STATISTICAL TECHNIQUE IN REVIEW

Mean (X) is a measure of central tendency and is the sum of the raw scores divided by the number of scores being summed. Standard deviation (SD) is calculated to measure dispersion or the spread of scores from the mean (Burns & Grove, 2007). The larger the value of the standard deviation for study variables, the greater the dispersion or variability of the scores for the variable in a distribution. (See Exercise 16 for a detailed discussion of mean and standard deviation.) Since the theoretical normal curve is symmetrical and unimodal, the mean, median, and mode are equal in the normal curve (see Figure 18-1). In the normal curve, 95% of the scores will be within 1.96 standard deviations of the mean, and 99% of scores are within 2.58 standard deviations of the mean. Figure 18-1 demonstrates the normal curve, with a.X = 0. The formula used to calculate the 95% rule to determine where 95% of the scores for the normal curve lie is: X±1.96(SD)

The formula used to calculate the 99% rule to determine where 99% of the scores for the normal curve lie is:

X ± 2.58 (SD)

FIGURE 18-1 • The Normal Curve

Mean

Median

Mode

Standard deviation -3

Zscore

-2.58

-+2.58

131

133

Mean, Standard Deviation, and 95% and 99% of the Normal Curve

EXERCISE 18

Participants reported a net increase in weight from 3 months prior (M= 2.4 Ib, SD – 12.9 Ib) and 12 months prior (M = 10.9 Ib, SD = 19.1 Ib) and that their weight was greater than their ideal weight (M = 9.2 Ib, SD = 22.9 Ib). SDs for the data indicated a wide range on weight at both 3 and 12 months before participation in the study.

Body image scores (0-100 scale) were significantly (F(1 37) = 5.41, p =.03) higher for women (73.1 ± 17.0) than men (60.2 ± 17.0). Although HIV-positive participants had slightly higher body image scores (M = 68.0, SD = 17.0) compared with participants with AIDS (M = 60.5, SD = 18.8), there was no significant difference (F(1 ,7, = 1.56, p —.22) in body image scores between [those with HIV and AIDS]. There was a weak, but significant, inverse association between body image score and weight changes from 3 months prior (r = -.30, p =.04). Body image and weight scores are summarized in Table 1″ (Corless et al, 2004, p. 294).

TABLE 1

Body Image and Weight Measures for Men and Women

GENDER

Male

Female

Mean

Body image

Weight change last 12 months

Weight change last 3 months

Weight relative to ideal

Body weight ratio

SD

Mean

SD

60.22

10.26

16.98

22.40

15.87

22,93

33.97

73.07

11.94

1.47

13.63

14.44

67.56

22.57

34.44

3.05

5.48

53.66

16.93

7.32

Corless, I. B., Nicholas, P. K., McGibbon, C. A., & Wilson, C., (2004). Weight change, body image, and quality of life in HIV disease: A pilot study. Applied Nursing Research, 77(4), p. 294.

“A summary of quality-of-life scores for men and women is shown in Table 2. The scales of the MOS-HIV Quality of Life instrument include General Health Perceptions, Physical Functioning, Role Functioning, Social Functioning, Cognitive Functioning, Pain, Mental Health, Vitality, Health Distress, Quality of Life, and Heath Transition. There were no significant differences between quality of life scores between men and women. Men did have lower scores on some MOS-HIV scales (Cognitive Functioning, Pain, Quality of Life, and Health Transition) and women were lower on others (Vitality and Health Distress). In addition, there were a number of differences in the relationships between quality of life scores, body image, and body weight…. The positive correlations indicated that improved quality of life was associated with improved body image” (Corless et al., 2004, pp. 294-5).

132

EXERCISE 18

Mean, Standard Deviation, and 95% and 99% of the Normal Curve

The data described below are the verbal SAT scores for high school seniors for one year with X = 490 and SD =100 (see Figure 18-2). The formula used to find where 95% of the scores lie is X ± 1.96 (SD). In this example, 490 + 1.96 (100) = 686, and 490 – 1.96 (100) = 294. Thus 95% of scores lie between 294 and 686, expressed as (294, 686). Since 95% of the scores are between 294 and 686, this leaves 5% of the scores outside this interval. Since a normal curve is symmetric, one-half of the scores, or 2.5%, are at each end of this distribution.

To find where 99% of scores lie,Z ± 2.58 (SD), where 490 + 2.58 (100) = 748 and 490 – 2.58 (100) = 232. Thus, 99% of the SAT scores lie between 232 and 748, which is expressed as (232, 748). Since the distribution of these scores is normal, 99% of the scores are between 232 and 748 and 0.5% of the scores are at each end of this distribution.

FIGURE 18-2 ‘ft Distribution of SAT Scores

SD=100

x = 490

Mean

RESEARCH ARTICLE

Source: Corless, I. B., Nicholas, P. K., McGibbon, C. A., & Wilson, C, (2004). Weight change, body image, and quality of life in HIV disease: A pilot study. Applied Nursing Research 77(4), 292-6.

Introduction

The purpose of this pilot study [conducted by Corless and colleagues (2004)] was to investigate the relationships of weight change, body image, length of time with HIV/AIDS diagnosis, and quality of life in individuals with HIV disease (Corless et al., 2004, p. 292). The sample consisted of 40 subjects: 23 men and 17 women. The HIV-positive adults in a primary care clinic were asked to participate, so this study has a sample of convenience. The participants reported an increase in weight, greater than their ideal weight. The body image scores were found to be significantly higher for women, with the HIV-positive participants having slightly higher body image scores. A survey and Medical Outcomes Study-HIV (MOS-HIV) instruments were used as measurement methods for this study. The results indicated that when a person’s weight is higher and closer to his or her ideal, HIV-positive individuals exhibit better quality of life. Thus, “education of clinicians and individuals living with HIV/AIDS should focus on the assessment, management, and evaluation of weight change during the course of HIV disease” (Corless et al., 2004, p. 292).

Relevant Study Results

“The sample consisted of 23 men with a mean age of 42.2 years (SD = 8.2), length of time since diagnosis with HIV was 9.2 years (SD = 5.3); and 17 women with a mean age of 36.8 years (SD = 5.2), and length of time since diagnosis with HIV was 7.2 years (SD = 4.8). For men, 23 were HIV-positive and 9 had a diagnosis of AIDS; and for women, 17 were HIV positive, and 5 had a diagnosis of AIDS. There was no significant difference in demographic characteristics of the sample by age, gender, HIV disease status, and time living with HIV.

Class:

Name:

Date:

EXERCISE 18

Questions to be Graded

1. Assuming that the distribution is normal for weight relative to the ideal and 99% of the male participants scored between (-53.68, 64.64), where did 95% of the values for weight relative to the ideal lie? Round your answer to two decimal places.

2. Which of the following values from Table 1 tells us about variability of the scores in a distribution?

a. 60.22

b. 11.94

c. 22.57

d. 53.66

3. Assuming that the distribution for General Health Perceptions is normal, 95% of the females’ scores around the mean were between what values? Round your answer to two decimal places.

4. Assuming that the distribution of scores for Pain is normal, 95% of the men’s scores around the mean were between what two values? Round your answernto two decimal places.

5. Were the body image scores significantly different for women versus men? Provide a rationale for your

138

EXERCISE 18

Mean, Standard Deviation, and 95% and 99% of the Normal Curve

6. Assuming that the distribution of Mental Health scores for men is normal, where are 99% of the men’s mental health scores around the mean in this distribution? Round your answer to two decimal places.

7. Assuming that the distribution of scores for Physical Functioning in women is normal, where are of the women’s scores around the mean in this distribution? Round your answer to two decimal places.

8. Assuming that the distribution of scores is normal, 99% of HIV-positive body image scores around the mean were between what two values? Round your answer to two decimal places.

9. Assuming that the distribution of scores for Role Functioning is normal, 99% of the men’s scores around the mean were between what values? Round your answer to two decimal places.

10. What are some of the limitations of this study that decrease the potential for generalizing the findings to the target population?

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