MEAN AND STANDARD DEVIATION

August 7th, 2017

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MEAN AND STANDARD DEVIATION

STATISTICAL TECHNIQUE IN REVIEW

The mean ( ) is a measure of central tendency for a set of data and is the arithmetic average calculated for the data. (Please refer to Exercise 15 for further information about the mean). The standard deviation (SD) is a measure of dispersion and is the average amount of points by which the scores of a distribution vary from the mean. When the scores of a distribution deviate from the mean considerably, the SD or spread of scores is large. When the degree of deviation of scores from the mean is small, the SD or spread of the scores is small. Both the and SD are descriptive statistics calculated to describe study variables (Burns & Grove, 2007).
RESEARCH ARTICLE
Source: Tsay, S. L., & Hung, L. O. (2004). Empowerment of patients with end-stage renal disease: A randomized controlled trial. International Journal of Nursing Studies, 41 (1), 59–65.
Introduction
Tsay and Hung (2004) conducted a randomized controlled trial examining the effectiveness of an empowerment program on empowerment level, self-care self-efficacy, and depression in patients with end-stage renal disease (ESRD). The researchers used the Empowerment Scale, the Strategies Used by People to Promote Health Tool, and the Beck Depression Inventory to collect data from the patients on their level of empowerment, self-care self-efficacy, and depression, respectively. The scales were administered to both the control (n = 25) and the experimental (n = 25) groups at baseline and 6 weeks after the program was completed. The control group, experimental group, and total sample’s empowerment, self-care self-efficacy, and depression baseline and posttest means and standard deviations are presented in Table 2 on p. 118.
Relevant Study Results
“The sample consisted of 50 hemodialysis patients. … Mean perceived renal disease severity was moderately severe (mean = 6.74, SD = 2.97, range = 0–10), and the mean length of dialysis was 52.56 months (SD = 36.51). There were no differences in clinical and demographic characteristics of the patients between the groups (p <0.05). The data indicates homogeneity of subjects across the groups” (Tsay & Hung, 2004, p. 61). “This study found that there were significant differences in improvement of empowerment, self-care self-efficacy, and depression in patients who were in the intervention group using empowerment strategies than with the control group patients. …The results from this study suggest that empowerment techniques might have an important role for patients in self-management of ESRD. … The study provides a foundation for future studies of empowerment interventions for self-managing of ESRD patients” (Tsay & Hung, 2004, pp. 63–4).

TABLE 2 Description of Studied Variables in Baseline and Post-test Between Groups

Tsay, S. L., & Hung, L. O. (2004). Empowerment of patients with end-stage renal disease: A randomized controlled trial. International Journal of nursing Studies, 41 (1), p. 62.
STUDY QUESTIONS
1.   The research hypothesis for the Tsay and Hung (2004) study can be formulated as follows: “Patients with ESRD who obtain the empowerment program have higher levels of empowerment and self-care self-efficacy and are less depressed than those who do not receive the program.” State the null hypothesis for this study.
2.   What was the average baseline depression score of the experimental group subjects?
3.   Compare the baseline and the posttest means of the self-care self-efficacy variable for the experimental group. Was this an expected finding? Provide a rationale for your answer.
4.   Which group showed more variability or greater dispersion in their depression posttest scores? Provide a rationale for your answer.
5.   What was the arithmetic average of all empowerment posttest scores collected in this study?
6.   What variable was affected the most by the empowerment program? Is this an expected result? Provide a rationale for your answer.
7.   On average, how long had the ESRD patients been on dialysis? Was there a significant difference between the control and the experimental groups in the length of time they had been on dialysis?
8.   The self-care self-efficacy posttest’s   = 96.00 means that:
a.   the total sample for the study was 96 subjects.
b.   96 was the average self-care self-efficacy posttest score for the experimental group.
c.   96 was the lowest score the participants could get in order to be accepted into the experimental group.
d.   the difference between the experimental and control groups was 96 for self-efficacy.
9.   The control group’s baseline empowerment SD = 8.99. What does this statement mean?
ANSWERS TO STUDY QUESTIONS
1.   The null hypothesis is: “There is no difference in the levels of empowerment, self-care self-efficacy, and depression of patients with ESRD who attend an empowerment program versus those who do not.”
2.   The average or mean baseline depression score of the experimental group was 14.00.
3.   The experimental group’s mean self-care self-efficacy posttest score (mean = 96.00) was 6.44 points higher than its baseline mean score (mean = 89.56) because on average the experimental group subjects scored higher on the posttest than at baseline or the beginning of the study. This was an expected finding because it was hypothesized that after the completion of the empowerment program, the experimental group’s self-care self-efficacy skills would improve. This finding indicates that the empowerment intervention had a positive impact on the self-care self-efficacy of ESRD patients.
4.   The experimental group’s posttest scores were slightly more dispersed as demonstrated by the larger SD = 10.55, as opposed to the SD = 10.34 for the control group. But there is really minimal difference in the SD for both groups.
5.   Mean = 101.08. The arithmetic average or mean of all empowerment posttest scores collected in this study was listed in Table 2 under total group mean.
6.   The experimental subjects’ mean empowerment scores showed the greatest increase from baseline to posttest, with a 6.64 point increase as compared to a 6.44 point increase for self-care self-efficacy and a 0.64 point decrease for depression. This is an expected result because the intervention was an empowerment program and one would expect that this type of program would have a greater effect on empowerment level and also on the self-care self-efficacy more than on the depression scores.
7.   The Relevant Study Results indicated that the mean or average length of time on dialysis was 52.56 months. The article indicated that there was no significant difference between the control and experimental groups in clinical and demographic characteristics (p <0.05), so there was no significant difference in length on time on dialysis for the two groups.
8.   Answer: b. 96 was the average self-care self-efficacy posttest score for the experimental group. Mean is an arithmetic average of the scores of a distribution (in this case, a distribution of the posttest self-care self-efficacy scores of the experimental group).
9.   The control group’s baseline empowerment SD = 8.99 indicates that one standard deviation from the mean for the empowerment variable equaled 8.99 and that this SD indicates the amount of dispersion or spread of the scores in the control group at baseline.

Name:_____________ _____________________________ Class: ____________________
Date: _________________________________________________________________________________
? EXERCISE 16    Questions to be Graded
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
2.   What was the mean posttest empowerment score for the control group?
3.   Compare the mean baseline and posttest depression scores of the experimental group. Was this an expected finding? Provide a rationale for your answer.
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.
5.Which group’s test scores had the least amount of variability or dispersion? Provide a rationale for your answer.
6.   Did the empowerment variable or self-care self-efficacy variable demonstrate the greatest amount of dispersion? Provide a rationale for your answer.
7.   The mean ( ) is a measure of _____________ ______________ of a distribution while the SD is a measure of _______________________ of its scores. Both   and SD are _______________________ 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.
9.   Which variable was least affected by the empowerment program? Provide a rationale for your answer.
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.
(Grove 117)
Grove, Susan K. Statistics for Health Care Research: A Practical Workbook. W.B. Saunders Company, 022007. VitalBook file.