ASSIGNMENT #3

Exercise 42 Effectiveness of an AIDS Prevention Program

Wilcoxon Matched-Pairs Test

Statistical Guide

The Wilcoxon Matched-Pairs test determines the significance of the difference between two sets of ranks obtained from matched pairs. For example, a person's rank on a pretest (before treatment) may be matched with the same person's rank on a posttest (after treatment).

Like other significance tests, when the Wilcoxon Matched-Pairs test indicates that p is equal to or less than .05, we usually declare the difference to be statistically significant (i.e., reject the null hypothesis). The smaller the value of p, the more significant the difference.

Excerpt from the Research Article

SECRETS, an AIDS prevention program, was a theatrical production performed by young actors portraying adolescents.... SECRETS provided HIV/AIDS information and role modeled HIV risk-reduction behaviors.

Data on sexual risk-taking behavior were collected prior to and 3 months after students attended the AIDS prevention program. Sexual risk-taking behavior was considered one variable by summing the frequency of six behaviors [such as number of times a student engaged in sexual intercourse without using a condom and number of sexual partners]. The responses were from 0 to 5 for each behavior with a potential range from 0 to 30.

The sample, at pretest, had a relatively low level of sexual risk-taking behavior. The mean sexual risk-taking score was 1.8 (SD = 3.5).... The sexual risk-taking scores ranged from 0 to 19 for this sample.

As the majority had not had sexual intercourse and there was a great variance in sexual behavior, the sample was categorized as low (51.8) and high (>1.8) sexual risk-taking groups.... The Wilcoxon Matched-Pairs test was performed for the low- and high-risk sexual risk-taking groups.

There was a significant difference between the pre- and posttest sexual risk-taking behavior for the low-risk group, Wilcoxon (129) = -4.9, p = .0000. For the low-risk group, 100 out of 127 (79%) had lower scores at posttest than at pretest.

There was also a significant difference between pre- and posttest sexual risk-taking behavior for the high-risk group, Wilcoxon (52) = -2.1, p = 0.04. For the high-risk group, 32 out of 52 (62%) had lower scores at posttest than at pretest.

The findings of the study suggested support for SECRETS in decreasing sexual risk-taking behavior among high school students.

Questions for Exercise 42

Part A: Factual Questions

1. For all students, what was the average pretest score?
2. Is the distribution for all students on the pretest skewed? If yes, is it a positive or negative skew? (Hint: Consider the mean and the range.)
3. The researchers state that "there was great variance in sexual behavior." What specific statistics were reported that give more information on this matter?
4. A student with a score on the pretest of 2 would have been classified as belonging to which group?
5. For the low-risk group, should the null hypothesis be rejected? Explain.
6. For the high-risk group, should the null hypothesis be rejected? Explain.
7. For which of the tests was the level of significance higher? Explain the basis for your choice.
   1. The one for the high-risk group
   2. The one for the low-risk group
8. Was the test for the low-risk group statistically significant at the .001 level? Explain.
9. Was the difference for the high-risk group statistically significant at the .05 level? Explain.
   Part B: Questions for Discussion
   10. The researchers reported the average pretest score for all students but not the corresponding posttest score. Speculate on why they did not report the latter.
   11. Was there a control group in this study? Explain.
   12. In their article, the researchers mention that the sample included only students who had consented to be in the study and also had parental consent for them to participate. Consent was provided by 36% of parents and participants. Is this a limitation of the study? Explain.
   13. Speculate on why the researchers used the Wilcoxon Matched-Pairs test instead of a t test or ANOVA.
   ASSIGNMENT #3
   Chi Square: II
   Statistical Guide
   To review chi square, see the statistical guide for Exercise 38. Excerpt from the Research Article
   Subjects were inmates incarcerated in Louisiana's only prison for adult female offenders. The crimes for which the inmates were serving time were dichotomized into violent or nonviolent. Violent crimes included murder, manslaughter, negligent homicide, battery, robbery, attempted robbery, and child abuse.
   Table 2 lists the significant relationship between marital status and criminal variables. Marital status was significant for the type of crime committed (x2 = 24.27,p 5 .0001).
   Table 2 [also] indicates the significant relationship between violence and marital status (x2 = 6.31, p 5 .05). Single subjects were least likely to have committed violent crimes; married subjects were most likely to have committed violent crimes. Previously married subjects fell between these two extremes. This is opposite of the predicted relationship.
   Table 3 indicates a significant association in number of inmates who were convicted of various types of crime by occupational status prior to arrest.... Table 3 [also] shows a significant ...relationship between violence and employment status.
   Questions for Exercise 39
   Part A: Factual Questions
   1. Which marital status group had the highest percentage found guilty of theft?
   2. The implied null hypothesis for the first significance test in the excerpt is that there are no true differences in the types of crime committed across marital status groups. Should this null hypothesis be rejected? Explain.
   3. State the implied null hypothesis for the second significance test.
   4. Which of the following relationships is statistically significant at a higher level? Explain the basis for your choice.
      A. Crime type and marital status
      B. Violence and marital status
   5. In Table 2, the chi square value of 6.31 has a footnote, which indicates that p is equal to or less than .05. If you have a statistics book, look up 6.31 with 2 degrees of freedom in the table of critical values. Is it significant at exactly p = .05? Explain.
   6. Is the association between employment status and crime type statistically significant? Explain.

7. Describe in your own words the general nature of the association between employment status and violence. Do not refer to the specific values of the percentages in your statement.

8. Should the null hypothesis for the association you described in question 7 be rejected? Explain.

9. The association between employment status and violence is reported to be significant at the .05 level. Is it also significant at the .01 level? (Hint: You should be able to figure out the answer using logic. If not, refer to the table of critical values using df=1.)

Part B: Questions for Discussion

10. Many researchers report the df associated with each chi square test. The researchers who wrote the excerpt did not. In your opinion, is this an important omission?

11. The researchers state in the excerpt that the association between violence and marital status was the opposite of what they had predicted (i.e., hypothesized). Before reading this excerpt, would you have predicted that married and previously married women would be more likely to commit violent crimes than single women? Explain.

12. Would you be willing to generalize the results in the excerpt to women offenders in states other than Louisiana (that is, would you be willing to assume that what is true of women offenders in Louisiana is also true of women offenders in other states)? Explain.

Exercise 27 : Sexual Harassment in the Navy

t Test for Independent Groups: I

Statistical Guide

The t test is often used to test the significance of the difference between two means. It yields a value of p, which indicates the probability that chance or random sampling errors created the difference between the means. Most researchers declare a difference to be significant when p is equal to or less than .05. The lower the probability, the more significant the difference. Thus, a p of .01 is more significant than a p of .05. When a researcher declares a difference to be statistically significant, he or she is rejecting the null hypothesis. Note that ns means not significant.

Ex cerpt from the Research Article

Women officers and women enlisted personnel [in the Navy] were categorized into two groups based on their survey responses: (1) sexually harassed and (2) not sexually harassed. Sexual harassment was reported by 182 women officers and not reported by 385 women officers. Of the women enlisted, 436 were sexually harassed and 582 were not. T tests were conducted between women who were harassed and those who were not harassed... [See Table 4.]

The significant differences found on questions pertaining to satisfaction with the Navy and intent to serve for at least 20 years suggest that...sexual harassment may negatively impact long-range outcomes in areas such as retention and turnover.

Questions for Exercise 27

Part A: Factual Questions

1. Which group of officers had a higher average score in response to item 1 in Table 4?
2. Is the difference between the two groups of officers on item 1 in Table 4 statistically significant?
3. Using conventional standards, should we reject the null hypothesis for the officers on item 1 in Table 4?
4. The difference is not statistically significant for which pair of means in Table 4?
5. Should the null hypothesis be rejected for the officers on item 2 in Table 4?
6. How many of the differences in Table 4 are statistically significant at the .01 level but not significant at the .001 level?
7. How many of the differences in Table 4 led to rejection of null hypotheses at the .001 level?
8. Both differences on item 7 in Table 4 are statistically significant. Which one is significant at a higher level?
   A. The difference for officers
   B. The difference for enlisted personnel
9. Consider the results for item 3 in Table 4. For which group can we reject the null hypothesis with greater confidence (i.e., for which group is there a smaller chance of making a Type I error)?
   A. Officers
   B. Enlisted personnel
10. The first difference at the top of Table 4 is statistically significant at the .001 level. Is it also significant at the .05 level? (Note: If you have a statistics textbook, examine the table of critical values oft to help you determine the answer to this question.)
11. The first difference at the top of Table 4 is statistically significant at the .001 level. Is it also statistically significant at the .01 level?
12. Consider the three statistics in the row at the bottom of Table 4 (i.e., 2.66, 3.22, and 5.63). Which one is an inferential statistic? To what group (or branch) of statistics do the other two belong?
    Part B: Questions for Discussion
13. Consider the first t test at the top of Table 4. For consumers of research, which of the following is more useful: (a) the value oft, which is 3.35, or (b) the value of p, which is p < .001? (In other words, if you were reading the excerpt for the first time, which value would give you more useful information?) Explain.
14. In your opinion, would it have been a good idea for the researchers to also report the standard deviations associated with each mean in Table 4? Explain.
15. The subtitle of this exercise is "t Test for Independent Groups: I." If you have a statistics textbook, look up this term and describe when it is appropriate to use an "independent t test." (Note: In some books, it is called a t test for uncorrelated data.)

ASSIGNMENT #4

Exercise 35 Effectiveness of Assertiveness Training

Two-Way ANOVA: I

Statistical Guide

To review the general purpose of ANOVA, see the statistical guide for Exercise 33. In a two-way ANOVA, there are two independent variables (usually nominal classification variables) and one outcome variable (usually a continuous score variable). To understand this, examine Figure 1 in the excerpt, where time of testing (pretest and posttest) is one of the classification variables, and level of nursing (nursing assistants, licensed vocational nurses, and registered nurses) is the other one. The outcome variable is discomfort scores.

A two-way ANOVA allows us to examine interactions between the independent variables. For example, if the different types of nurses responded differently to the treatments given between the pretest and posttest, we would say that there is an interaction (i.e., the treatments interacted with level of nursing skill).

Ex cerpt from the Research Article

The participants in this study were the 62 members of the nursing staff working in a 47-bed Department of Veterans Affairs spinal cord injury center.

The purpose of this study was to evaluate the effectiveness of the training course in [reducing discomfort when engaging in difficult] staff interactions. A behavioral approach was selected as the basis for the training. It consisted of a combination of techniques such as lecture and discussion, modeling, and behavior rehearsal, with feedback provided by group members and the trainers....

The study included the Spinal Cord Injury Assertiveness Inventory (SCIAI) as preprogram and postprogram measures to assess the effectiveness of the training.... At the request of the nurse managers, all nursing staff participated in the training, so we had no control group.

A repeated measures ANOVA on the total score of the SCIAI showed no simple effect [i.e., main effect, p = .1069] related to the time of testing [i.e., the mean on the pretest (M = 2.40) for all participants was not significantly different from the mean on the posttest for all participants (M = 2.27)].... However, when we examined the participants' education, we found a statistically significant interaction effect between the time of testing and education (F2,58 = 3.468,p = .0378) (see Figure 1). After the class, the NAs (nursing assistants), all of whom had a high school education, showed an increased discomfort level, whereas the discomfort level of the LVNa (licensed vocational nurses) and the RNs (registered nurses) decreased. However, paired t tests on the various groups' data showed that only the RNs (t = 2.692, df = 36, p = .0107) exhibited a statistically significant change in their discomfort level related to time of testing.

Figure 1 Interaction between time of testing (pretest vs. posttest) and educational level

Questions for Exercise 35

Part A: Factual Questions

1. Should the null hypothesis for the main effect (for time of testing) be rejected? Explain.
2. Does Figure 1 indicate that there is an interaction? Explain.
3. Is the interaction statistically significant at the .05 level?
4. Is the interaction statistically significant at the .01 level?
5. What is the precise probability that the null hypothesis regarding the interaction is true?

6. Did discomfort of the nursing assistants change significantly from pretest to post-test?

7. Should the null hypothesis regarding the change in the registered nurses' level of discomfort be rejected? Explain.

Part B: Questions for Discussion

8. If the findings are correct, would it be desirable to use the training with all types of nurses in the future? Explain.

9. The authors could not use a control group. Is this a limitation of the study? Explain.

10. Suppose you conducted a similar study but used a different type of training that produced a reduction in discomfort scores equally strong in all three groups of nurses. Draw a figure like the one in the excerpt showing this hypothetical result.

ASSIGNMENT #5

Exercise 21 New Parents Project

Correlation Coefficient and Coefficient of Determination: II

Statistical Guide

To review correlation coefficients, see Exercise 19. To review coefficients of determination and percentage of explained variance, see Exercise 20. In addition, you need to know that the interpretation of a coefficient of determination for a negative value of r is the same as for a positive value except that it applies to an inverse relationship. For example, .16 (a positive value) is the coefficient of determination for an r of –.40 (a negative value). Multiplying by 100, we learn that a value of –.40 is 16% away from 0.00 in the negative direction.

Coefficients of determination are always positive because of the squaring. Hence, we use positive values to interpret both positive and negative values of r.

Ex cerpt from the Research Article

The 21 adolescent mothers were between the ages of 16 and 19 years.... [They had been recruited by Parents Project] personnel and then contacted by one of the researchers to solicit their participation. [The instruments that were used were]:

Revised UCLA Loneliness Scale.... Scores range from 20 to 80; the higher the score, the greater the loneliness.

Rosenberg Self-Esteem Scale. Self-esteem was measured using the 10-item...scale. Positively and negatively worded items were included in the scale to reduce the likelihood of response set. When five items are reverse-scored, higher scores indicate greater self-esteem.

Social Support Questionnaire—Short Form. Respondents list the people they can rely on for support in a given set of circumstances and indicate overall level of satisfaction with the support provided.

Center for Epidemiologic Studies Depression Scale for Children [CES-DC; with 20 items]. Scores higher than 15 indicate the presence of depressive symptomatology.

There was a negative relationship between depression and social support (r = –.61).

Social support was positively associated with self-esteem (r = .65) and negatively associated with loneliness (r = –.50). Loneliness was correlated with depression (r = .53) and inversely correlated with self-esteem (r = –.74).

Questions for Exercise 21

Part A: Factual Questions

1. Which value of r in the excerpt represents the strongest relationship?

2. Those who are high on depression tend to have what type of score on social support?

1. A relatively high score.
2. A relatively low score.

3. Those who are high on self-esteem tend to have what type of score on social support?

1. A relatively high score.
2. A relatively low score.

4. Which of the five correlation coefficients shown above has the smallest coefficient of determination? (Try to answer this question without performing any computations.)

5. What is the value of the coefficient of determination for the correlation you referred to in your answer to question 4?

6. What is the percentage of explained variance (variance accounted for) that corresponds to your answer to question 5?

7. To two decimal places, what is the value of the coefficient of determination for the relationship between loneliness and self-esteem?

8. To two decimal places, what is the percentage of explained variance (variance accounted for) that corresponds to your answer to question 7?

9. To two decimal places, for the relationship between depression and social support, what is the percentage of variance accounted for?

Part B: Questions for Discussion

10. Would you characterize any of the relationships in the excerpt as being "strong"? Explain.

11. Before this study was conducted, would you have hypothesized that the relationship between loneliness and depression would be direct or inverse? Explain.

12. Would you be willing to generalize the results of this study to all adolescent mothers in the country? Explain.

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