Statistics - Hypothesis Testing for Two Groups

Using your Statistics Alive! text:

***For problems that require calculations, please show your work to receive full credit.***

1. Complete problem 4 on page 230.

Problem 4. In two separate studies, the actual difference between the means of a treated group and an untreated group is 3 points. However, in one study, the σM1-M2 is very large and so the 3 points is not found to be significant. In the other study, the σM1-M2 is very small and so the 3 points is found to be significant. What might have caused this big difference in the σM1-M2 for the two studies?

2. Complete problem 8 on page 231.

Problem 8. In a study of the effect of a new drug on the alleviation of asthma symptoms, the σM for symptom relief in the patient group that received the new drug is 1.45, and the σM for symptom relief in the group that did not receive the new drug is 1.22. Calculate the σM1-M2.

3. Repeat the SPSS Connection from pages 245–246 on your computer. Note: Please switch "width" of Typtreat variable from 24 to 1 to run the analysis. Copy and paste the SPSS output for the independent samples t test to a Word document.

Here is the information from pages 245 – 246 below:

Looking Ahead

As we saw in Module 17, the ability to reject the null hypothesis depends not only on how different the observed group means are but also on what level of Type 1 error you are willing to accept. In Module 23, we will look at this concept of error in more detail, just as we did in Module 18. As it turns out, dichotomous decisions (reject/do not reject) are less meaningful than reports of actual Type 1 error.

SPSS Connection

Download the file data_depression relief due to med couns.sav from www.sagepub.com/steinberg2e. These data are used in the textbook example.

Alternatively, manually enter the 18 scores from the depression example in Module 20 into the SPSS Data View spreadsheet. Data entry for a t test with equal sample sizes is not intuitively obvious. In the textbook, the data are set up as two groups of 9 clients. In SPSS, all 18 scores (9 + 9) are entered in a single column. Then their group membership (medication vs. counseling) is entered in the second column. Thus, enter the data as follows:

Click on the Variable View tab to define the variables. Name the first variable deprscor, set the decimals at 0, and label the variable as Depression Score. Name the second variable typtreat, and label the variable as Type of Treatment. Label the value as follows: c = counseling and m = medication.

If the file is not already in Data View, click that tab in the lower left of the screen.

In the toolbar at the top of the screen, click on Analyze, then Compare Means, then Independent-Samples T Test. Highlight the variable Depression Score in the left window, and then click on the arrow before the Test Variable window to send the variable into that window. This is the study's dependent variable. Click on the variable Type of Treatment in the left window, and then click on the arrow before the Grouping Variable window to send the variable into that window. This is the study's independent variable. Click on Define Groups beneath the Grouping Variable window. Enter m for Group 1 and enter c for Group 2. Click

4. Complete problem 2 on page 241, using SPSS to complete part c. Copy and paste the SPSS output to the Word document and enter your information for 2a and 2b, and your decision about the null hypothesis for problem 2c.

Problem 2. A large furniture store stations salespeople near its entrance to greet customers and offer assistance in shopping. The salespeople, who work on a commission basis, tell the customers their name and hand them a business card. A psychologist thinks that the salespersons' intrusiveness might cause customers to buy less furniture rather than more furniture. She convinces the store's management to let her study the issue. Customers are randomly selected to either receive or not receive a salesperson's offer of assistance immediately on entering the store. The amount of customers' purchases are then logged as they leave the store. Here are the data:

a. What are the independent and dependent variables in this study?

b. State the null hypothesis and the directional (one-tailed) research hypothesis.

c. Calculate t and compare it with the tabled critical t at the .01 and .05 a levels. Can you reject the null hypothesis?

5. Complete problem 4 on page 264.

Problem 4. State whether the investigator used independent samples, repeated measures, or matched samples:

a. An investigator wants to know if elementary-age children who have experienced the death of a parent are helped by a counseling group consisting of other children who have experienced a death in the family. He randomly selects children for this special counseling group, comparing their emotional adjustment at the beginning of treatment with their emotional adjustment following a year of the specialized group counseling.

b. An investigator wants to know if elementary-age children who have experienced the death of a parent are better helped by a counseling group consisting only of other children who have experienced a death in the family or by a counseling group consisting of children demonstrating a wide range of behavioral and emotional issues. He randomly assigns children to the two groups and compares each group's emotional adjustment following a year of group counseling.

6. Repeat the SPSS Connection from pages 274–275 on your computer. Copy and paste the SPSS output for the paired samples t test to your Word document.

Here is the information from pages 274-275:

SPSS Connection

Download the file data_potato taste due to white blue.sav from www.sagepub.com/steinberg2e. These data are used in the textbook example.

Alternatively, manually enter the 30 scores from the potato example in Module 21 into the SPSS Data View spreadsheet. Data entry for a related-samples t test differs in layout from that of an independent samples t test. The data are set up as in the textbook, as two groups of 15 clients. Thus, enter the data as follows:

See the next page for the data:

Click on the Variable View tab to define the variable. Name the first variable tastwhit, set the decimals at 0, and label the variable as Taste for White Potatoes. Name the second variable tastblue, set the decimals at 0, and label the variable as Taste for Blue Potatoes.

If the file is not already in Data View, click that tab in the lower left of the screen.

In the toolbar at the top of the screen, click on Analyze, then Compare Means, then Paired-Samples T Test. Highlight the variable Taste for White Potatoes in the left window, and then click on the arrow before the Paired Variables window, to send the variable into that window. Click on the variable Taste for Blue Potatoes in the left window and then click on the arrow before the Paired Variables window to send the variable into that window. Click OK. This is what you will see.

7. Complete problem 7 on pages 271–272 using SPSS. Copy and paste the SPSS output to the Word document and enter your information about the decision about the null hypothesis.

Clearly, the difference in participants' taste ratings of white mashed potatoes versus blue mashed potatoes was very large. In a journal article, the results would be reported like this:

t(14) = 3.834, p < .001.

This is read as “t at 14 degrees of freedom is 3.834. There is less than one chance in a thousand that the difference in taste ratings is due to mere chance.” In other words, we can be very confident that the difference in taste ratings is due to the treatment variable, which was the color of the potatoes.

Problem 7. The following data are from a study of aggression in 40 children (20 pairs) after viewing either a violent film or an educational film. Participants were first matched on gender and their typical aggression level. Here are participants' scores on an aggression test given after viewing the film. Higher scores indicate more aggression.

Calculate t and compare it with the one-tailed critical t at the .01 a level. Did the children who viewed the violent film show significantly more aggression?

8. Read the SPSS connection from page 287. Go back to your SPSS output from Module 20 and highlight the output or type the 95 percent confidence interval.

SPSS Connection

Look again at the SPSS output that you produced in Module 20. Here it is again:

The two rightmost cells in the bottom chart show the following values for a 95% confidence interval: −17.614 and −1.053. Now recall that the values reported for confidence intervals for a one-sample t test differed significantly from those that we had calculated in the textbook because SPSS stopped short of the final calculations (see SPSS section in Module 18). We had to use information from the SPSS output to complete the calculations. Fortunately. This is not the case for two-sample t tests. For two-sample t tests, SPSS completes the calculations. Thus, the reported values agree with those we computed in the textbook (within rounding error), so no further calculation is needed.

***For problems that require calculations, please show your work to receive full credit.***

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