math statastics

math homework help

Complete Exercises 11 and 16 in Statistics for Health Care Research: A Practical Workbook, and submit as directed by the instructor.

In order to receive full credit on calculated answers, please show your work. (Use Word's equation editors, etc., and/or provide a short written description as to how you obtained the final result.)

STATISTICAL TECHNIQUE IN REVIEW Most studies describe the subjects that comprise the study sample. This description of the sample is called the sample characteristics which may be presented in a table or the narrative of the article. The sample characteristics are often presented for each of the groups in a study (i.e. experimental and control groups). Descriptive statistics are used to generate sample characteristics, and the type of statistic used depends on the level of measurement of the demographic variables included in a study (Burns & Grove, 2007). For example, measuring gender produces nominal level data that can be described using frequencies, percentages, and mode. Measuring educational level usually produces ordinal data that can be described using frequencies, percentages, mode, median, and range. Obtaining each subject’s specific age is an example of ratio data that can be described using mean, range, and standard deviation. Interval and ratio data are analyzed with the same type of statistics and are usually referred to as interval/ratio level data in this text. RESEARCH ARTICLE Source: Troy, N. W., & Dalgas-Pelish, P. (2003). The effectiveness of a self-care intervention for the management of postpartum fatigue. Applied Nursing Research, 16(1), 38–45. Introduction Troy and Dalgas-Pelish (2003) conducted a quasi-experimental study to determine the effectiveness of a self-care intervention (Tiredness Management Guide [TMG]) on postpartum fatigue. The study subjects included 68 primiparous mothers, who were randomly assigned to either the experimental group (32 subjects) or the control group (36 subjects) using a computer program. The results of the study indicated that the TMG was effective in reducing levels of morning postpartum fatigue from the 2nd to 4th weeks postpartum. These researchers recommend that “mothers need to be informed that they will probably experience postpartum fatigue and be taught to assess and manage this phenomenon” (Troy & Dalgas-Pelish, 2003, pp. 44-5). Relevant Study Results “A total of 80 women were initially enrolled [in the study] . . . twelve of these women dropped out of the study resulting in a final sample of 68.” (Troy & Dalgas-Pelish, 2003, p. 39). The researchers presented the characteristics of their sample in a table format for the experimental and control groups (see Table 1). The researchers found no significant differences between the control and experimental groups for any of the demographic or attribute variables. USING STATISTICS TO DESCRIBE 11 A STUDY SAMPLE EXERCISE STUDY QUESTIONS 1. What demographic variables were included in this study? 2. Which of the demographic variables provided ordinal level data? Provide a rationale for your answer. TABLE 1 ■ Sample Characteristics by Group Variable EXPERIMENTAL GROUP CONTROL GROUP n M SD N M SD Age (yrs) 32 26.72 5.05 35 26.89 5.25 Income (annual)($) 30 $35,675 $23,969 34 $41,450 $17,527 Length of labor (hrs) 30 14.63 7.78 33 12.79 7.2 Return to work (wks) 8 5.0 1.41 9 5.78 .67 Number of hours working per week 8 34.25 9.15 9 36.68 7.02 n % n % Race White 23 92 28 96.55 Black 1 4 0 Interracial 1 4 0 Middle Eastern 0 1 3.45 Marital status Married 25 78.1 3.1 18.8 31 86.1 2.8 8.3 Separated/divorced 1 1 Single 6 3 Education High school 7 21.9 34.4 43.8 6 16.7 41.7 36.2 Some college 11 15 College graduate or higher 14 13 Type of feeding Breast 13 40.6 53.1 6.3 15 41.7 50.0 5.6 Bottle 17 18 Both breast and bottle 2 2 Amount of household and infant care responsibilities All 2 6.3 71.9 15.6 4 11.1 61.1 19.4 Most 23 22 One half 5 7 None 1 3.1 0 Note: Numbers do not always total 32 for experimental group or 36 for control group because of missing data. The percentages do not always total 100% because of missing data. Troy, N. W., & Dalgas-Pelish, P. (2003). The effectiveness of a self-care intervention for the management of postpartum fatigue. Applied Nursing Research, 16(1), p. 40. 76 EXERCISE 11 • Using Statistics to Describe a Study Sample Using Statistics to Describe a Study Sample • EXERCISE 11 77 3. What level of measurement is the data for race? 4. What statistics were used to describe race in this study? Were these appropriate? 5. Could a mean be calculated on the race data? Provide a rationale for your answer. 6. Describe the race of both the experimental and control groups. What does this tell you about the population of this study? 7. What statistics were used to describe age in this study? Were these appropriate? Provide a rationale for your answer. 8. Were the groups similar in age? Provide a rationale for your answer. 9. What was the mode for the type of feeding provided by the experimental and the control groups? Is this mode what you would have expected? 78 EXERCISE 11 • Using Statistics to Describe a Study Sample 10. Did the experimental group earn similar income to the control group? Provide a rationale for your answer. ANSWERS TO STUDY QUESTIONS 1. Demographic variables described in the study were: age, income, length of labor, return to work, number of hours working per week, race, marital status, education, type of feeding, and amount of household and infant care responsibilities. 2. The variables education and amount of household and infant care responsibilities are both measured at the ordinal level since the data for each is sorted into categories that can be rank ordered. With education, high school is the lowest level of education, some college is the next level of education, and college graduate or higher is the highest level of education. Care responsibilities include ordinal data that are ranked from a low of “None” to a high of “All.” 3. The data collected for race is nominal level since race was measured using mutually exclusive categories of White, Black, Interracial, and Middle Eastern that cannot be rank ordered. 4. Frequencies and percentages were used to describe race for the experimental and control groups. Since the data are nominal, frequencies and percentages were appropriate. The researchers might have also identifi ed the mode, which was White. 5. No, a mean cannot be calculated on the race data. A mean can only be calculated on interval and ratio level data that have numerically equal distances between intervals and not on nominal level data that can only be organized into categories. (See Exercises 1, 2, and 3, which are focused on identifying the level of measurements.) 6. Both the experimental and control groups are predominantly White, 92% and 96.55%, respectively. Thus, the sample is predominately White, and the results are refl ective of a White or Caucasian population and not Black, Interracial, or Middle Eastern populations. 7. Age was described for both the experimental and control groups using means and standard deviations. The exact age of the subjects was obtained, providing ratio level data that are descriptively analyzed with means and standard deviations. The researchers might have also provided the range for age for both experimental and control groups. 8. The groups were very similar in age since the mean age for the experimental group was 26.72 and the mean age for the control group was 26.89. The distribution of the ages for the experimental and control groups were also very similar, with standard deviation of 5.05 for the experimental group and 5.25 for the control group. 9. Bottle-feeding was the mode for the experimental (53.1%) and the control (50%) groups since it was the most frequent type of feeding used by both groups. Either a “no” or “yes” answer is correct here as long as you provide a rationale. No, one might expect the mode to be breastfeeding since these were fi rsttime mothers (primiparous) and breastfeeding has such positive outcomes for both infant and mother. Yes, one might expect bottle-feeding to be the mode since many of these mothers planned on returning to work. 10. No, the incomes were not similar for the two groups, but nor was the income signifi cantly different for the groups. The means (M) and standard deviations (SD) for income indicate that the experimental (M = $35,675; SD = $23,969) and control groups (M = $41,450; SD = $17,527) were different. The control group subjects had an M, or mean, that was $5,775 higher than the experimental group, and the SD was much higher ($6,442) for the experimental group, indicating a larger range of incomes for that group. However, the narrative from the study indicated that the groups were not signifi cantly different for any of the demographic variables. Name: ___________________________________________________ Class: ______________________ Date: _________________________________________________________________________________ ■ EXERCISE 11 Questions to be Graded 1. What demographic variables were measured at least at the interval level of measurement? 2. What statistics were used to describe the length of labor in this study? Were these appropriate? 3. What other statistic could have been used to describe the length of labor? Provide a rationale for your answer. 4. Were the distributions of scores similar for the experimental and control groups for the length of labor? Provide a rationale for your answer. 5. Were the experimental and control groups similar in their type of feeding? Provide a rationale for your answer. 80 EXERCISE 11 • Using Statistics to Describe a Study Sample 6. What was the marital status mode for the subjects in the experimental and control groups? Provide both the frequency and percentage for the marital status mode for both groups. 7. Could a median be determined for the education data? If so, what would the median be for education for the experimental and the control groups? Provide a rationale for your answer. 8. Can the fi ndings from this study be generalized to Black women? Provide a rationale for your answer. 9. If there were 32 subjects in the experimental group and 36 subjects in the control group, why is the income data only reported for 30 subjects in the experimental group and 34 subjects in the control group? 10. Was the sample for this study adequately described? Provide a rationale for your answer. 117 Statistical Technique in Review The mean (X–) 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 X– 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. 16 Mean and Standard Deviation Exercise 118 Exercise 16 • Mean and Standard Deviation . . .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 n Description of Studied Variables in Baseline and Post-test Between Groups Experiment (n = 25) Control (n = 25) Total (n = 50) Variables Mean SD Mean SD Mean SD Empowerment Baseline Post-test 98.40 9.19 97.08 8.99 97.74 9.02 105.04 7.28 97.12 8.73 101.08 8.91 Self-care self-efficacy Baseline Post-test 89.56 14.88 93.00 13.62 91.28 14.02 96.00 13.55 91.40 10.55 93.70 12.24 Depression Baseline Post-test 14.00 11.31 10.40 10.34 12.20 10.88 13.36 10.55 10.40 10.34 11.88 10.45 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. S tudy 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 selfefficacy 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. Mean and Standard Deviation • Exercise 16 119 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 X— = 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? 120 Exercise 16 • Mean and Standard Deviation 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. n 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. Name: ___________________________________________________ Class: ______________________ Date: _________________________________________________________________________________ 122 Exercise 16 • Mean and Standard Deviation 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 (X—) is a measure of _____________ ______________ of a distribution while the SD is a measure of _______________________ of its scores. Both X — 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. 131 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) 18 MEAN, STANDARD DEVIATION,       Click here to Reply or Forward       8.66 GB (57%) of 15 GB used Manage Terms - Privacy Last account activity: 0 minutes ago Details