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**Assignment 4:** **t****Tests**

**The one sample** **t****Test for a** * mean* (5 points) Reminder: Please include all SPSS output by pasting the relevant tables/figures from SPSS in your assignment.

A market research company found that children in America between the ages of 5 and 12 years old watch on average 196 minutes of TV per day. A survey was conducted by randomly selecting 20 British children within this age group to see if British Children are statistically different in the amount of TV watched per night from their American counterparts. Use data = Assignment 4 data one sample ttest.sav

Based on this example answer the following questions:

1. Why is a one sample *t* Test the most appropriate technique to test the example?2. State (in words) the *null* and the *alternate* hypothesis.3. Use the data set provided and conduct a one sample *t* Test using SPSS.

__Hint:__ Once you are in the **One Sample** **t** **Test** dialogue box in SPSS, your test value will be 196 (minutes).

4. What is the *Mean* number of minutes watched per night?5. What is the *t* statistic?6. What is the *p* value or significance?7. Discuss the findings in regard to the *null* and *alternate*hypothesis using Morgan et al. (2002) pp. 10-12.

**The two samples** **t****test for the equality of** **Means****between two groups of people** (5 points)

A survey was conducted by randomly selecting 20 American children and 20 British children to determine if there is a statistical difference in amount of time they watch TV. Use data = Assignment 4 two sample ttest.sav

Based on this example answer the following questions:

1. Why is a two samples *t* test most appropriate techniquefor this research example?2. State (in words) the *null* and the *alternate* hypothesis.3. Use the data set provided and conduct a two samples *t* test using SPSS. Use the SPSS command/actions listed below to conduct the analysis:

__Hint__: Once you are in the **Independent-Samples** **t****Test** dialog box in SPSS, you will have to Define your groups.

1. Click on **Define Groups**2. In the area next to **Group 1**: type **1**, and in the next to Group **2**: type **2**3. Click on **Continue**4. Click on **OK**

4. What is the *mean* number of minutes of TV watched by the British children?5. What is the *mean* number of minutes of TV watched by the American children?6. In the Equal Variances Assumed row, what is the *t* statistic?7. What is the *p* value or significance?8. Discuss the findings in regard to the *null* and *alternate*hypothesis using Morgan et al. (2002) pp. 10-12. 9. Why might these results be inaccurate due to the technique of Random Sampling (see Creswell, 2008)?

**The** **dependent** **samples** **t****test for the equality of** **Means****for the same people between pretest and posttest** (5 points)

An outpatient clinic for clinical depression commissioned an evaluation of the efficacy of their services. They randomly sampled and administered a normed clinical depression inventory to 30 patients during two time points. The first time point was just before the first therapy session. The second session was after the sixth therapy session. The administrators of the outpatient clinic wanted to know if there was a significant reduction in clinical depression after the size sessions of therapy. Also, the wanted to know how much of a difference was found between the two time periods in terms of a small, medium, or large difference. Use data = Assignment 4 dependent sample ttest.sav

Based on this example answer the following questions:

1. Why is a dependent samples *t* test most appropriate technique for this research example?2. State (in words) the *null* and the *alternate* hypothesis.3. Use the data set provided and conduct a dependent samples *t* test using SPSS. 4. What was the *mean* clinical depression score at the first time point before therapy was given?5. What was the *mean* clinical depression score after therapy was given?6. What is the *t* statistic?7. What is the *p* value or significance for the dependent samples t test?8. Discuss the findings in regards to the *null* and *alternate*hypothesis using Morgan et al. (2002) pp. 10-12.

9. Calculate the Effect size (Cohen’s *d*) for the paired samples *t* test output: (5 points)

Use the following equation: *d* = *M*1 – *M*2/*σ* D (Mean of Post-total Social Competency – Mean of Pre-total Social Competency)/Paired Differences Std. Deviation

Cohen (1988) defined effect sizes as "small, *d* = .2," "medium, *d* = .5," and "large, *d* = .8", stating that "there is a certain risk in inherent in offering conventional operational definitions for those terms for use in power analysis in as diverse a field of inquiry as behavioral science" (p. 25).

Discuss the meaning of the findings (1-2 sentences).

Cohen, J. (1988). *Statistical power analysis for the behavioral sciences* (2nd ed.).

Hillsdale, NJ: Lawrence Earlbaum Associates.

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