Hypothesis Testing got simple ! Part 3

 <<< Click here go one step back

So far we have covered One Sample and two sample T-Tests. Let's now understand the third one, which is :

3.  Paired t-test

In this test, we hypothesize that two samples are same. However in this case, the samples are related to each other (can be paired) e.g.

Few students started taking a tuition course and we need to see if there is any difference between their test scores before tuition and post tuition course.

We are using a different data from what we have used for one and two sample T-test . Download the data using following link :

Data for tests

Download the data, keep it at a location and assign the location to library "a" in SAS.

In the data, we have 3 columns : Id of student, his/her score before taking tuition and after taking tuition. Our hypothesis is " The score in pre-tuition phase and post-tuition phase are same.

H0   :   Score (pre) = Score (Post)

   H1   :   Score (pre)  ~= Score (Post)

Let's now run the test on SAS.

Proc ttest data = a.paired;
paired before * after ;
run;

Now as the p value of the test has come > 0.05 or 0.01, we are not able to reject the null hypothesis and hence we can say that score are same.

So we can also say that tuition didn't help or was not effective.

Cut-off p value varies domain to domain. In clinical analysis, generally stringent cut-off is taken as the risk is high.

Also, the hypothesis testing only tests for presence of any relationship but not the strength of relationship. For strength of relationship we generally refer to stats such as coefficient of correlation.

Next Part of the Series : Hypothesis Testing got Simple ... ANOVA

                                 Also check : Chi-Square Test

Enjoy reading our other articles and stay tuned with ...

Kindly do provide your feedback in the 'Comments' Section and share as much as possible.