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Independent t-test Calculator

Parametric test comparing the means of two independent groups.

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t Statistic

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Overview

The Independent t-test is a null hypothesis significance test used to compare the means of two distinct and unrelated groups. It determines whether the difference between the sample means is statistically significant or if it likely occurred due to random sampling error.

Symbols

Variables

t = t Statistic, M_1 = Mean Group 1, M_2 = Mean Group 2, SE = Std. Error Diff.

t Statistic
Mean Group 1
Mean Group 2
Std. Error Diff.

Apply it well

When To Use

When to use: Use this test when comparing exactly two independent groups measured on a continuous scale. Key assumptions include independence of observations, approximate normality of the data distribution, and homogeneity of variances between the groups.

Why it matters: In psychology, this equation is essential for evaluating the effectiveness of experimental interventions against control groups. It allows researchers to quantify the impact of a variable, such as a new therapy or drug, on a target population's behavior or mental state.

Avoid these traps

Common Mistakes

  • Using it on ordinal data.
  • Failing to check for homogeneity of variance.

One free problem

Practice Problem

A clinical psychologist measures the stress levels of two groups: one practicing mindfulness (m1 = 42) and a control group (m2 = 48). If the standard error of the difference (se) is calculated as 2.4, what is the resulting t-statistic?

Mean Group 142
Mean Group 248
Std. Error Diff.2.4

Solve for:

Hint: Subtract the second group mean from the first, then divide the result by the standard error.

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Wikipedia: Student's t-test
  2. Statistics for Psychology by Arthur Aron, Elaine Aron, and Elliot Coups
  3. Discovering Statistics Using IBM SPSS Statistics by Andy Field (5th ed., 2018)
  4. Field, A. (2018). Discovering Statistics Using IBM SPSS Statistics (5th ed.). SAGE Publications.
  5. Howell, D. C. (2013). Statistical Methods for Psychology (8th ed.). Wadsworth Cengage Learning.
  6. Wikipedia: Student's t-test, section 'Assumptions'.
  7. AQA Psychology A-level Specification (7181, 7182) or equivalent standard A-level Psychology textbook.