Welch's T-Test Calculator

Formula

The formula to calculate the T-Score in Welch's T-Test is:

\[ t = \frac{M1 - M2}{\sqrt{\frac{s1^2}{n1} + \frac{s2^2}{n2}}} \]

Where:

\(t\) is the t-score
\(M1\) and \(M2\) are the means of the two groups
\(s1\) and \(s2\) are the standard deviations of the two groups
\(n1\) and \(n2\) are the sizes of the two groups

What is Welch's T-Test?

Welch's T-Test is a statistical hypothesis test used to compare the means of two populations that may have different variances. It is an adaptation of the Student's T-Test and is more reliable when the two samples have unequal variances and unequal sample sizes. The test is named after British statistician Bernard Lewis Welch and is often used in scientific research to determine whether there is a significant difference between two groups.

Example Calculation 1

Let's assume the following values:

Mean of Group 1 (M1) = 5.0
Mean of Group 2 (M2) = 3.0
Standard Deviation of Group 1 (s1) = 1.2
Standard Deviation of Group 2 (s2) = 1.5
Size of Group 1 (n1) = 30
Size of Group 2 (n2) = 25

Using the formula:

\[ t = \frac{5.0 - 3.0}{\sqrt{\frac{1.2^2}{30} + \frac{1.5^2}{25}}} = 5.3838 \]

The T-Score is 5.3838.

Example Calculation 2

Let's assume the following values:

Mean of Group 1 (M1) = 10.0
Mean of Group 2 (M2) = 8.0
Standard Deviation of Group 1 (s1) = 2.0
Standard Deviation of Group 2 (s2) = 2.5
Size of Group 1 (n1) = 40
Size of Group 2 (n2) = 35

Using the formula:

\[ t = \frac{10.0 - 8.0}{\sqrt{\frac{2.0^2}{40} + \frac{2.5^2}{35}}} = 3.7893 \]

The T-Score is 3.7893.