EXERCISE 31

Exercise 31: t-TEST FOR DEPENDENT

GROUPS



Exercise 31: t-TEST FOR DEPENDENT

What are the two groups whose results are reflected by the t ratios in Tables 2 and 3?

Solution

This study is based on quasi experimental with a one group pretest and post, the two groups that are used in the study and were reflected by the t ratios in table 2 & 3 are 3-Months and 6-Months.

Which t ratio in Table 2 represents the greatest relative or standardized difference between the pretest and 3 months outcomes? Is this t ratio statistically significant? Provide a rationale for your answer.

Solution

Table 2 represents the t ratios results for the health-promotion program's effects on cardiovascular risk factors, it can be seen from the table that Cholesterol variable has the greatest relative or standardized difference of around 3.8 units between the pretest and 3 months outcome. The t value for cholesterol variable is significant as it is sig. value is less than 0.05 which is the level of significance, it has been mentioned in the note that t values with a “*” sign are significant values.

Which t ratio listed in Table 3 represents the smallest relative difference between the pretest and 3 months? Is this t ratio statistically significant? What does this result mean?

Solution

Table 3 represents the t ratios results for the effects on health behaviors, results in table 3 suggest that exercise and smoking behavior variables has no relative or standardized difference between the pretest and 3 months outcome. The t value for exercise variable is significant as it is sig. value is less than 0.05 which is the level of significance, however, the magnitude of t value for smoking behavior i.e. -1.45 is not significant as it has been mentioned in the note that t values with a “*” sign are significant values.

What are the assumptions for conducting a t-test for dependent groups in a study? Which of these assumptions do you think were met by this study?

Solution

Assumptions

The two primary requirements for the paired samples t test to produce accurate results are independent observations and normality.

The first assumption of the paired t test is independent observations. Observations in a study are independent to the extent that each observation is not predictive of another observation in the study. Note that it is the scores within each group that must be independent of each other (or more precisely, the difference scores that need to be independent). For example, assume that in the previous hypothetical stress study, the researcher tested multiple members of one family. It is plausible that the difference scores would not be independent, because it is likely that stress would influence the family members in a near identical way.

The second assumption of the paired t test is that the population distribution of difference scores is normal. Partly because of the Central Limit Theorem, however, this assumption can typically be violated as long as the sample size is reasonably large. “Reasonably large” is often defined as n > 30; however, as long as the departure from ...