Two Sample T Test Calculator

Two Sample T Test Formula:

\[ t = \frac{Mean1 - Mean2}{\sqrt{\frac{Var1}{n1} + \frac{Var2}{n2}}} \]

Mean1:

Mean2:

Var1:

Var2:

n1:

n2:

T-Statistic (t):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Two Sample T Test?

The Two Sample T Test is a statistical method used to determine if two population means are significantly different from each other. It's commonly used when comparing the means of two independent groups.

2. How Does the Calculator Work?

The calculator uses the Two Sample T Test formula:

\[ t = \frac{Mean1 - Mean2}{\sqrt{\frac{Var1}{n1} + \frac{Var2}{n2}}} \]

Where:

\( Mean1 \) — Mean of the first sample
\( Mean2 \) — Mean of the second sample
\( Var1 \) — Variance of the first sample
\( Var2 \) — Variance of the second sample
\( n1 \) — Size of the first sample
\( n2 \) — Size of the second sample

Explanation: The formula calculates the t-statistic by comparing the difference between means relative to the variability in the data and sample sizes.

3. Importance of T-Test Calculation

Details: The t-test is crucial for hypothesis testing in research, allowing researchers to determine if observed differences between groups are statistically significant or due to random chance.

4. Using the Calculator

Tips: Enter the means, variances, and sample sizes for both groups. All values must be valid (variances > 0, sample sizes > 0).

5. Frequently Asked Questions (FAQ)

Q1: When should I use a two sample t-test?
A: Use it when you want to compare the means of two independent groups and you don't know the population variances.

Q2: What's the difference between one-tailed and two-tailed tests?
A: One-tailed tests check for a difference in one direction only, while two-tailed tests check for any difference in either direction.

Q3: What assumptions does the t-test make?
A: The test assumes that both samples are normally distributed, have approximately equal variances, and that observations are independent.

Q4: How do I interpret the t-statistic?
A: A larger absolute t-value indicates a greater difference between groups relative to the variability in the data.

Q5: What is degrees of freedom in a t-test?
A: For the two sample t-test, degrees of freedom are typically calculated as (n1 + n2 - 2), which affects the critical values for significance.