CUMULATIVE PERCENTAGES AND PERCENTILE RANKS

EXERCISE 6     CUMULATIVE PERCENTAGES AND PERCENTILE RANKS
STATISTICAL TECHNIQUE IN REVIEW
A cumulative percentage distribution involves the summing of percentages from the top of a table to the bottom. Therefore, the bottom category has a cumulative percentage of 100. Cumulative percentages can also be used to determine percentile ranks, especially when discussing standardized test scores. For example, if 75% of a group scored equal to or lower than a particular examinee’s score, then that examinee’s rank is at the 75th percentile. When reported as a percentile rank, the percentage is often rounded to a whole number. Percentile ranks can be used to analyze ordinal data that can be assigned to categories able to be ranked. Percentile ranks and cumulative percentages are often applied to exam scores, but may be used in any frequency distribution where subjects have only one value for a variable. For example, demographic characteristics are usually reported with the frequency (f) or number (n) of subjects and percentage of subjects (%) for each level of a demographic variable. Income level for 200 subjects is presented as an example.
Income Level
Frequency (f)
Percentage (%)
Cumulative %
1. < $40,000
20
10
10
2. $40,000–59,999
50
25
35
3. $60,000–79,999
80
40
75
4. $80,000–100,000
40
20
95
5. > $100,000
10
5
100
RESEARCH ARTICLE
Source: Katsma, D. L., & Souza, C. H. (2000). Elderly pain assessment and pain management knowledge of long-term care nurses. Pain Management Nursing, 1 (3), 88–95.
Introduction
Katsma and Souza (2000) conducted a descriptive study using a convenience sample of long-term care nurses from six rural counties in California to evaluate the nurses’ knowledge base of assessment and management of pain in the elderly. Questionnaires were mailed to selected nursing homes and 89 nurses responded. The nurses reviewed two scenarios and responded to questions related to these scenarios. The scenarios were identical, except one involved a smiling patient and the other a grimacing patient. The researchers found that the nurses surveyed “were more likely to believe and document the grimacing patient’s self-report of pain than the smiling patient” (Katsma & Souza, 2003, p. 88). Fewer than half of the respondents chose to increase the analgesic dose for either patient scenario. “Nursing implications include the importance of ongoing pain assessment and management education tailored to the geriatric population and in long term care” (Katsma & Souza, 2000, p. 88).
Relevant Study Results
Three tables adapted from Katsma and Souza’s (2000) study are presented in this section. The tables address the research questions and include the number (n) and percent (%) of the nurses’ assessment of elders’ pain score and their medication management of that pain. The tables might have been clearer if an f had been used for frequencies versus the n. Tables 1a and 1b contain the nurses’ private opinions and documentations of their assessment of the patients’ self-reported pain score. Table 2 shows the numbers and percentages of nurses’ medication choices for the management of the elders’ pain score. The younger nurses with less clinical experience were more likely to believe and document their patients’ self-report of pain and to manage that pain with medication than the older more experienced nurses (Katsma & Souza, 2000).
TABLE 1a     Nurses’ Belief and Documentation of Assessment of the Smiling Patient
OPINION
DOCUMENTATION
Pain Assessment Scale
n
%
Cumulative %
N
%
Cumulative %
0
7
8.1
8.1
3
3.5
3.5
1
7
8.1
16.2
5
5.8
9.3
2
5
5.8
22.0
6
7.0
16.3
3
8
9.4
31.4
4
4.7
21.0
4
10
11.6
43.0
4
4.7
25.7
5
11
12.8
55.8
7
8.0
33.7
6
5
5.8
61.6
1
1.2
34.9
7
2
2.3
63.9
0
0.0
34.9
8*
31
36.1
100.0
56
65.1
100.0
9
0
0.0
100.0
0
0.0
100.0
10
0
0.0
100.0
0
0.0
100.0
Adapted from Katsma, D. L., & Souza, C. H. (2000). Elderly pain assessment and pain management knowledge of long-term care nurses. Pain Management Nursing, 1 (3), p. 91. Copyright © 2000 with permission from The American Society for Pain Management Nursing.
*    Correct Answer.
TABLE 1b     Nurses’ Belief and Documentation of Assessment of the Grimacing Patient
OPINION
DOCUMENTATION
Pain Assessment Scale
n
%
Cumulative %
N
%
Cumulative %
0
0
0.0
0.0
0
0.0
0.0
1
0
0.0
0.0
0
0.0
0.0
2
1
1.2
1.2
1
1.2
1.2
3
1
1.2
2.4
1
1.2
2.4
4
1
1.2
3.6
1
1.2
3.6
5
4
4.7
8.3
4
4.7
8.3
6
8
9.3
17.6
7
8.0
16.3
7
8
9.3
26.9
3
3.5
19.8
8*
48
55.8
82.7
60
69.8
89.6
9
8
9.3
92.0
6
7.0
96.6
10
7
8.0
100.0
3
3.4
100.0
*    Correct Answer.
TABLE 2     Nurses’ Medication Choice
SMILING PATIENT
GRIMACING PATIENT
Medication Choice
n
%
Cumulative %
n
%
Cumulative %
No pain medication now
9
10.5
10.5
0
0.0
0.0
Extra Strength Tylenol
17
19.8
30.3
2
2.3
2.3
Vicodin 1 Tablet
33
38.4
68.7
37
43.0
45.3
Vicodin 2 Tablets*
26
30.1
98.8
47
54.7
100.0
Response Missing
1
1.2
100.0
0
0.0
100.0
*    Correct Answer.
Adapted from Katsma, D. L., & Souza, C. H. (2000). Elderly pain assessment and pain management knowledge of long-term care nurses. Pain Management Nursing, 1 (3), p. 91. Copyright © 2000 with permission from The American Society for Pain Management Nursing.
STUDY QUESTIONS
1.    What number and percentage of nurses documented the correct pain assessment score for the grimacing patient?
2.    What number of nurses and cumulative percentage of nurses had an opinion lower than the self-reported pain score of the smiling patient?
3.    How many nurses undermedicated the smiling patient?
4.    What cumulative percentage of nurses undermedicated the grimacing patient?
5.    What number of nurses and percentage of nurses chose the correct medication plan for the grimacing patient?
6.    How many nurses had an opinion that differed from the grimacing patient’s self-report of a pain score of 8?
7.    What cumulative percentage of nurses’ opinions was that the grimacing patient was in less pain than reported?
8.    What number and percentage of nurses documented the smiling patient’s pain score at or below 6?
9.    What percentage of nurses documented a pain score higher than the correct score for the grimacing patient? Compare that percentage with the percentage of nurses whose opinion was that the grimacing patient was in more pain than reported.
10.    Why do you think so many nurses undermedicated the grimacing patient?
ANSWERS TO STUDY QUESTIONS
1.    60 nurses or 69.8% of the nurses documented a pain score of 8 for the grimacing patient. The key for Table 1b indicates that * designates the correct answer; thus 8* is the correct pain score for the grimacing patient.
2.    55 nurses or 63.9% of the nurses had the opinion that the smiling patient’s actual pain was less than his self-report. The 63.9% is obtained from Table 1a, and the figure of 55 nurses is obtained by adding the number of nurses whose opinions were that the pain score was less than 8 or those who gave a score of 0 to 7.
3.    59 nurses undermedicated the smiling patient. This number is obtained by adding the number of nurses giving no pain medication (9), the number giving extra-strength Tylenol (17), and the number giving 1 tablet of Vicodin (33), which equals 59 nurses.
4.    45.3% of nurses undermedicated the grimacing patient, which is found in Table 2.
5.    47 nurses or 54.7% chose to medicate the grimacing patient with 2 Vicodin tablets, which was the correct choice of medication indicated in Table 2.
6.    38 nurses’ opinions differed from the self-report of an 8 pain score by the grimacing patient. This number is found by adding the number of nurses who had an opinion that the pain score was less than 8, which was 23 nurses, and those nurses who thought the pain score was greater than 8, which was 15 nurses. Thus, 23 + 15 = 38 nurses’ opinions differed from the reported pain score of 8 (see Table 1b).
7.    26.9% of nurses were of the opinion that the grimacing patient’s actual pain was less than 8 (see Table 1b).
8.    30 (34.9%) of the nurses documented a pain score of 6 or less for the smiling patient (see Table 1a).
9.    10.4% of nurses documented a higher pain score than the correct score of 8. This number is obtained by adding the percent of nurses giving a score of 9 and 10. 17.3% of the nurses were of the opinion that the grimacing patient’s actual pain was higher than his self-reported pain score of 8. Thus, not all the nurses who had the opinion that the patients were in more pain (17.3%) than reported documented (10.4%) his or her opinion. The difference was 17.3% – 10.4% = 6.9%.
10.    Answers may vary. The grimacing patient may have been undermedicated for any of the following reasons: limited pain assessment skills of the nurse; underestimating the medication needed to treat the pain; lack of knowledge or experience with pain medications; reluctance to give narcotics to the elderly; or nurses are often very cautious about overmedicating patients, sometimes resulting in undermedication.
Name:____________________________________________ Class: ____________________
Date: _________________________________________________________________________________
? EXERCISE 6     Questions to be Graded
1.    What number and percentage of nurses documented the correct pain assessment for the smiling patient?
2.    What number and cumulative percentage of nurses had an opinion that the smiling patient had a 5 or lower pain score?
3.    What number and percentage of nurses chose the correct medication plan for the smiling patient?
4.    What number and percentage of nurses documented the pain score higher than the correct score for the smiling patient?
5.    What number and percentage of nurses documented a different pain score from the grimacing patient’s self-reported pain score of 8?
6.    What cumulative percentage of nurses’ opinions was that the smiling patient was in less pain than reported?
7.    What number and percentage of the nurses documented the grimacing patient’s pain score at or below 6?
8.    Why do you think so many nurses undermedicated the smiling patient?
9.    Is this study only applicable to the elderly population? Do you think younger patients’ self-reports of pain are believed and their pain appropriately treated?
10.    What can you learn from this study for your practice?
(Grove 35)
Grove, Susan K. Statistics for Health Care Research: A Practical Workbook. W.B. Saunders Company, 022007. VitalBook file.

EXERCISE 8     INTERPRETING LINE GRAPHS
STATISTICAL TECHNIQUE IN REVIEW
Tables and figures are commonly used to present findings from a study or to provide a way for researchers to become familiar with research data (Burns & Grove, 2005). Using tables and figures, researchers are able to illustrate the results from descriptive data analyses, assist in identifying patterns in data, and interpret exploratory findings. A line graph is a figure that is developed by joining a series of points with a line to show how a variable changes over time. A line graph includes a horizontal scale or x-axis and a vertical scale or y-axis. The x-axis is used to document time, and the y-axis is used to document the number or quantity of a variable. Below is an example line graph that documents time in weeks on the x-axis and weight loss in pounds on the y-axis.

RESEARCH ARTICLE
Source: Kang, N. M., Song, Y., Hyun, T. H., & Kim, K. N. (2005). Evaluation of the breastfeeding intervention program in a Korean community health center. International Journal of Nursing Studies, 42 (4), 409–13.
Introduction
Kang, Song, Hyun, and Kim (2005) conducted an observational study to examine a new breastfeeding intervention implemented in a Korean community health center. The purpose of the study was to determine if breastfeeding rates increased after trained health care professionals and peers gave information on breastfeeding to pregnant and lactating women. Breastfeeding rates after the educational program significantly increased, indicating that the community-based breastfeeding intervention program was effective in promoting breastfeeding among these women (Kang et al., 2005).
Relevant Study Results
The researchers presented their results in a line graph format to display outcomes comparing the pre-intervention group to the post-intervention group (see Figures 1 to 3). The x-axis represents age of the babies in months in the three figures, and the y-axis represents breastfeeding rate in Figure 1, formula-feeding rate in Figure 2, and mixed-feeding rate in Figure 3.
FIGURE 1     Breastfeeding rate of pre- and post-intervention (* Significance <0.05 by ?2-test).

FIGURE 2     Formula-feeding rate of pre- and post-intervention (* Significance <0.05 by ?2-test).

FIGURE 3     Mixed-feeding rate of pre- and post-intervention.

STUDY QUESTIONS
1.    Which axis shows the length of time of the study? Provide a rationale for the use of length of time in a line graph. What time interval was used in this study?
2.    According to the line graphs in Figures 1–3, this study included babies up to how many months old?
3.    What was the breastfeeding rate pre-intervention at 1 month?
4.    What was the formula-feeding rate for babies pre-intervention at 5 months? Was this pre-intervention rate significantly different from the post-intervention rate? Provide a rationale for your answer.
5.    Was there a significant difference in breastfeeding pre- and post-intervention? Provide a rationale for your answer.
6.    The highest percentage of formula-feeding occurred during which pre-intervention month? Was this an expected or unexpected finding? Provide a rationale for your answer.
7.    What information does Figure 1 provide you about the effectiveness of the breastfeeding educational program?
8.    What percentages of 7-month-old babies were breastfed pre-intervention? Was this breastfeeding rate significantly different from the post-intervention breastfeeding rate? Provide a rationale for your answer.
9.    Were formula-feeding rates affected by the intervention? Provide a rationale for your answer.
ANSWERS TO STUDY QUESTIONS
1.    The x-axis of a line graph shows the length of time examined in a study. The use of time in a line graph helps you to see how a variable changes or varies over time. In this study, time was measured in months to show a trend of feeding methods used for new babies over the course of 12 months.
2.    This study included babies up to 12 months old.
3.    The breastfeeding rate pre-intervention was 30% for the 1-month-old infants.
4.    The pre-intervention formula-feeding rate for babies at 5 months was 60%. At 5 months the pre-intervention and post-intervention rates were significantly different, as indicated by the asterisk (*) below the 5. The * indicates significant differences at p < 0.05.
5.    Yes, at 1 month and 9 months there were significant differences in the breastfeeding rates pre- and post-intervention. This is represented by *s on the x-axis at 1 and 9 months, indicating that at these two particular months, there were significant differences in pre- and post-intervention at p < 0.05. The content presented from the research article indicated that breastfeeding rates after the educational program significantly increased, indicating that the community-based breastfeeding intervention program was effective in promoting breastfeeding among these women (Kang et al., 2005).
6.    The highest percentage of formula-feeding occurred at 12 months pre-intervention. This is an expected finding considering that most women decrease the amount of breastfeeding to their child as the child gets older. So the 12th and final month of the study would be expected to show the highest formula-feeding rate.
7.    Figure 1 indicates that breastfeeding rates for the post-intervention group were higher every month than those for the pre-intervention group. Although, no statistically significant differences were found between pre- and post-intervention breastfeeding rates, except for months 1 and 9. Thus, the findings indicate that the educational program was effective in increasing breastfeeding rates among the women, but with limited significant differences between pre- and post-intervention.
8.    At 7 months pre-intervention, the breastfeeding rate was 20%, which was not significantly different from the post-intervention rate since there was no * below the month indicating a statistically significant difference. In addition, the line diagram indicates very limited difference between the pre- and post-intervention groups at 7 months.
9.    Yes. When compared to pre-intervention rates, formula-feeding rates declined post-intervention at the same time that the breastfeeding rates increased. This indicates that people changed from formula-feeding to breastfeeding after the educational program.
Name:____________________________________________ Class: ____________________
Date: _________________________________________________________________________________
? EXERCISE 8     Questions to be Graded
1.    Can the exact percentage for the type of feeding rate per month for the pre- and post-intervention groups be determined from the line graphs? Provide a rationale for your answer.
2.    Did the breastfeeding rate decline at the 12th month post-intervention? Provide a rationale for your answer.
3.    If the level of statistical significance was determined at p < 0.05 level for this study, at what months were the rates of formula-feeding statistically significant between pre- and post-interventions? Provide a rationale for you answer.
4.    What were the trends for mixed-feeding rates post-intervention? Were these results significant? Provide a rationale for your answer.
5.    At 9 months of age, the breastfeeding rate post-intervention (28%) was significantly different from the pre-intervention rate (18%). Is this statement true or false?
6.    The breastfeeding rate post-intervention was greater than the pre-intervention rate over the 12 months of the study. Is this statement true or false? Provide a rationale for your answer.
7.    Were the mixed-feeding rates for the pre-intervention and post-intervention groups significantly different at 7 months? Provide a rationale for your answer.
8.    Do the results of this study support the hypothesis that the breastfeeding program would contribute to an increase in the breastfeeding rate in the community? Provide a rationale for you answer.
9.    Were the breastfeeding rates statistically significant at 1 and 9 months of age? Provide a rationale for your answer.
10.    What implications for practice do you note from these study results?
(Grove 49)
Grove, Susan K. Statistics for Health Care Research: A Practical Workbook. W.B. Saunders Company, 022007. VitalBook file.

EXERCISE 9     IDENTIFYING PROBABILITY AND NONPROBABILITY SAMPLING METHODS
STATISTICAL TECHNIQUE IN REVIEW
A sampling method is the process researchers use to select subjects from the population being studied, and sampling methods are categorized as either probability or nonprobability. Descriptions of the common probability and nonprobability sampling methods used in quantitative studies, and the nonprobability sampling methods used most frequently in qualitative studies, are discussed in this exercise.
Probability Sampling
Probability sampling, also known as random sampling, requires that every member of the study population have an equal opportunity to be chosen as a study subject. For each member of the population to have an equal opportunity to be chosen, the sampling method must select members randomly. Probability sampling allows every facet of the study population to be represented without researcher bias. Four common sampling designs have been developed for selection of a random sample: simple random sampling, stratified random sampling, cluster sampling, and systematic sampling (Burns & Grove, 2007). Simple random sampling is achieved by random selection of members from the sampling frame. The random selection can be accomplished many different ways, but the most common is using a computer program to randomly select the sample. Another example would be to assign each potential subject a number, and then randomly select numbers from a random numbers table to fulfill the required number of subjects for the sample. Stratified random sampling is used when the researcher knows some of the variables within a population that will affect the representativeness of the sample. Some examples of variables include age, gender, ethnicity, and medical diagnosis. Thus, subjects are selected randomly on the basis of their classification into the selected stratum. The strata ensure that all levels of the variable(s) are represented in the sample. For example, age could be the variable, and after stratification, the sample might include equal numbers of subjects in the established age ranges of 20–39, 40–59, 60–79, and over 80.
Researchers use cluster sampling in two different situations: (1) when the time and travel necessary to use simple random sampling would be prohibitive, and (2) when the specific elements of a population are unknown, therefore making it impossible to develop a sampling frame. In either of these cases, a list of institutions or organizations associated with the elements of interest can often be obtained. To conduct cluster sampling, a list of all the states, cities, institutions, or organizations associated with the elements of the population is developed. The states, cities, institutions, or organizations are then randomly selected from the list to form the sample. Of note is the fact that subjects obtained from the same institution are likely to be somewhat correlated, thus not completely independent (Burns & Grove, 2005). Systematic sampling requires an ordered list of all of the members of the population. Individuals are selected through a process that accepts every kth member on the list using a randomly selected starting point. k is calculated based on the size of population and the sample size desired. For example, if the population has 1,000 potential subjects and a sample size of 100 is desired, then k = 1,000 ÷ 100 = 10. The initial starting point must be random for the sample to be considered a probability sample. Also, steps must be taken to ensure that the original list was not ordered in any way that could affect the study.
Nonprobability Sampling in Quantitative Research
Nonprobability sampling is a nonrandom sampling technique that does not extend equal opportunity for selection to all members of the study population. Readers should never assume a probability sampling method was used; rather, the researchers must identify the sampling method used as probability or nonprobability. Following are descriptions of two common nonprobability sampling methods, convenience and quota, used in quantitative research. Remember that quantitative research is an objective research method used to describe, examine relationships, and determine cause-and-effect interactions among variables (Burns & Grove, 2007). Researchers obtain a convenience sample by enrolling subjects who are in the right place at the right time. Subjects are enrolled until the target sample size is obtained. Convenience sampling does not allow for the opportunity to control for biases. To counter the inability to control for biases, researchers must carefully examine the population being studied and adjust the sampling criteria to appropriately include or exclude the identified biases.
Researchers use quota sampling to ensure adequate representation of types of subjects who are likely to be underrepresented, such as women, minorities, the elderly, or the poor. A convenience sampling method is used in conjunction with a strategy to ensure the inclusion of the identified subject type. Quota sampling can be used to mimic the known characteristics of the population or to ensure adequate numbers of subjects in each stratum. This is similar to the strategy used for stratified random sampling. Quota sampling is recognized as an improvement over convenience sampling with a decreased opportunity for bias.
Nonprobability Sampling in Qualitative Research
The following sampling methods are still nonprobability sampling methods, meaning that members of the study population do not have equal opportunity to be selected for the sample. These three sampling methods, purposive, network, and theoretical, are more commonly used in qualitative research than quantitative research. Remember that qualitative studies are subjective and are conducted to describe life experiences, cultures, or historical events and give them meaning. Purposive sampling occurs when the researcher consciously selects subjects, elements, events, or incidents to include in the study. Those selected by the researchers are information-rich cases, or those from which a lot can be learned. Researchers may make the effort to include typical and atypical cases. This type of sampling has been criticized because the researcher’s judgments in the selection of cases cannot be evaluated. However, this sampling method can be a good way to explore new areas of study.
Network sampling makes use of social networks and the fact that friends often have common characteristics. The researcher identifies a few subjects who meet the sampling criteria and then asks them to assist in recruiting others with similar characteristics. Network sampling is sometimes referred to as “snowballing,” and is useful for obtaining samples that are difficult to obtain or have not been previously identified for study. Biases are inherent in networking samples since the study subjects are not independent of one another. Theoretical sampling is used in the research process to advance the development of a theory. Data are gathered from individuals or groups who can provide relevant information for theory generation. For example, a researcher might interview family members and patients to develop a theory of surviving a near-death experience. The researcher continues to seek subjects and data until saturation of the theory concepts and relationships has occurred. Subject diversity in the sample is promoted to ensure that the developed theory is applicable to a wide range of behaviors and settings (Burns & Grove, 2005).
STUDY QUESTIONS
Directions: For each of the following research article excerpts, (1) decide whether the sampling method presented is either a probability or nonprobability sampling method; (2) identify the specific sampling method used, which might include convenience, quota, purposive, network, or theoretical sampling for nonprobability samples or simple random, stratified random, cluster, or systematic sampling for probability samples; and (3) provide a rationale for the sampling method you selected. Some of the examples might include more than one sampling method to obtain the study sample.
1.    Study excerpt: “All registered and enrolled nurses who had patient contact and were employed in the ED [Emergency Department] setting were invited to participate in the study.” Crilly, J., Chaboyer, W., & Creedy, D. (2004). Violence towards emergency department nurses by patients. Accident and Emergency Nursing??, 12 (2), 67–73. Excerpt from page 69.
2.    Study excerpt: “Participants were recruited from a women’s shelter with the help of a colleague as contact person, from church support groups within the community by the researcher who made church members aware of the study and the search for participants, and … each participant interviewed suggested the name of a potential new participant.” Wright, V. L. (2003). A phenomenological exploration of spirituality among African American women recovering from substance abuse. Archives of Psychiatric Nursing??, 17 (4), 173–85. Excerpt from page 176.
3.    Study excerpt: “A cross-sectional study was carried out that included 30 prevalent adult patients from a single PD [Peritoneal Dialysis] center. The sample was randomly selected from the outpatient clinic …” Vicente-Martinez, M., Martinez-Ramirez, L., Munoz, R., Avila, M., Ventura, M., Rodriguez, E., Amato, D., & Paniagua, R. (2004). Inflammation in patients on peritoneal dialysis is associated with increased extracellular fluid volume. Archives of Medical Research, 35 (3), 220–4. Excerpt from page 221.
4.    Study excerpt: “Participants were recruited from one middle school and two high schools during general assemblies, homeroom classes, or in other required classes (e.g., physical education) so that no student enrolled in particular courses would be excluded … The three schools, located within a large, public school district in Houston, Texas, were selected so that (a) a wide range of socioeconomic strata, (b) a balance of males and females, and (c) a locally representative tri-ethnic sample could be attained.” Reyes, L. R., Meininger, J. C., Liehr, P., Chan, W., & Mueller, W. H. (2003). Anger in adolescents: Sex, Ethnicity, Age Differences, and Psychometric Properties. Nursing Research, 52 (1), 2–11. Excerpt from page 4.
5.    Study excerpt: “[T]he parents of 120 children aged 5 to 12 years admitted to one of six South Australian hospitals for elective surgery requiring general anesthesia were approached to participate in this study.” Wollin, S. R., Plummer, J. L., Owen, H., Hawkins, R. M. F., Materazzo, F., & Morrison, V. (2004). Anxiety in children having elective surgery. Journal of Pediatric Nursing??, 19 (2), 128–32. Excerpt from page 128.
6.    Study excerpt: “Doctors were requested to distribute information packs to women in their care, who fulfilled the inclusion criteria of having a diagnosis of Parkinson’s Disease and who were still menstruating. … [T]he Research Assistant invited an existing participant to introduce or refer her to another woman who might be willing to take part.” Fleming, V., Tolson, D., & Schartau, E. (2004). Changing perceptions of womanhood: Living with Parkinson’s disease. International Journal of Nursing Studies, 41 (5), 515–24. Excerpt from page 516.
7.    Study excerpt: “A 2-stage … sampling method was used to draw a national sample of nurses working in ICUs. … After units in U.S. military installations and territories were excluded, the sampling frame provided by the American Hospital Association listed 5,191 ICUs. Based on a power analysis calculation, a random sample of 421 ICUs was chosen using a systematic interval technique.” Binkley, C., Furr, L. A., Carrico, R., & McCurren, C. (2004). Survey of oral care practices in U.S. intensive care units. American Journal of Infection Control, 32 (3), 161–9. Excerpt from page 163.
8.    Study excerpt: “All patients were referred by their GP [General Practitioner] to the researcher (L.T.) who, after obtaining informed consent and taking baseline data, randomized the patients” into the experimental group receiving acupuncture and the comparison group receiving standard care. MacPherson, H., Thorpe, L., Thomas, K., & Campbell, M. (2003). Acupuncture for low back pain: Traditional diagnosis and treatment of 148 patients in a clinical trial. Complementary Therapies in Medicine, 12 (1), 38–44. Excerpt from page 39.
9.    Study excerpt: “Potential participants were recruited from youths seeking health and social services from a street outreach program … This age group represented the majority of youths seeking services from this program… Saturation (sufficient or adequate data had been collected to meet the goal of the study [to develop a theory]) was reached at the end of 12 interviews; three additional participants were recruited to verify the findings.” Rew, L. (2003). A theory of taking care of oneself grounded in experiences of homeless youth. Nursing Research, 52 (4), 234–41. Excerpt from page 235.
10.    Study excerpt: “This study recruited a … sample of HIV-positive participants from an Internet Website sponsored by the University of California, San Francisco… as well as HIV-positive patients from five geographic data collection clinical sites located in Boston, MA; New York, NY; Oslo, Norway; Paterson, NJ; and the San Francisco Bay Area from July 1999 to February 2000” and invited them to participate in the study. Chou, F. Y., Holzemer, W. L., Portillo, C. J., & Slaughter, R. (2004). Self-care strategies and sources of information for HIV/AIDS symptom management. Nursing Research, 53 (5), 332–9. Excerpt from page 333.
ANSWERS TO STUDY QUESTIONS
1.    Nonprobability, convenience sampling method. The key is that all the participants were invited to participate in the study. Recall that with convenience sampling, subjects are recruited because they happen to be in the right place at the right time and are invited to participate in a study.
2.    Nonprobability, convenience and network sampling methods. Those subjects recruited from the women’s shelter and the church support groups were obtained by a sample of convenience. Those subjects were interviewed and asked to suggest the names of other potential subjects, which is network sampling. Network sampling is used by researchers on the basis that members of social sets have similar characteristics.
3.    Probability, simple random sampling method. The excerpt states that the subjects were randomly selected. The most common form of probability sampling is simple random sampling.
4.    Nonprobability, quota sampling method. The strata identified in this example of quota sampling are socioeconomic status, gender, and ethnicity. Quota sampling is used by researchers to ensure adequate representation by types of subjects that are likely to be underrepresented. This excerpt is not an example of stratified random sampling method because the students were recruited from selected schools and asked to participate, which is convenience sampling. The students were not randomly selected then stratified as is needed for stratified random sampling. The subjects were obtained by a sample of convenience and then organized into strata (socioeconomic status, gender, and ethnicity), which is consistent with the quota sampling method.
5.    Nonprobability, convenience sampling method. The participants were admitted to one of six hospitals and asked to participate in the study.
6.    Nonprobability, convenience and network sampling methods. The distribution of packets by the doctors to women in their practices represents the convenience sampling method. Participants were invited by the Research Assistant to refer someone else who may be a willing participant, which is network sampling.
7.    Probability, cluster and systematic sampling methods. The identification of the sampling frame of ICUs that include the nurses desired for the sample was done using cluster sampling. The sample of 421 ICUs was chosen using a systematic sampling technique. The authors did not describe the interval used during the systematic sampling, but according to the formula given in the discussion of systematic sampling methods, k could be calculated. Thus, k = 5,191 ÷ 421 = 12.33, or every 12th ICU was systematically selected from a random starting point to be included in the study.
8.    Nonprobability, convenience sampling method. The subjects were all referred by their general practitioners. After the sample was selected, the subjects were randomized to the experimental group (acupuncture) and comparison group (standard care). The random assignment to groups is part of the design and not the sampling method.
9.    Nonprobability, theoretical sampling method. The researchers sought out those who could give information-rich data for the further explanation of a theory. A total of 12 subjects were recruited to achieve saturation of the data for the theory to be developed.
10.    Nonprobability, convenience sampling method. Of note, participants were recruited from five differing geographic areas as well as an Internet website and invited to participate in the study, which is consistent with convenience sampling.
Name:____________________________________________ Class: ____________________
Date: _________________________________________________________________________________
? EXERCISE 9     Questions to be Graded
Directions: For each of the following excerpts, (1) decide whether the sampling method presented is probability or nonprobability; (2) identify the specific type of nonprobability or probability sampling method used; and (3) provide a rationale for the sampling method you selected. Some of the examples might include more than one sampling method to obtain the study sample.
1.    Study excerpt: “The sample for this study included 27 Chinese immigrant elders, 11 adult children who were caregivers for Chinese parents, and 12 health and social service providers who served this immigrant group. … Elders were initially recruited through two social service agencies that target Chinese elders in the greater Boston area. … Providers from various disciplines and practice areas were identified by case workers at two social service agencies. … People already participating in the study were asked to refer elders who were not using services at the two initial recruitment sites.” Aroian, K. J., Wu, B., & Tran, T. V. (2005). Health care and social service use among Chinese immigrant elders. Research in Nursing & Health, 28 (2), 95–105. Excerpt from page 97.
2.    Study excerpt: “Subjects were recruited through advertisements placed in various newspapers in Lexington, Kentucky. … Individuals reporting any past or present drug- or alcohol-related problems, serious head injuries, learning disabilities, or psychotic symptomatology were excluded from participation.” Giancola, P. R. (2004). Difficult temperament, acute alcohol intoxication, and aggressive behavior. Drug and Alcohol Dependence, 74 (2), 135–45. Excerpt from page 136.
3.    Study excerpt: “A mailing list comprising 3,500 randomly selected names and addresses of the 68,000 AACN [American Association of Critical Care Nurses] members was purchased. Every seventh nurse was … sampled to yield a group of 500 nurses, all of whom were invited by mail to participate in the study. Two hundred and forty-seven nurses consented to participate (49% response rate) and completed the surveys.” Ruggiero, J. S. (2003). Correlates of fatigue in critical care nurses. Research in Nursing & Health, 26 (6), 434–44. Excerpt from page 437.
4.    Study excerpt: “In brief, women 18–35 years old were randomly sampled from census blocks located within a 0.5–miles radius of drug copping sites (sites where crack, cocaine, or heroine are sold).” Alegria, M., Vera, M., Shrout, P., Canino, G., Lai, S., Albizu, C., Marin, H., Pena, M., & Rusch, D. (2004). Understanding hardcore drug use among urban Puerto Rican women in high-risk neighborhoods. Addictive Behaviors, 29 (4), 643–64. Excerpt from page 645.
5.    Study excerpt: “Every weekday, the team selected a minimum of five patients among patients admitted during the preceding 24 h[ours], by a random numbers system. … After informed consent, the patients were stratified by age: < or = 60 years, and randomized in blocks of 6, usually sequentially numbered sealed non-transparent envelopes, which were opened to allocate patients into one of two groups: control or intervention.” Johansen, N., Kondrup, J., Plum, L. M., Bak, L., Norregaard, P., Bunch, E., Baernthsen, H., Andersen, J. R., Larsen, I. H., & Martinsen, A. (2004). Effect of nutritional support on clinical outcome in patients at nutritional risk. Clinical Nutrition, 23 (4), 539–50. Excerpt from pages 540-1.
6.    Study excerpt: “The 679 subjects who comprise the initial DANDY [Development and Assessment of Nicotine Dependence in Youths] cohort represent a response rate of 94% of the 721 students who were invited, and 76% of all seventh graders (n = 900).” DiFranza, J. R., Savageau, J. A., Fletcher, K., Ockene, J. K., Rigotti, N. A., McNeill, A. D., Coleman, M., & Wood, C. (2004). Recollections and repercussions of the first inhaled cigarette. Addictive Behaviors, 29 (2), 261–72. Excerpt from page 264.
7.    Study excerpt: “National lists of NPs [nurse practitioners] and PAs [physician assistants] were obtained from Medical Marketing Services and a total of 3,900 individuals (NPs [n = 1,950] and PAs [n = 1,950]) were randomly selected from the lists. … The stratified samples were assigned randomly in equal allocations to one of three incentive groups.” Ulrich, C. M., Danis, M., Koziol, D., Garrett-Mayer, E., Hubbard, R., & Grady, C. (2005). Does it pay to pay? A randomized trial of prepaid financial incentives and lottery incentives in surveys of nonphysician healthcare professionals. Nursing Research, 54 (3), 178–83. Excerpt from page 179.
8.    Study excerpt: “Participants were recruited from a local hospital, a visiting nurse association, a mall health center, and professional referral. … Participants were selected to allow diversity of ages, gender, and ethnicity to capture information-rich data that could be used for extrapolation of patterns and themes central to the heart failure experience rather than demographics.” Zambroski, C. H. (2003). Qualitative analysis of living with heart failure. Heart & Lung, 32(1), 32–40. Excerpt from page 33.
9.    Study excerpt: “Participants were recruited through personal acquaintances and professional contacts with several local black ministers …” Rodgers, L. S. (2004). Meaning of bereavement among older African American widows. Geriatric Nursing, 25 (1), 10–16. Excerpt from page 12.
10.    Study excerpt: “Patients with baseline [hemoglobin A1c] levels = 7.5% were invited to enroll in the study and assigned randomly to the intervention or control group.” Krein, S. L., Klamerus, M. L., Vijan, S., Lee, J. L., Fitzgerald, J. T., Pawlow, A., Reeves, P., & Hawyard, R. A. (2004). Case management for patients with poorly controlled diabetes: A randomized trial. The American Journal of Medicine, 116 (11), 732–9. Excerpt from page 733.
(Grove 57)
Grove, Susan K. Statistics for Health Care Research: A Practical Workbook. W.B. Saunders Company, 022007. VitalBook file.

EXERCISE 27     SIMPLE LINEAR REGRESSION
STATISTICAL TECHNIQUE IN REVIEW
Linear regression provides a means to estimate or predict the value of a dependent variable based on the value of one or more independent variables. The regression equation is a mathematical expression of a causal proposition emerging from a theoretical framework. The linkage between the theoretical statement and the equation is made prior to data collection and analysis. Linear regression is a statistical method of estimating the expected value of one variable, y, given the value of another variable, x. The term simple linear regression refers to the use of one independent variable, x, to predict one dependent variable, y.
The regression line is usually plotted on a graph, with the horizontal axis representing x (the independent or predictor variable) and the vertical axis representing the y (the dependent or predicted variable) (see Figure 27-1). The value represented by the letter a is referred to as the y intercept or the point where the regression line crosses or intercepts the y-axis. At this point on the regression line, x = 0. The value represented by the letter b is referred to as the slope, or the coefficient of x. The slope determines the direction and angle of the regression line within the graph. The slope expresses the extent to which y changes for every 1-unit change in x. The score on variable y (dependent variable) is predicted from the subject’s known score on variable x (independent variable). The predicted score or estimate is referred to as Y (expressed as y-hat) (Burns & Grove, 2005).
FIGURE 27-1     Graph of a Simple Linear Regression Line

Simple linear regression is an effort to explain the dynamics within a scatter plot by drawing a straight line through the plotted scores. No single regression line can be used to predict with complete accuracy every y value from every x value. However, the purpose of the regression equation is to develop the line to allow the highest degree of prediction possible, the line of best fit. The procedure for developing the line of best fit is the method of least squares. If the data were perfectly correlated, all data points would fall along the straight line or line of best fit. However, not all data points fall on the line of best fit in studies, but the line of best fit provides the best equation for the values of y to be predicted by locating the intersection of points on the line for any given value of x.
The algebraic equation for the regression line of best fit is:   = a + b, where:
is the predicted value of y,
a is the y intercept and represents the value of y when x = 0 (see Figure 27-1),
a is also called the regression constant,
b is the slope of the line that is the amount of change in y for each one unit of change in x,
b is also called the regression coefficient.
In Figure 27-2, the x-axis represents Gestational Age and the y-axis represents Birth Weight. As gestational age increases from 20 weeks to 34 weeks, birth weight also increases. In other words, the slope of the line is positive. This line of best fit can be used to predict the birth weight (dependent variable) for an infant based on his or her gestational age in weeks (independent variable). Figure 27-2 is an example of a line of best fit and was not developed from research. In addition, the x-axis was started with 22 weeks rather than 0, which is the usual start in a regression figure. Using the formula Y = a + bx, the birth weight of a baby born at 28 weeks of gestation is calculated below.
FIGURE 27-2     Example Line of Best Fit for Gestational Age and Birth Weight

Formula:   = a + bx
In this example, a = 500, b = 20, and x = 28 weeks
= 500 + 20(28) = 500 + 560 = 1,060 grams
The regression line represents Y for any given value of x. As you can see, some data points fall above the line and some fall below the line. If we substitute any x value in the regression equation and solve for y, we will obtain Y that will be somewhat different from the actual values. The distance between the Y and the actual value of y is called residual, and this represents the degree of error in the regression line. The regression line or the line of best fit for the data points is the unique line that will minimize error and yield the smallest residual (Burns & Grove, 2005).
STUDY QUESTIONS
1.    What are the variables on the x- and y-axes in Figure 27-2?
2.    What is the name of the type of variable represented by x and y in Figure 27-2? Is x or y the score to be predicted?
3.    What is the purpose of simple linear regression analysis and the regression equation?
4.    What is the point where the regression line meets the y-axis called? Is there more than one term for this point?
5.    In   = a + bx, is a or b the slope? What does the slope represent in regression analysis?
6.    Using the values a = 500 and b = 20 in Figure 27-2, what is the predicted birth weight in grams for an infant at 36 weeks of gestation?
7.    Using the values a = 500 and b = 20 in Figure 27-2, what is the predicted birth weight in grams for an infant at 22 weeks of gestation?
8.    Using the values a = 500 and b = 20 in Figure 27-2, what is the predicted birth weight in grams for an infant at 35 weeks of gestation?
9.    Does Figure 27-2 have a positive or negative slope? Provide a rationale for your answer. Discuss the meaning of the slope of Figure 27-2.
ANSWERS TO STUDY QUESTIONS
1.    The x variable is gestational age in weeks, and the y variable is birth weight in grams in Figure 27-2.
2.    x is the independent or predictor variable. y is the dependent variable or the variable that is to be predicted by the independent variable, x.
3.    Simple linear regression is conducted to estimate or predict the values of a dependent variable based on the values of an independent variable. Regression analysis is used to calculate a line of best fit based on the relationship of the independent variable x with the dependent variable y. The formula developed with regression analysis can be used to predict the dependent variable (y) values based on values of the independent variable x.
4.    The point where the regression line meets the y-axis is called the y intercept and is also represented by a (see Figure 27-1). a is also called the regression constant. At the y intercept, x = 0.
5.    b is the slope of the line of best fit (see Figure 27-1). The slope of the line indicates the amount of change in y for each one unit of change in x. b is also called the regression coefficient.
6.    Y = a + bx
Y = 500 + 20(36) = 500 + 720 = 1,220 grams
7.    Y = a + bx
Y = 500 + 20(22) = 500 + 440 = 940 grams
8.    Y = a + bx
Y = 500 + 20(35) = 500 + 700 = 1,200 grams
9.    Figure 27-2 has a positive slope since the line extends from the lower left corner to the upper right corner and shows a positive relationship. This line shows that the increase in x (independent variable) is also associated with an increase in y (dependent variable). Thus, the independent variable gestational age is used to predict the dependent variable of birth weight. As the weeks of gestation increase, the birth weight in grams also increases, which is a positive relationship.
RESEARCH ARTICLE
Source: LeFlore, J. L., Engle, W. D., & Rosenfeld, C. (2000). Determinants of blood pressure in very low birth weight neonates: Lack of effect of antenatal steroids. Early Human Development, 59 (1), 37–50.
Introduction
LeFlore, Engle, and Rosenfeld (2000) conducted a retrospective, cohort study (Group 1 received antenatal steroids [n = 70]) with matched controls (Group II did not receive antenatal steroids [n = 46]) to examine the effect of antenatal steroids on neonatal blood pressure (BP) in the first 72 hours of life in very low birth weight (VLBW) neonates. Additionally, the effect of other perinatal factors on BP were studied, which included estimated gestational age (EGA), birth weight (BW), and postnatal age. The results indicate that there are positive linear relationships between BP and BW, BP and EGA, and BP and postnatal age.
Relevant Study Results
BP for Group I and Group II were compared over the first 72 hours of the neonate’s life. Since there were no significant differences in initial and subsequent measurements of BP between the groups, subsequent analyses were performed with the groups combined (n = 116). To assess the effect of BW on BP, the infants were grouped into those with BW = 1,000 grams (n = 36) and those with BW 1,001–1,500 grams (n = 80). The researchers displayed the results of their analyses in figures. Figure 2 displays the relationships between postnatal age in hours and 3 BPs, systolic BP (SBP), diastolic BP (DBP), and mean BP (MBP), for infants with BW = 1,000 grams. Figure 3 displays the relationship between postnatal age in hours and SBP, DBP, and MBP for infants with a BW 1,001–1,500 grams.
FIGURE 2     Change in (A) systolic blood pressure (SBP), (B) diastolic blood pressure (DBP), and (C) mean blood pressure (MBP) in neonates = 1,000 grams birth weight (n = 36) during the initial 72 hours postnatal. Lines represent means and 95% confidence intervals (p < 0.0001). Equations for lines of best fit were: SBP = 43.2 + 0.17x; DBP = 25.8 + 0.13x; MBP = 32.9 + 0.14x. In each instance, the y intercept was significantly lower (p < 0.001) than the value for comparable lines of best fit in infants with birth weights 1,001–1,500 grams; however, no significant differences in slopes for the lines of best fit were observed between the two birth weight groups.

LeFlore, J. L., Engle, W. D., & Rosenfeld, C. (2000). Determinants of blood pressure in very low birth weight neonates: Lack of effect of antenatal steroids. Early Human Development, 59 (1), p. 44
FIGURE 3     Change in (A) systolic blood pressure (SBP), (B) diastolic blood pressure (DBP), and (C) mean blood pressure (MBP) in neonates 1,001–1,500 grams birth weight (n = 80) during the initial 72 hours postnatal. Lines represent means and 95% confidence intervals (p < 0.0001). Equations for lines of best fit were: SBP = 50.3 + 0.12x; DBP = 30.4 + 0.11x and MBP = 37.4 + 0.12x. In each instance, the y intercept was significantly greater (p < 0.001) than the value for comparable lines of best fit in infants with birth weight =1,000 grams; however, no significant differences in the slopes for the lines of best fit were observed between the two birth weight groups. LeFlore, J. L., Engle, W. D., & Rosenfeld, C. (2000). Determinants of blood pressure in very low birth weight neonates: Lack of effect of antenatal steroids. Early Human Development, 59 (1), p. 45.

Name:____________________________________________ Class: ____________________
Date: _________________________________________________________________________________
? EXERCISE 27     Questions to be Graded
1.    What are the independent and dependent variables in Figures 2, A, B, and C? How would you describe the relationship between the variables in Figures 2, A, B, and C?
2.    What are the independent and dependent variables in Figures 3, A, B, and C? How would you describe the relationship between the variables in Figures 3, A, B, and C?
3.    Was there a significant difference in the y intercept for the lines of best fit in Figure 2 from the y intercept for the lines of best fit in Figure 3? Provide a rationale for your answer.
4.    Y represents the predicted value of y calculated using the equation Y = a + bx. In Figure 2, the formula for SBP is Y = 43.2 + 0.17x. Identify the y intercept and the slope in this formula. What does x represent in this formula?
5.    In the legend beneath Figure 2, the authors give an equation indicating that systolic blood pressure is SBP = 43.2 + 0.17x. If the value of x is postnatal age of 30 hours, what is the value for Y or SBP for neonates =1,000 grams? Show your calculations.
6.    In the legend beneath Figure 2, the authors give an equation indicating that systolic blood pressure is SBP = 50.3 + 0.12x. If the value of x is postnatal age of 30 hours, what is the value for Y or SBP for neonates 1,001–1,500 grams? Show your calculations.
7.    Compare the SBP readings you found in Questions 5 and 6. Explain the difference in these two readings.
8.    In the legend beneath Figure 2, the authors give an equation indicating that diastolic blood pressure is DBP = 25.8 + 0.13x. If the value of x is postnatal age of 30 hours, what is the value for Y for neonates = 1,000 grams? Show your calculations.
9.    In the legend beneath Figure 3, the authors give an equation indicating that diastolic blood pressure is DBP = 30.4 + 0.11x. If the value of x is postnatal age of 30 hours, what is the value for Y for neonates 1,001–1,500 grams? Show your calculations.
10.    In the legend beneath Figure 3, the authors give an equation indicating that diastolic blood pressure is DBP = 30.4 + 0.11x. How different is the DBP when the value of x is postnatal age of 60 hours versus the 30 hours examined in Question 9?
(Grove 199)
Grove, Susan K. Statistics for Health Care Research: A Practical Workbook. W.B. Saunders Company, 022007. VitalBook file.

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