Question

How are paired t-tests different from two-sample t-tests?

1. When are they used: population parameters

2. Data types they are used on

3. Which sample statistics are used as estimates for the population parameter

4. Test statistics, including conditions and Minitab command

Answer 1

How are paired t-tests different from two-sample t-tests?

1. When are they used: population parameters?

We use the paired t test if the given data is related to each other or samples are dependent. When samples are independent then we use the two sample t test. Population parameter for the paired t test is considered as the difference between two means of paired populations while the population parameter for the two sample t tests is considered as the difference between the two means of two independent populations.

2. Data types they are used on

For paired t tests, we use the paired data, while using two sample t test, we use the independent samples. In paired t test, there is one to one relationship between the observations of the two samples.

3. Which sample statistics are used as estimates for the population parameter?

For paired t test, we use the sample statistic as Dbar which is the mean of the differences between the paired observations. For two sample t test, we use the sample statistic as the difference between the two sample means.

4. Test statistics, including conditions and Minitab command

Test statistic for paired t test is given as below:

t = (Dbar - µ_D) / [S_D/sqrt(n)]

Test statistic for two sample t test is given as below:

t = (X1bar – X2bar) / sqrt[S_p²*((1/n1)+(1/n2))]

Where S_p² is pooled variance

S_p² = [(n1 – 1)*S1^2 + (n2 – 1)*S2^2]/(n1 + n2 – 2)

By using Minitab, follow the following commands

Open Minitab > Click on Stat > Basic Statistic > select 2 sample t or paired t > input ranges > click OK