b @Controls.json --measure cliffs-delta

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

Design sensitivity

d = 0.33

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

n = 123 vs 177

98.9%

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 123 --n2 177 --mode mde --power 0.8

stats.power

labtools stats power --n1 123 --n2 177 --effect-size 0.5

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

The ROC curve is a Mann–Whitney test

0.846

AUC from Mann–Whitney U

U = 18,425 of 21,771 pairs

0.846

AUC from Cliff's δ

δ = 0.693

1.9 × 10⁻²⁴

p (H0: AUC = 0.5)

Mann–Whitney, two-sided

Methods paragraph

Written to go straight into a manuscript.

The biomarker discriminated cases from controls with AUC = 0.846 (Mann–Whitney U = 18,425, p < 0.0001).

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