Raw Data Independent Samples t-Test Calculator

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Group 1

Enter values separated by spaces, commas, or newlines. Non-numeric entries will be ignored.

Group 2

Enter values separated by spaces, commas, or newlines. Non-numeric entries will be ignored.

Hypothesis & Significance

Default is 0, testing if means are equal.

Default is 0.05 (5% significance level).

Results

Please enter valid raw data above (at least two numeric values per group) and click "Calculate".

Sample Distributions (Normal Approximation)

Export Results

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How to Use This Independent Samples t-Test Calculator (Raw Data)

  1. Paste your raw data: Enter the numeric values for each group into the appropriate text boxes. You can separate values with commas, spaces, or line breaks.
  2. Choose your significance level (α): Typically set to 0.05, this determines the threshold for rejecting the null hypothesis.
  3. Run the analysis: Click the "Calculate" button to perform the test.
  4. Review the variance test: The calculator first performs Levene’s test to assess whether the two groups have equal variances.
  5. Interpret the results:
    • If variances are equal, the calculator uses the Student's t-test.
    • If variances differ significantly, it uses the Welch's t-test.
    • You'll see the t-statistic, degrees of freedom, and p-value.
  6. Make a conclusion: If the p-value is less than your chosen α, you can reject the null hypothesis and conclude that the group means differ significantly.

Note: This calculator requires raw numerical data for both groups. If you only have summary statistics (means, standard deviations, sample sizes), use the summary-based t-test calculator instead.

Theoretical Background: Independent Samples t-Test

The independent samples t-test is designed to assess whether the means of two unrelated groups differ significantly. It assumes that the data is approximately normally distributed and that the samples are independent.

  • Null hypothesis (H₀): The group means are equal (μ₁ = μ₂).
  • Alternative hypothesis (H₁): The means are not equal (μ₁ ≠ μ₂).
  • The test calculates a t-value based on the difference in group means, standard deviations, and sample sizes.
  • This t-value is then used to compute a p-value, which indicates whether the observed difference is statistically significant at a chosen α level (e.g., 0.05).

Depending on the variance equality (see below), the calculator applies either Student’s or Welch’s version of the t-test.

Testing for Equality of Variances

Before running a t-test, it’s important to determine whether the two groups have similar variability. This affects which version of the t-test should be used:

  • Levene’s test is used here to check if the group variances can be considered equal. It’s a robust test that doesn’t assume normal distribution.
  • If Levene’s test indicates equal variances (p ≥ α), the Student’s t-test is applied.
  • If variances differ significantly (p < α), the calculator uses the Welch’s t-test, which adjusts for unequal variances and sample sizes.

This automatic selection helps ensure more accurate and reliable statistical inference.