Additional problem using the dependent t-test

Let's do an additional problem involving the dependent t test, to make certain that we know how to do it. For this problem lets use one from the textbook. The problem we will now do is on pages 184-186 of the text.

Research Problem: A special program, developed to enhance children's self-concept, is implemented with four- and five-year-old children in Sunny Days Preschool. The intervention lasts six weeks and involves various activities in the class and at home. All the children in the program are pretested and posttested using the Purdue Self-Concept Scale for Preschool Children (PSCS). The test is comprised of a series of 40 pairs of pictures, and scores can range from 0 to 40. The dependent t test will be used to test the hypothesis that students would improve significantly on the posttest, compared with their pretest scores.

Let's put this data into an Excel Worksheet and then calculate the value of the dependent t:

Looking at the data we calculated we can see that the value of the dependent t Stat is 3.50324525 which we can round off to 3.503 (which is the same answer found in the textbook). The probability for this result is .00861227, which is less than .01, however since we are going to set our alpha level at .05, we will say that p < .05, rather than that p = .00861227. We can also see that the critical value for t is 2.01504918 which we will round off to 2.015.

We have all the information we need to complete the six step statistical inference process:

1. State the null hypothesis and the alternative hypothesis based on your research question.
   
   
2. Set the alpha level.
   
3. Calculate the value of the appropriate statistic. Also indicate the degrees of freedom for the statistical test if necessary.
   t = 3.503
   df = n - 1 = 6 - 1 = 5
4. Write the decision rule for rejecting the null hypothesis.
   Reject H₀ if t is >= 2.015
5. Write a summary statement based on the decision.
   Reject H₀, p < .05, one-tailed
6. Write a statement of results in standard English.
   Students who participated in the test-taking course, scored significantly higher on the practice form of the PSCS, than did the control group of students.