Question

In: Statistics and Probability

How are paired t-tests different from two-sample t-tests? 1. When are they used: population parameters 2....

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

Solutions

Expert Solution

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 - µD) / [SD/sqrt(n)]

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

t = (X1bar – X2bar) / sqrt[Sp2*((1/n1)+(1/n2))]

Where Sp2 is pooled variance

Sp2 = [(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


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