Welch’s t-Test – How and When to Use it

Welch’s t-test
The Welch’s t-test is also called unequal variances t-test that is used to test if the means of two populations are equal. This test is different from the Student’s t-test and is normally applied when the there is difference in variance between the two population variances. It can also be applied when the sample sizes are unequal.

Learn about paird-samples t-test here
 
When to use Welch’s t-test
The Welch’s t-test can be applied in the following scenario

• When the distribution is assumed to be normal
• When the samples have unequal variances
• Sample sizes are unequal

See a solved example here

Procedure in Performing Welch’s t-test
Step 1: State your null and alternate hypothesis

H₀: μ₁ = μ₂
H_a: μ₂ ≠ μ₁

Here the null hypothesis states that the means of the two populations are the same
The alternate hypothesis states that the means of the two populations are not the same
So a test is needed to decided this!

Step 2: Calculate the means of the two samples
Take the sum of of each sample and divide by the total number of items

Step 3: Calculate the standard deviation of the two samples
Standard deviation can be found using the formular

 Don’t worry about this formular, it would become clearer when we take an example.

Step 4: Calculate the t-value using the formula

 where

•   is the mean of the first sample
• s₁ is the standard deviation of the first sample
• N₂ is the first sample size
• the same is calculated for the second sample

Step 5: Calculate the degrees of freedom

The degrees of freedom given by v is calulated using the formular belows:

where v1 is the degrees of freedom from the first sample and is given by the formula
v₁ = N₁ – 1

and v₂ is the degrees of freedom from the second sample and is given by the formula
and v₂ = N₂ – 1

Step 6: Compare the calculated t with the tabulated t
Normally, the calulcated value of t (called the test statistic) would either be greater thanor less than the tabulated value of t(called the critical value)

Step 7: Draw your conclusion
The conclution would be wether the null hypothesis is accepted or rejected based on the problem being solved.
If the value of the test statistic is greater than the critical value, then we reject the null hypothesis. Otherwise  the null hypothesis is accepted if the test statistic is less than(or within) the critical value.
Try a sample exercise solved here
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