critical_es_value

Calculate critical effect size values for t-Tests, correlation tests and linear regression coefficients.

Installation

pip install critical-es-value

Overview

This package offers 8 main functions. Either provide the raw sample data to the main version of the function, or provide the summary statistics to the from_values() version.

Main version	from_values()
critical_for_one_sample_ttest()	critical_for_one_sample_ttest_from_values()
critical_for_two_sample_ttest()	critical_for_two_sample_ttest_from_values()
critical_for_correlation_test()	critical_for_correlation_test_from_values()
critical_for_linear_regression()	critical_for_linear_regression_from_values()

Main Usage

import numpy as np
import pingouin as pg
import critical_es_value as cev

np.random.seed(123)
mean, cov, n = [4, 5], [(1, .6), (.6, 1)], 30
x, y = np.random.multivariate_normal(mean, cov, n).T

t-Test

pg.ttest(x, 0)
cev.critical_for_one_sample_ttest(x)

	T	dof	alternative	p-val	CI95%	cohen-d	BF10	power
T-test	16.0765	29	two-sided	5.54732e-16	[3.37 4.35]	2.93515	1.031e+13	nan

	T	dof	T_critical	d	d_critical	b_critical	g	g_critical
critical	16.0765	29	2.04523	2.93515	0.373406	0.491162	2.85847	0.363651

pg.ttest(x, y, paired=False)
cev.critical_for_two_sample_ttest(x, y, paired=False)

	T	dof	alternative	p-val	CI95%	cohen-d	BF10	power
T-test	-3.40071	58	two-sided	0.0012224	[-1.68 -0.43]	0.878059	26.155	0.916807

	T	dof	T_critical	d	d_critical	b_critical	g	g_critical
critical	-3.40071	58	2.00172	-0.878059	0.516841	0.62077	-0.866647	0.510124

Correlation Test

pg.corr(x, y)
cev.critical_for_correlation_test(x, y)

	n	r	CI95%	p-val	BF10	power
pearson	30	0.594785	[0.3 0.79]	0.00052736	69.723	0.950373

	n	r	dof	r_critical	se_r	se_r_critical
critical	30	0.594785	28	0.361007	0.15192	0.176238

Linear Regression

import pandas as pd

np.random.seed(123)
data = pd.DataFrame({"X": x, "Y": y, "Z": np.random.normal(5, 1, 30)})

pg.linear_regression(data[["X", "Z"]], data["Y"])
cev.critical_for_linear_regression(data[["X", "Z"]], data["Y"])

	names	coef	se	T	pval	r2	adj_r2	CI[2.5%]	CI[97.5%]
0	Intercept	3.15799	0.844129	3.74112	0.000874245	0.354522	0.306709	1.42598	4.88999
1	X	0.487772	0.126736	3.84871	0.000659501	0.354522	0.306709	0.22773	0.747814
2	Z	-0.0249309	0.140417	-0.177548	0.860403	0.354522	0.306709	-0.313044	0.263182

	names	coef	coef_critical
0	Intercept	3.15799	1.73201
1	X	0.487772	0.260042
2	Z	-0.0249309	0.288113

Usage of from_values() version

t-Test

t_test_result = pg.ttest(x, 0).iloc[0]
cev.critical_for_one_sample_ttest_from_values(
    t=t_test_result["T"],
    n=len(x),
    dof=t_test_result.dof,
    std=np.std(x, ddof=1),
)

	T	dof	T_critical	d	d_critical	g	g_critical	b_critical
critical	16.0765	29	2.04523	2.93515	0.373406	2.85847	0.363651	0.491162

t_test_result = pg.ttest(x, y, paired=False).iloc[0]
cev.critical_for_two_sample_ttest_from_values(
    t=t_test_result["T"],
    n1=len(x),
    n2=len(y),
    dof=t_test_result.dof,
    paired=False,
    std1=np.std(x, ddof=1),
    std2=np.std(y, ddof=1),
)

	T	dof	T_critical	d	d_critical	g	g_critical	b_critical
critical	-3.40071	58	2.00172	-0.878059	0.516841	-0.866647	0.510124	0.62077

Correlation Test

corr_test = pg.corr(x, y).iloc[0]
cev.critical_for_correlation_test_from_values(
    r=corr_test["r"],
    n=corr_test["n"],
    variant="ttest",
)

	n	r	dof	r_critical	se_r	se_r_critical
critical	30	0.594785	28	0.361007	0.15192	0.176238

Linear Regression

model = pg.linear_regression(data[["X", "Z"]], data["Y"])

cev.critical_for_linear_regression_from_values(
    coeffs=model["coef"].values,
    coeffs_se=model["se"].values,
    coeffs_names=model["names"].values,
    dof=model.df_resid_,
    variant="ttest",
)

	names	coef	coef_critical
0	Intercept	3.15799	1.73201
1	X	0.487772	0.260042
2	Z	-0.0249309	0.288113

Resources

• R package
• Original paper

Perugini, A., Gambarota, F., Toffalini, E., Lakens, D., Pastore, M., Finos, L., ... & Altoè, G. (2025). The Benefits of Reporting Critical-Effect-Size Values. Advances in Methods and Practices in Psychological Science, 8(2), 25152459251335298.