All examples · Example 19 of 34

Correlation HeatmapRelationshipsStatistical report

Correlation Heatmap: Metabolomics

Pairwise Pearson correlation between 20 metabolites across 60 samples (purple positive, orange negative).

Key findings

46 of 190 metabolite pairs are significantly correlated after Benjamini–Hochberg correction (45 after Bonferroni).
The strongest pair is Succinate – Alanine (r = 0.772); Spearman and Kendall rank the top pairs the same way, so they are not driven by outliers.

220 LabTools stats calls

4 of 15 stats methods

LabTools 0.14.3

600 dpi PNG Data (CSV) Raw LabTools output

Descriptive statistics (20 metabolites)

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
Glucose	60	10.04	1.893	0.2444	9.873	8.941 – 11.65	5.654 – 14.46	-0.00328	-0.263
Lactate	60	9.85	1.948	0.2514	9.912	8.705 – 11	5.796 – 13.98	-0.0645	-0.239
Pyruvate	60	9.922	1.956	0.2525	9.979	8.694 – 11.11	4.979 – 14.37	-0.227	0.173
Citrate	60	10.11	1.785	0.2305	10.37	8.879 – 11.58	6.416 – 14.27	-0.0769	-0.559
Succinate	60	9.764	2.173	0.2805	10.1	8.107 – 11.3	3.932 – 13.63	-0.501	-0.167
Fumarate	60	9.779	2.145	0.277	9.279	8.297 – 11.27	4.406 – 15.19	0.309	-0.186
Malate	60	9.998	2.189	0.2826	10.31	8.265 – 11.77	4.883 – 14.12	-0.178	-0.843
Alanine	60	10.09	2.101	0.2713	10.5	8.573 – 11.75	4.338 – 14.62	-0.413	-0.201
Glutamate	60	9.818	2.211	0.2854	9.989	8.199 – 11.37	4.997 – 14.05	-0.16	-0.758
Glutamine	60	9.813	1.776	0.2293	9.922	8.698 – 10.76	4.844 – 13.52	-0.164	0.138
Aspartate	60	10.06	1.767	0.2281	10.06	8.845 – 11.28	5.585 – 13.32	-0.199	-0.424
Serine	60	9.873	1.929	0.249	10.02	8.86 – 11.27	5.273 – 13.3	-0.412	-0.511
Glycine	60	10.26	2.127	0.2746	10.43	8.86 – 11.61	5.278 – 14.56	-0.14	-0.184
Leucine	60	10.07	1.961	0.2532	10.27	9.098 – 11.04	4.504 – 14.37	-0.418	0.828
Isoleucine	60	9.805	1.943	0.2508	9.936	8.314 – 11.02	5.634 – 15.18	0.403	-0.0381
Valine	60	9.85	1.829	0.2362	9.94	8.479 – 11.06	5.89 – 14.48	-0.0052	0.0544
Taurine	60	10.2	2.055	0.2653	10.14	8.744 – 11.52	4.762 – 14.54	-0.283	-0.0605
Creatine	60	10.04	1.776	0.2293	10.02	8.605 – 11.47	5.905 – 14.29	0.102	-0.539
Choline	60	10.25	1.866	0.2409	10.53	8.976 – 11.7	4.909 – 13.9	-0.496	-0.135
Betaine	60	9.891	1.899	0.2452	9.768	8.508 – 11.22	4.942 – 13.87	-0.109	0.0747

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

Shapiro–Wilk on every metabolite: the Pearson coefficients in the heatmap assume roughly normal, outlier-free variables.

Group	n	Shapiro–Wilk W	p	Verdict
Glucose	60	0.9857	0.71	Consistent with normal
Lactate	60	0.9811	0.48	Consistent with normal
Pyruvate	60	0.9888	0.86	Consistent with normal
Citrate	60	0.986	0.72	Consistent with normal
Succinate	60	0.9755	0.27	Consistent with normal
Fumarate	60	0.9738	0.22	Consistent with normal
Malate	60	0.9738	0.22	Consistent with normal
Alanine	60	0.977	0.31	Consistent with normal
Glutamate	60	0.9787	0.38	Consistent with normal
Glutamine	60	0.9889	0.86	Consistent with normal
Aspartate	60	0.9837	0.60	Consistent with normal
Serine	60	0.9693	0.13	Consistent with normal
Glycine	60	0.9876	0.80	Consistent with normal
Leucine	60	0.9695	0.14	Consistent with normal
Isoleucine	60	0.9835	0.59	Consistent with normal
Valine	60	0.9861	0.73	Consistent with normal
Taurine	60	0.991	0.94	Consistent with normal
Creatine	60	0.9847	0.66	Consistent with normal
Choline	60	0.9743	0.23	Consistent with normal
Betaine	60	0.9854	0.69	Consistent with normal

LabTools call

stats.normality

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

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

All 190 pairwise correlations, corrected

Every pair of metabolites is correlated (Pearson), which is one family of 190 tests. The p-values are corrected four ways; the table lists the strongest pairs, with Spearman and Kendall alongside as a robustness check.

190 tests, α = 0.05

Correction	Controls	Tests	Raw p < 0.05	Significant after correction
Bonferroni	family-wise error	190	50	45
Holm	family-wise error	190	50	45
Benjamini–Hochberg	false discovery rate	190	50	46
Benjamini–Yekutieli	false discovery rate	190	50	45

LabTools calls (4)

stats.adjust

labtools stats adjust --p-values @p_values.json --labels @labels.json --method bonferroni --alpha 0.05

stats.adjust

labtools stats adjust --p-values @p_values.json --labels @labels.json --method holm --alpha 0.05

stats.adjust

labtools stats adjust --p-values @p_values.json --labels @labels.json --method benjamini-hochberg --alpha 0.05

stats.adjust

labtools stats adjust --p-values @p_values.json --labels @labels.json --method benjamini-yekutieli --alpha 0.05

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

LabTools notes

5 comparison(s) were significant on the raw p-values but are not after correction. Report the adjusted values.
Holm controls the same familywise error rate as Bonferroni and rejects at least as much, so there is no statistical reason to prefer bonferroni.
4 comparison(s) were significant on the raw p-values but are not after correction. Report the adjusted values.

Strongest 12 pairs

Pair	Pearson r	p	BH-adjusted p	Spearman ρ	Kendall τ
Succinate – Alanine	0.772	5.0 × 10⁻¹³	9.4 × 10⁻¹¹	0.742	0.558
Glutamate – Creatine	0.758	2.4 × 10⁻¹²	2.3 × 10⁻¹⁰	0.784	0.564
Fumarate – Isoleucine	0.734	2.6 × 10⁻¹¹	1.6 × 10⁻⁹	0.683	0.506
Pyruvate – Creatine	0.716	1.2 × 10⁻¹⁰	5.9 × 10⁻⁹	0.731	0.542
Alanine – Leucine	0.712	1.8 × 10⁻¹⁰	6.4 × 10⁻⁹	0.672	0.488
Fumarate – Glutamate	0.711	2.0 × 10⁻¹⁰	6.4 × 10⁻⁹	0.742	0.546
Alanine – Taurine	0.702	4.1 × 10⁻¹⁰	1.0 × 10⁻⁸	0.668	0.482
Serine – Creatine	0.7	4.9 × 10⁻¹⁰	1.0 × 10⁻⁸	0.7	0.515
Fumarate – Creatine	0.7	4.9 × 10⁻¹⁰	1.0 × 10⁻⁸	0.701	0.494
Glucose – Malate	0.692	8.9 × 10⁻¹⁰	1.7 × 10⁻⁸	0.7	0.507
Pyruvate – Isoleucine	0.691	9.8 × 10⁻¹⁰	1.7 × 10⁻⁸	0.688	0.505
Citrate – Glutamine	0.689	1.1 × 10⁻⁹	1.8 × 10⁻⁸	0.672	0.497

LabTools calls (3)

stats.correlation

labtools stats correlation --a @Glucose.json --b @Lactate.json --method pearson

stats.correlation

labtools stats correlation --a @Succinate.json --b @Alanine.json --method spearman

stats.correlation

labtools stats correlation --a @Succinate.json --b @Alanine.json --method kendall

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

Methods paragraph

Written to go straight into a manuscript.

Pearson correlations were computed for all 190 metabolite pairs (n = 60 samples); 45 pairs had |r| > 0.5, forming three co-varying blocks.

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.

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All examples · Example 19 of 34

Correlation HeatmapRelationshipsStatistical report

Correlation Heatmap: Metabolomics

Pairwise Pearson correlation between 20 metabolites across 60 samples (purple positive, orange negative).

Key findings

46 of 190 metabolite pairs are significantly correlated after Benjamini–Hochberg correction (45 after Bonferroni).
The strongest pair is Succinate – Alanine (r = 0.772); Spearman and Kendall rank the top pairs the same way, so they are not driven by outliers.

220 LabTools stats calls

4 of 15 stats methods

LabTools 0.14.3

600 dpi PNG Data (CSV) Raw LabTools output

Descriptive statistics (20 metabolites)

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
Glucose	60	10.04	1.893	0.2444	9.873	8.941 – 11.65	5.654 – 14.46	-0.00328	-0.263
Lactate	60	9.85	1.948	0.2514	9.912	8.705 – 11	5.796 – 13.98	-0.0645	-0.239
Pyruvate	60	9.922	1.956	0.2525	9.979	8.694 – 11.11	4.979 – 14.37	-0.227	0.173
Citrate	60	10.11	1.785	0.2305	10.37	8.879 – 11.58	6.416 – 14.27	-0.0769	-0.559
Succinate	60	9.764	2.173	0.2805	10.1	8.107 – 11.3	3.932 – 13.63	-0.501	-0.167
Fumarate	60	9.779	2.145	0.277	9.279	8.297 – 11.27	4.406 – 15.19	0.309	-0.186
Malate	60	9.998	2.189	0.2826	10.31	8.265 – 11.77	4.883 – 14.12	-0.178	-0.843
Alanine	60	10.09	2.101	0.2713	10.5	8.573 – 11.75	4.338 – 14.62	-0.413	-0.201
Glutamate	60	9.818	2.211	0.2854	9.989	8.199 – 11.37	4.997 – 14.05	-0.16	-0.758
Glutamine	60	9.813	1.776	0.2293	9.922	8.698 – 10.76	4.844 – 13.52	-0.164	0.138
Aspartate	60	10.06	1.767	0.2281	10.06	8.845 – 11.28	5.585 – 13.32	-0.199	-0.424
Serine	60	9.873	1.929	0.249	10.02	8.86 – 11.27	5.273 – 13.3	-0.412	-0.511
Glycine	60	10.26	2.127	0.2746	10.43	8.86 – 11.61	5.278 – 14.56	-0.14	-0.184
Leucine	60	10.07	1.961	0.2532	10.27	9.098 – 11.04	4.504 – 14.37	-0.418	0.828
Isoleucine	60	9.805	1.943	0.2508	9.936	8.314 – 11.02	5.634 – 15.18	0.403	-0.0381
Valine	60	9.85	1.829	0.2362	9.94	8.479 – 11.06	5.89 – 14.48	-0.0052	0.0544
Taurine	60	10.2	2.055	0.2653	10.14	8.744 – 11.52	4.762 – 14.54	-0.283	-0.0605
Creatine	60	10.04	1.776	0.2293	10.02	8.605 – 11.47	5.905 – 14.29	0.102	-0.539
Choline	60	10.25	1.866	0.2409	10.53	8.976 – 11.7	4.909 – 13.9	-0.496	-0.135
Betaine	60	9.891	1.899	0.2452	9.768	8.508 – 11.22	4.942 – 13.87	-0.109	0.0747

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

Shapiro–Wilk on every metabolite: the Pearson coefficients in the heatmap assume roughly normal, outlier-free variables.

Group	n	Shapiro–Wilk W	p	Verdict
Glucose	60	0.9857	0.71	Consistent with normal
Lactate	60	0.9811	0.48	Consistent with normal
Pyruvate	60	0.9888	0.86	Consistent with normal
Citrate	60	0.986	0.72	Consistent with normal
Succinate	60	0.9755	0.27	Consistent with normal
Fumarate	60	0.9738	0.22	Consistent with normal
Malate	60	0.9738	0.22	Consistent with normal
Alanine	60	0.977	0.31	Consistent with normal
Glutamate	60	0.9787	0.38	Consistent with normal
Glutamine	60	0.9889	0.86	Consistent with normal
Aspartate	60	0.9837	0.60	Consistent with normal
Serine	60	0.9693	0.13	Consistent with normal
Glycine	60	0.9876	0.80	Consistent with normal
Leucine	60	0.9695	0.14	Consistent with normal
Isoleucine	60	0.9835	0.59	Consistent with normal
Valine	60	0.9861	0.73	Consistent with normal
Taurine	60	0.991	0.94	Consistent with normal
Creatine	60	0.9847	0.66	Consistent with normal
Choline	60	0.9743	0.23	Consistent with normal
Betaine	60	0.9854	0.69	Consistent with normal

LabTools call

stats.normality

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

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

All 190 pairwise correlations, corrected

190 tests, α = 0.05

Correction	Controls	Tests	Raw p < 0.05	Significant after correction
Bonferroni	family-wise error	190	50	45
Holm	family-wise error	190	50	45
Benjamini–Hochberg	false discovery rate	190	50	46
Benjamini–Yekutieli	false discovery rate	190	50	45

LabTools calls (4)

stats.adjust

labtools stats adjust --p-values @p_values.json --labels @labels.json --method bonferroni --alpha 0.05

stats.adjust

labtools stats adjust --p-values @p_values.json --labels @labels.json --method holm --alpha 0.05

stats.adjust

labtools stats adjust --p-values @p_values.json --labels @labels.json --method benjamini-hochberg --alpha 0.05

stats.adjust

labtools stats adjust --p-values @p_values.json --labels @labels.json --method benjamini-yekutieli --alpha 0.05

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

LabTools notes

5 comparison(s) were significant on the raw p-values but are not after correction. Report the adjusted values.
Holm controls the same familywise error rate as Bonferroni and rejects at least as much, so there is no statistical reason to prefer bonferroni.
4 comparison(s) were significant on the raw p-values but are not after correction. Report the adjusted values.

Strongest 12 pairs

Pair	Pearson r	p	BH-adjusted p	Spearman ρ	Kendall τ
Succinate – Alanine	0.772	5.0 × 10⁻¹³	9.4 × 10⁻¹¹	0.742	0.558
Glutamate – Creatine	0.758	2.4 × 10⁻¹²	2.3 × 10⁻¹⁰	0.784	0.564
Fumarate – Isoleucine	0.734	2.6 × 10⁻¹¹	1.6 × 10⁻⁹	0.683	0.506
Pyruvate – Creatine	0.716	1.2 × 10⁻¹⁰	5.9 × 10⁻⁹	0.731	0.542
Alanine – Leucine	0.712	1.8 × 10⁻¹⁰	6.4 × 10⁻⁹	0.672	0.488
Fumarate – Glutamate	0.711	2.0 × 10⁻¹⁰	6.4 × 10⁻⁹	0.742	0.546
Alanine – Taurine	0.702	4.1 × 10⁻¹⁰	1.0 × 10⁻⁸	0.668	0.482
Serine – Creatine	0.7	4.9 × 10⁻¹⁰	1.0 × 10⁻⁸	0.7	0.515
Fumarate – Creatine	0.7	4.9 × 10⁻¹⁰	1.0 × 10⁻⁸	0.701	0.494
Glucose – Malate	0.692	8.9 × 10⁻¹⁰	1.7 × 10⁻⁸	0.7	0.507
Pyruvate – Isoleucine	0.691	9.8 × 10⁻¹⁰	1.7 × 10⁻⁸	0.688	0.505
Citrate – Glutamine	0.689	1.1 × 10⁻⁹	1.8 × 10⁻⁸	0.672	0.497

LabTools calls (3)

stats.correlation

labtools stats correlation --a @Glucose.json --b @Lactate.json --method pearson

stats.correlation

labtools stats correlation --a @Succinate.json --b @Alanine.json --method spearman

stats.correlation

labtools stats correlation --a @Succinate.json --b @Alanine.json --method kendall

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

Methods paragraph

Written to go straight into a manuscript.

Pearson correlations were computed for all 190 metabolite pairs (n = 60 samples); 45 pairs had |r| > 0.5, forming three co-varying blocks.

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