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: