The p-value is the probability of obtaining test results at least as extreme as the observed results, assuming the null hypothesis is true.

What is the standard alpha significance level?

The conventional threshold in scientific research is alpha = 0.05 (a 5% probability of a Type I false positive error).

What is Welch's t-test?

Welch's t-test is an adaptation of the two-sample t-test that is more reliable when the two samples have unequal variances and sample sizes.

Mathematics Tools• Inferential Stats

Student's T-Test Calculator & Hypothesis Tester

Perform statistical hypothesis testing to determine whether there is a statistically significant difference between the means of two independent or paired groups.

Dataset calculations run client-side. Zero data uploaded.

Sample Datasets

Sample 1 (Group A)

Sample 2 (Group B)

Welch's T-Statistic

t = 5.546

Statistically Significant (p < 0.05)

Group 1: N = 7, Mean = 28.71, SD = 2.69

Group 2: N = 7, Mean = 21.14, SD = 2.41

Degrees of Freedom (df): 11.9Std Error: 1.365

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How to Use Student's T-Test Calculator

Select T-Test Type

Choose Independent Two-Sample (equal/unequal variance) or Paired T-Test.

Enter Datasets

Paste comma- or space-separated numbers for Sample 1 and Sample 2.

Review T-Score & Statistics

Inspect sample sizes, means, standard deviations, t-value, and degrees of freedom.

About Student's T-Test Calculator

Computes t = (Mean1 - Mean2) / sqrt(s1^2/n1 + s2^2/n2) with Welch-Satterthwaite degrees of freedom for unequal variances to assess statistical significance.

Supported Formats

Raw NumbersCSVWhitespace Separated

Operational Limits

•Assumes approximately normally distributed sample data for small sample sizes.

Key Features

Supports Independent Two-Sample (Student's and Welch's) and Paired T-Tests
Calculates mean, variance, standard deviation, and pooled standard error
Computes exact t-statistic and degrees of freedom (df)
P-value approximation and hypothesis decision (reject / fail to reject null at alpha = 0.05)
One-click copy of statistical summary for academic reports

Frequently Asked Questions

Use an independent t-test for two distinct groups (e.g. control vs treatment), and a paired t-test for the same subjects tested before and after an intervention.

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