How do you run an independent samples t-test in R from summary statistics?

Install and load the BSDA package, then use its tsum.test() function, passing the mean, standard deviation, and sample size for each group. Set var.equal to FALSE for Welch's t-test or TRUE for Student's t-test.

How do you run an independent samples t-test in Python from summary statistics?

Use scipy.stats.ttest_ind_from_stats(), passing mean, standard deviation, and sample size for each group, with equal_var set to True or False depending on your variance assumption.

Can SPSS run a t-test directly from summary statistics (mean, SD, N)?

The standard SPSS Independent-Samples T Test dialog requires raw data. To test from summary statistics only, you can use SPSS syntax with a manual COMPUTE formula, or reconstruct a representative dataset with the given mean and SD.

Independent samples t-test calculator

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Group 1

Group 1 Name: Mean (M₁): Standard Deviation (SD₁): Sample Size (N₁):

Group 2

Group 2 Name: Mean (M₂): Standard Deviation (SD₂): Sample Size (N₂):

Hypothesis & Significance

Hypothesized Mean Difference (H₀: μ₁ - μ₂ = d₀): Default is 0, testing if means are equal.

Significance Level (α): Default is 0.05 (5% significance level).

Results

Please enter valid summary data above and click "Calculate".

Sample Distributions (Normal Approximation)

Export Results

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How to Use This Independent Samples t-Test Calculator

Enter the summary statistics for each group: Input the sample size (N), mean, and standard deviation (SD) for both groups you want to compare.
Set the significance level (α): Choose your desired significance level, usually 0.05, which determines your threshold for rejecting the null hypothesis.
Calculate: Click the “Calculate” button to run the test.
Review the results:
- The calculator performs an F-test for equality of variances using the provided summary data.
- Based on the F-test p-value, it automatically selects and runs either the Student’s t-test (equal variances assumed) or Welch’s t-test (unequal variances assumed).
- Check the t-statistic, degrees of freedom, and p-value to understand whether the difference between group means is statistically significant.
Interpretation: If the p-value is less than α, you can reject the null hypothesis and conclude that there is a significant difference between the two group means.

Note: This calculator uses summary statistics and assumes normally distributed data. For raw data or non-normal distributions, consider using variance tests like Levene’s test and running the t-test accordingly.

About the Independent Samples t-Test

The independent samples t-test is used to determine whether there is a statistically significant difference between the means of two independent groups.

Null hypothesis (H₀): There is no difference between group means (μ₁ = μ₂).
Alternative hypothesis (H₁): The group means are different (μ₁ ≠ μ₂).
The test calculates a t-statistic based on group means, standard deviations, and sample sizes.
The resulting p-value is compared to a chosen significance level (α, typically 0.05) to decide whether to reject H₀.

This calculator uses either:

Student’s t-test: when equal variances are assumed
Welch’s t-test: when equal variances are not assumed

About Variance Testing

The choice between Student’s and Welch’s t-tests depends on whether the two groups are assumed to have equal variances.

F-test for equality of variances: This calculator uses the F-test because it works with summary statistics (means, SDs, sample sizes). It compares the ratio of sample variances: F = s₁² / s₂².
Limitations: The F-test assumes normally distributed data and can be unreliable if that assumption is violated.

More robust tests, such as Levene’s or O’Brien’s, exist but require raw data and cannot be performed with summary statistics.

Based on the F-test p-value and chosen α-level, the calculator automatically selects:

Student’s t-test if p ≥ α
Welch’s t-test if p < α

Statistical Guide

How to Perform an Independent Samples t-Test

An independent samples t-test compares the means of two independent groups. It tests the null hypothesis (H₀) that the population means are equal. A p-value below your chosen significance level (commonly α = .05) is evidence of a statistically significant difference.

To run this test from summary statistics alone, you need the mean, standard deviation, and sample size (N) for each group. When variances differ between groups, Welch's t-test is the safer choice.

R / RStudio

Direct summary-statistics input

The BSDA package's tsum.test() function accepts mean, SD, and N directly — no raw data needed.

install.packages("BSDA")
library(BSDA)

tsum.test(
  mean.x = 72, s.x = 5.2, n.x = 30,
  mean.y = 68, s.y = 6.1, n.y = 28,
  var.equal = FALSE
)

Set var.equal = TRUE for Student's t-test if you're assuming equal variances; use FALSE for Welch's t-test.

Python

Direct summary-statistics input

SciPy's ttest_ind_from_stats() takes mean, SD, and N directly, just like R's tsum.test().

from scipy import stats

result = stats.ttest_ind_from_stats(
    mean1=72, std1=5.2, nobs1=30,
    mean2=68, std2=6.1, nobs2=28,
    equal_var=False
)

print(result.statistic, result.pvalue)

Set equal_var=True for Student's t-test, or False for Welch's t-test (the default assumption is safer when unsure).

SPSS

Via syntax, from summary statistics

The point-and-click Independent-Samples T Test dialog needs raw data, but SPSS syntax can compute a t-test directly from summary statistics using the standard formula:

COMPUTE se = SQRT((sd1**2/n1) + (sd2**2/n2)).
COMPUTE t  = (mean1 - mean2) / se.
COMPUTE df = ((sd1**2/n1 + sd2**2/n2)**2) /
  (((sd1**2/n1)**2/(n1-1)) + ((sd2**2/n2)**2/(n2-1))).
COMPUTE p  = 2*(1 - CDF.T(ABS(t), df)).
EXECUTE.

This reproduces Welch's t-test (unequal variances). If you have the raw dataset instead, use Analyze → Compare Means → Independent-Samples T Test.

JASP

Best with raw data

JASP's Independent Samples T-Test module is built for raw observations and has no direct summary-statistics input option.

With raw data:

Open your dataset in JASP.
Select T-Tests → Independent Samples T-Test.
Move the outcome variable to Dependent Variables.
Move the group variable to Grouping Variable.
Check assumption tests and effect sizes as needed.

If you only have summary statistics, R's tsum.test() or Python's ttest_ind_from_stats() above are more direct routes.

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What should you report?

Typically report the mean and standard deviation for each group, followed by the t statistic, degrees of freedom (df), p-value, and an effect size such as Cohen's d when appropriate.