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# Statistics Exercise Essay Sample

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## Statistics Exercise Essay Sample

Exercise 16: Mean and Standard Deviation
1. The researchers analyzed the data they collected as though it were at what level of measurement?
a. Nominal
b. Ordinal
c. Interval/ratio
d. Experimental
Answer: c. The researchers analyzed the data as though it were at the interval/ratio level since they calculated means (the measure of central tendency that is appropriate only for interval/ratio level data) and standard deviations (the measure of dispersion for interval/ratio data) to describe their study variables.

2. What was the mean posttest empowerment score for the control group? Answer: Mean = 97.12.

3. Compare the mean baseline and posttest depression scores of the experimental group. Was this an expected finding? Provide a rationale for your answer. Answers may vary. The experimental group subjects scored lower on the depression posttest (mean = 13.36 vs. the baseline score of mean = 14.00), meaning that they were less depressed after the completion of the empowerment program. This was an expected finding, because the researchers hypothesized that the empowerment program would be beneficial to ESRD patients and result in a decrease in their depression scores. However, the difference in the depression baseline and posttest means for the experimental group was only 0.64, which is less than what might have been expected.

4. Compare the mean baseline and posttest depression scores of the control group. Do these scores strengthen or weaken the validity of the research results? Provide a rationale for your answer. Answer: The mean baseline and posttest depression scores of the control group were identical. Both means equaled 10.40, which indicates that there was no change in the level of depression of the control group subjects from baseline to posttest. This result strengthens the validity of the study findings, indicating that the empowerment program resulted in a decrease in the depression scores for the experimental group.

5. Which group’s test scores had the least amount of variability or dispersion? Provide a rationale for your answer. Answer: The experimental group’s empowerment posttest scores had the smallest amount of dispersion or variability, as indicated by the smallest SD of 7.28.

6. Did the empowerment variable or self-care self-efficacy variable demonstrate the greatest amount of dispersion? Provide a rationale for your answer. Copyright © 2007 by Saunders, an imprint of Elsevier Inc.

Answer: The experimental group’s baseline self-care self-efficacy scores had the greatest dispersion as evidenced by the largest SD of 14.88.

7. The mean ( X ) is a measure of ________________ __________________ of a distribution while the SD is a measure of _____________________ of its scores. Both X and SD are _________________ statistics.

Answer: The mean ( X ) is a measure of central tendency of a distribution while SD is a measure of dispersion of its scores. Both X and SD are descriptive statistics.

8. What was the mean severity for renal disease for the research subjects? What was the dispersion or variability of the renal disease severity scores? Did the severity scores vary significantly between the control and the experimental groups? Is this important? Provide a rationale for your answer.

Answer: The mean severity score for renal disease was 6.74 and was provided in the Relevant Study Results. The dispersion of the renal disease severity scores was SD = 2.97, with the range of severity scores being 0–10. There was no significant difference in renal disease severity scores for the control and the experimental groups as indicated in the Relevant Study Results. It is important to indicate that the research subjects were similar in demographic characteristics at the start of the study, and the differences noted in the study variables are assumed to be due to the treatment and not to differences in the groups at the start of the study.

9. Which variable was least affected by the empowerment program? Provide a rationale for your answer. Answer: The subjects’ mean or average depression scores showed the least change as compared to their baseline values (only 0.64 points as compared to 6.64 points for empowerment and 6.44 points for self-care self-efficacy). However, it is important to note that the mean score for the depression scale was lower than for the empowerment and self-care self-efficacy scales.

10. Was it important for the researchers to include the total means and SDs for the study variables in Table 2 to promote the readers’ understanding of the study results? Provide a rationale for your answer.

Answers may vary. No, it was not important to the readers’ understanding to have the total means and SDs for the study variables. The main focus of the table was to describe (using X and SD) the study variables for the experimental and control groups. Although it is interesting to have the total sample means and SDs, these do not add to the overall understanding of the information presented in this study. These total means and SDs for study variables are not useful in determining sample size for future studies or for conducting meta-analyses of several studies’ results.

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