All examples · Example 11 of 34

Bar ChartComparisonStatistical report

Bar Chart: ELISA Results

Cytokine concentrations (pg/mL) in control and LPS-stimulated cultures; bars show mean ± SEM with individual wells (n = 6).

Key findings

Two-way ANOVA: treatment F = 198.5 (p = 9.1 × 10⁻¹⁵), and a strong cytokine × treatment interaction (p = 6.8 × 10⁻¹⁰) — LPS does not raise every cytokine equally.
Within cytokines, all three increases survive Benjamini–Hochberg correction; the largest is IL-6 (Hedges' g = -6.86).

18 LabTools stats calls

8 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
IL-6 · Control	6	46.23	9.667	3.947	44.25	40.33 – 46.22	38.2 – 64.8	1.84	3.78
IL-6 · LPS	6	303.8	48.09	19.63	300.1	261 – 348.4	256.4 – 354.1	0.0654	-3.08
TNF-α · Control	6	59.33	8.669	3.539	59.75	51.47 – 66.15	49.9 – 69.6	-0.0175	-2.57
TNF-α · LPS	6	205.3	51.61	21.07	191.6	176.7 – 236.2	142.5 – 283.3	0.573	-0.63
IL-10 · Control	6	83.62	13.27	5.416	86.6	73.47 – 94.62	65.7 – 96.4	-0.388	-2.21
IL-10 · LPS	6	104.6	11.3	4.613	102.8	97.5 – 114.8	90.2 – 117.4	0.0817	-1.96

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	K–S D	p	Verdict
IL-6 · Control	6	0.7966	0.055	0.3306	0.039	Normality rejected
IL-6 · LPS	6	0.7832	0.041	0.2862	0.13	Normality rejected
TNF-α · Control	6	0.8728	0.24	0.2244	0.45	Consistent with normal
TNF-α · LPS	6	0.9535	0.77	0.1968	0.66	Consistent with normal
IL-10 · Control	6	0.8643	0.20	0.2786	0.15	Consistent with normal
IL-10 · LPS	6	0.8971	0.36	0.2273	0.43	Consistent with normal

LabTools calls (2)

stats.normality

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

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 'IL-10 · Control' has n = 6; normality screening has very low power at this size, so a non-significant Shapiro–Wilk is weak evidence of normality.
Group 'IL-10 · LPS' has n = 6; normality screening has very low power at this size, so a non-significant Shapiro–Wilk is weak evidence of normality.
Group 'IL-6 · Control' has n = 6; normality screening has very low power at this size, so a non-significant Shapiro–Wilk is weak evidence of normality.
Group 'IL-6 · LPS' has n = 6; normality screening has very low power at this size, so a non-significant Shapiro–Wilk is weak evidence of normality.
Group 'TNF-α · Control' has n = 6; normality screening has very low power at this size, so a non-significant Shapiro–Wilk is weak evidence of normality.
Group 'TNF-α · LPS' has n = 6; normality screening has very low power at this size, so a non-significant Shapiro–Wilk is weak evidence of normality.
Group 'IL-6 · LPS' rejects normality (p = 0.0413); prefer a rank-based test.
Group 'IL-6 · Control' rejects normality (p = 0.0392); 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)	8.146	6.0 × 10⁻⁵	35.4	Variances differ
Bartlett	29.5	1.9 × 10⁻⁵	35.4	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

Group 'IL-10 · Control' has n = 6; normality screening has very low power at this size, so a non-significant Shapiro–Wilk is weak evidence of normality.
Group 'IL-10 · LPS' has n = 6; normality screening has very low power at this size, so a non-significant Shapiro–Wilk is weak evidence of normality.
Group 'IL-6 · Control' has n = 6; normality screening has very low power at this size, so a non-significant Shapiro–Wilk is weak evidence of normality.
Group 'IL-6 · LPS' has n = 6; normality screening has very low power at this size, so a non-significant Shapiro–Wilk is weak evidence of normality.
Group 'TNF-α · Control' has n = 6; normality screening has very low power at this size, so a non-significant Shapiro–Wilk is weak evidence of normality.
Group 'TNF-α · LPS' has n = 6; normality screening has very low power at this size, so a non-significant Shapiro–Wilk is weak evidence of normality.
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'.

Two-way ANOVA: Cytokine × Treatment

Cytokine and treatment are crossed, so a two-way ANOVA separates the treatment effect, the cytokine effect, and — the interesting term — the interaction: does LPS raise every cytokine by the same amount?

Source	SS	df	MS	F	p	Partial η²
Cytokine	39,326	2	19,663	21.65	1.5 × 10⁻⁶	0.591
Treatment	180,285	1	180,285	198.5	9.1 × 10⁻¹⁵	0.869
Cytokine × Treatment	84,058	2	42,029	46.28	6.8 × 10⁻¹⁰	0.755
Residual	27,244	30	908.13

LabTools call

stats.anova

labtools stats anova --design two-way --cells @cells.json --factor-a-name Cytokine --factor-b-name Treatment

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

LabTools notes

The interaction is significant, so the main effects are not interpretable on their own — the effect of one factor depends on the level of the other. Report simple effects at each level instead.

Treatment effect within each cytokine

The interaction says the treatment effect differs between cytokines, so each cytokine is compared separately (Welch t and Mann–Whitney) and the three p-values are corrected as one family.

Cytokine	Control mean	LPS mean	Welch t	p	BH	Holm	Hedges' g [95% CI]	Mann–Whitney p
IL-6	46.23	303.8	-12.86	2.9 × 10⁻⁵	8.8 × 10⁻⁵	8.8 × 10⁻⁵	-6.86 [-9.975, -3.706]	0.005
TNF-α	59.33	205.3	-6.832	0.0008	0.001	0.002	-3.64 [-5.502, -1.727]	0.005
IL-10	83.62	104.6	-2.954	0.015	0.015	0.015	-1.57 [-2.794, -0.3005]	0.020

LabTools calls (3)

stats.ttest

labtools stats ttest --a @IL-6_Control.json --b @IL-6_LPS.json --test welch

stats.mannwhitney

labtools stats mannwhitney --a @IL-6_Control.json --b @IL-6_LPS.json

stats.adjust

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

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

Design sensitivity

d = 1.8

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

n = 6 vs 6

12.3%

Power to detect d = 0.5

24.1%

Power to detect d = 0.8

46.8%

Power to detect d = 1.2

LabTools calls (2)

stats.power

labtools stats power --n1 6 --n2 6 --mode mde --power 0.8

stats.power

labtools stats power --n1 6 --n2 6 --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.

Each cytokine was compared between control and LPS by Welch’s t-test (n = 6 per group) with Benjamini–Hochberg correction across the three cytokines. LPS raised IL-6 6.6-fold (p_adj < 0.0001), TNF-α 3.5-fold (p_adj = 0.001) and IL-10 1.25-fold (p_adj = 0.015).

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 11 of 34

Bar ChartComparisonStatistical report

Bar Chart: ELISA Results

Cytokine concentrations (pg/mL) in control and LPS-stimulated cultures; bars show mean ± SEM with individual wells (n = 6).

Key findings

Two-way ANOVA: treatment F = 198.5 (p = 9.1 × 10⁻¹⁵), and a strong cytokine × treatment interaction (p = 6.8 × 10⁻¹⁰) — LPS does not raise every cytokine equally.
Within cytokines, all three increases survive Benjamini–Hochberg correction; the largest is IL-6 (Hedges' g = -6.86).

18 LabTools stats calls

8 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
IL-6 · Control	6	46.23	9.667	3.947	44.25	40.33 – 46.22	38.2 – 64.8	1.84	3.78
IL-6 · LPS	6	303.8	48.09	19.63	300.1	261 – 348.4	256.4 – 354.1	0.0654	-3.08
TNF-α · Control	6	59.33	8.669	3.539	59.75	51.47 – 66.15	49.9 – 69.6	-0.0175	-2.57
TNF-α · LPS	6	205.3	51.61	21.07	191.6	176.7 – 236.2	142.5 – 283.3	0.573	-0.63
IL-10 · Control	6	83.62	13.27	5.416	86.6	73.47 – 94.62	65.7 – 96.4	-0.388	-2.21
IL-10 · LPS	6	104.6	11.3	4.613	102.8	97.5 – 114.8	90.2 – 117.4	0.0817	-1.96

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	K–S D	p	Verdict
IL-6 · Control	6	0.7966	0.055	0.3306	0.039	Normality rejected
IL-6 · LPS	6	0.7832	0.041	0.2862	0.13	Normality rejected
TNF-α · Control	6	0.8728	0.24	0.2244	0.45	Consistent with normal
TNF-α · LPS	6	0.9535	0.77	0.1968	0.66	Consistent with normal
IL-10 · Control	6	0.8643	0.20	0.2786	0.15	Consistent with normal
IL-10 · LPS	6	0.8971	0.36	0.2273	0.43	Consistent with normal

LabTools calls (2)

stats.normality

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

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 'IL-10 · Control' has n = 6; normality screening has very low power at this size, so a non-significant Shapiro–Wilk is weak evidence of normality.
Group 'IL-10 · LPS' has n = 6; normality screening has very low power at this size, so a non-significant Shapiro–Wilk is weak evidence of normality.
Group 'IL-6 · Control' has n = 6; normality screening has very low power at this size, so a non-significant Shapiro–Wilk is weak evidence of normality.
Group 'IL-6 · LPS' has n = 6; normality screening has very low power at this size, so a non-significant Shapiro–Wilk is weak evidence of normality.
Group 'TNF-α · Control' has n = 6; normality screening has very low power at this size, so a non-significant Shapiro–Wilk is weak evidence of normality.
Group 'TNF-α · LPS' has n = 6; normality screening has very low power at this size, so a non-significant Shapiro–Wilk is weak evidence of normality.
Group 'IL-6 · LPS' rejects normality (p = 0.0413); prefer a rank-based test.
Group 'IL-6 · Control' rejects normality (p = 0.0392); prefer a rank-based test.

Equal variances

Test	Statistic	p	Largest / smallest variance	Verdict
Levene (Brown–Forsythe, median-centred)	8.146	6.0 × 10⁻⁵	35.4	Variances differ
Bartlett	29.5	1.9 × 10⁻⁵	35.4	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

Group 'IL-10 · Control' has n = 6; normality screening has very low power at this size, so a non-significant Shapiro–Wilk is weak evidence of normality.
Group 'IL-10 · LPS' has n = 6; normality screening has very low power at this size, so a non-significant Shapiro–Wilk is weak evidence of normality.
Group 'IL-6 · Control' has n = 6; normality screening has very low power at this size, so a non-significant Shapiro–Wilk is weak evidence of normality.
Group 'IL-6 · LPS' has n = 6; normality screening has very low power at this size, so a non-significant Shapiro–Wilk is weak evidence of normality.
Group 'TNF-α · Control' has n = 6; normality screening has very low power at this size, so a non-significant Shapiro–Wilk is weak evidence of normality.
Group 'TNF-α · LPS' has n = 6; normality screening has very low power at this size, so a non-significant Shapiro–Wilk is weak evidence of normality.
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'.

Two-way ANOVA: Cytokine × Treatment

Source	SS	df	MS	F	p	Partial η²
Cytokine	39,326	2	19,663	21.65	1.5 × 10⁻⁶	0.591
Treatment	180,285	1	180,285	198.5	9.1 × 10⁻¹⁵	0.869
Cytokine × Treatment	84,058	2	42,029	46.28	6.8 × 10⁻¹⁰	0.755
Residual	27,244	30	908.13

LabTools call

stats.anova

labtools stats anova --design two-way --cells @cells.json --factor-a-name Cytokine --factor-b-name Treatment

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

LabTools notes

The interaction is significant, so the main effects are not interpretable on their own — the effect of one factor depends on the level of the other. Report simple effects at each level instead.

Treatment effect within each cytokine

The interaction says the treatment effect differs between cytokines, so each cytokine is compared separately (Welch t and Mann–Whitney) and the three p-values are corrected as one family.

Cytokine	Control mean	LPS mean	Welch t	p	BH	Holm	Hedges' g [95% CI]	Mann–Whitney p
IL-6	46.23	303.8	-12.86	2.9 × 10⁻⁵	8.8 × 10⁻⁵	8.8 × 10⁻⁵	-6.86 [-9.975, -3.706]	0.005
TNF-α	59.33	205.3	-6.832	0.0008	0.001	0.002	-3.64 [-5.502, -1.727]	0.005
IL-10	83.62	104.6	-2.954	0.015	0.015	0.015	-1.57 [-2.794, -0.3005]	0.020

LabTools calls (3)

stats.ttest

labtools stats ttest --a @IL-6_Control.json --b @IL-6_LPS.json --test welch

stats.mannwhitney

labtools stats mannwhitney --a @IL-6_Control.json --b @IL-6_LPS.json

stats.adjust

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

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

Design sensitivity

d = 1.8

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

n = 6 vs 6

12.3%

Power to detect d = 0.5

24.1%

Power to detect d = 0.8

46.8%

Power to detect d = 1.2

LabTools calls (2)

stats.power

labtools stats power --n1 6 --n2 6 --mode mde --power 0.8

stats.power

labtools stats power --n1 6 --n2 6 --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.

Each cytokine was compared between control and LPS by Welch’s t-test (n = 6 per group) with Benjamini–Hochberg correction across the three cytokines. LPS raised IL-6 6.6-fold (p_adj < 0.0001), TNF-α 3.5-fold (p_adj = 0.001) and IL-10 1.25-fold (p_adj = 0.015).

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