Testing the Difference between two means(Small Samples)

In testing the difference between two means with small samples, you should first know if the samples are DEPENDENT or INDEPENDENT. If it is INDEPENDENT, you should first perform the F-Test in order to know if the variances are equal or unequal. While if it is DEPENDENT, there is another formula for it.

This is the formula for Small Independent Samples with Variances which are Unequal

 

This is the formula  for Small Independent Samples with Variances which are Equal

  where

This is the steps in finding the test value for Small DEPENDENT Samples 

1. Find the Differences of the values of the pairs of the data

2. Find the mean of the differences by dividing the sum of the differences in step 1 by the number of samples.

3. Find the standard deviation of the differences

4. Find the estimated standard error of the differences by dividing the value that you obtain in the step 3 by the square root of n(number of samples)

5. Find the test value t= (D-μd)/(Sd /√n)

Testing 

By: Dustin Joshua Esquia III-Gold