Welch's T Test Calculator Statistics

Welch's T Test Formula:

\[ t = \frac{x_1 - x_2}{\sqrt{\frac{var_1}{n_1} + \frac{var_2}{n_2}}} \]

Mean 1 (x1):

Mean 2 (x2):

Variance 1 (var1):

Variance 2 (var2):

Count 1 (n1):

Count 2 (n2):

Welch's T Test Statistic:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Welch's T Test?

Welch's t-test is a statistical test used to compare the means of two independent groups when the variances are not assumed to be equal. It is an adaptation of Student's t-test that is more reliable when the two samples have unequal variances and/or unequal sample sizes.

2. How Does the Calculator Work?

The calculator uses Welch's t-test formula:

\[ t = \frac{x_1 - x_2}{\sqrt{\frac{var_1}{n_1} + \frac{var_2}{n_2}}} \]

Where:

\( x_1 \) — Mean of the first sample
\( x_2 \) — Mean of the second sample
\( var_1 \) — Variance of the first sample
\( var_2 \) — Variance of the second sample
\( n_1 \) — Size of the first sample
\( n_2 \) — Size of the second sample

Explanation: The test statistic measures the difference between the two sample means relative to the variability in the data, accounting for unequal variances.

3. Importance of Welch's T Test

Details: Welch's t-test is particularly important when dealing with real-world data where the assumption of equal variances (homoscedasticity) is violated. It provides a more accurate and robust comparison of means in such situations.

4. Using the Calculator

Tips: Enter the means, variances, and sample sizes for both groups. All variance values must be non-negative, and sample sizes must be positive integers.

5. Frequently Asked Questions (FAQ)

Q1: When should I use Welch's t-test instead of Student's t-test?
A: Use Welch's t-test when the two samples have unequal variances or unequal sample sizes, as it doesn't assume equal variances.

Q2: How do I interpret the t-statistic value?
A: The t-statistic measures the difference between means relative to the variability. A larger absolute value indicates a greater difference between groups.

Q3: What are the assumptions of Welch's t-test?
A: The test assumes that the two samples are independent, normally distributed, but does not assume equal variances between groups.

Q4: How is the degrees of freedom calculated in Welch's t-test?
A: The degrees of freedom are calculated using a more complex formula that accounts for unequal variances: \( \frac{(s_1^2/n_1 + s_2^2/n_2)^2}{(s_1^2/n_1)^2/(n_1-1) + (s_2^2/n_2)^2/(n_2-1)} \)

Q5: Can Welch's t-test be used for paired samples?
A: No, Welch's t-test is designed for independent samples. For paired samples, use a paired t-test instead.