Enter the means, standard deviations, and sizes of the two groups into the calculator to determine the t-score in Welch’s t-test.
Welch’S T Test Formula
The following formula is used to calculate the t-score in Welch’s t-test.
t = (M1 - M2) / sqrt((s1^2/n1) + (s2^2/n2))
Variables:
- 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
To calculate the t-score in Welch’s t-test, subtract the mean of the second group from the mean of the first group. Then, divide the square of the standard deviation of the first group by its size and add it to the square of the standard deviation of the second group divided by its size. Take the square root of this sum. Finally, divide the difference of the means by this result.
What is a Welch’S T Test?
A 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.
How to Calculate Welch’S T Test?
The following steps outline how to calculate a Welch’s T Test:
- First, determine the means of the two groups (M1 and M2).
- Next, determine the standard deviations of the two groups (s1 and s2).
- Next, determine the sizes of the two groups (n1 and n2).
- Using the formula t = (M1 – M2) / sqrt((s1^2/n1) + (s2^2/n2)), calculate the t-score.
- Finally, interpret the results of the t-test to determine if there is a significant difference between the means of the two groups.
Example Problem:
Use the following variables as an example problem to test your knowledge:
M1 = 10
M2 = 8
s1 = 2
s2 = 3
n1 = 20
n2 = 25
