# How can graphics and/or statistics be used to misrepresent data? Where have you seen this done?

how much would it cost to do the following:

How can graphics and/or statistics be used to misrepresent data? Where have you seen this done?

What are the characteristics of a population for which it would be appropriate to use mean/median/mode? When would the characteristics of a population make them inappropriate to use?

Questions to Be Graded: Exercises 6, 8 and 9

Complete Exercises 6, 8, and 9 in Statistics for Nursing Research: A Workbook for Evidence-Based Practice, and submit as directed by the instructor.

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Questions to Be Graded: Exercise 27

Use MS Word to complete “Questions to be Graded: Exercise 27” in Statistics for Nursing Research: A Workbook for Evidence-Based Practice. Submit your work in SPSS by copying the output and pasting into the Word document. In addition to the SPSS output, please include explanations of the results where appropriate.

Copyright © 2017, Elsevier Inc. All rights reserved. 67 EXERCISE 6 Questions to Be Graded Follow your instructor ’ s directions to submit your answers to the following questions for grading. Your instructor may ask you to write your answers below and submit them as a hard copy for grading. Alternatively, your instructor may ask you to use the space below for notes and submit your answers online at http://evolve.elsevier.com/Grove/statistics/ under “Questions to Be Graded.”

Name: _______________________________________________________

Class: _____________________

Date: ___________________________________________________________________________________ 68EXERCISE 6 •

What are the frequency and percentage of the COPD patients in the severe airﬂ ow limitation group who are employed in the Eckerblad et al. (2014) study?

What percentage of the total sample is retired? What percentage of the total sample is on sick leave?

What is the total sample size of this study? What frequency and percentage of the total sample were still employed? Show your calculations and round your answer to the nearest whole percent.

What is the total percentage of the sample with a smoking history—either still smoking or former smokers? Is the smoking history for study participants clinically important? Provide a rationale for your answer.

What are pack years of smoking? Is there a signiﬁ cant difference between the moderate and severe airﬂ ow limitation groups regarding pack years of smoking? Provide a rationale for your answer.

What were the four most common psychological symptoms reported by this sample of patients with COPD? What percentage of these subjects experienced these symptoms? Was there a sig-niﬁ cant difference between the moderate and severe airﬂ ow limitation groups for psychological symptoms?

What frequency and percentage of the total sample used short-acting β 2 -agonists? Show your calculations and round to the nearest whole percent.

Is there a signiﬁ cant difference between the moderate and severe airﬂ ow limitation groups regarding the use of short-acting β 2 -agonists? Provide a rationale for your answer.

Was the percentage of COPD patients with moderate and severe airﬂ ow limitation using short-acting β 2 -agonists what you expected? Provide a rationale with documentation for your answer.

Are these ﬁ ndings ready for use in practice? Provide a rationale for your answer.

Understanding Frequencies and Percentages STATISTICAL TECHNIQUE IN REVIEW Frequency is the number of times a score or value for a variable occurs in a set of data. Frequency distribution is a statistical procedure that involves listing all the possible values or scores for a variable in a study. Frequency distributions are used to organize study data for a detailed examination to help determine the presence of errors in coding or computer programming ( Grove, Burns, & Gray, 2013 ). In addition, frequencies and percentages are used to describe demographic and study variables measured at the nominal or ordinal levels. Percentage can be deﬁ ned as a portion or part of the whole or a named amount in every hundred measures. For example, a sample of 100 subjects might include 40 females and 60 males. In this example, the whole is the sample of 100 subjects, and gender is described as including two parts, 40 females and 60 males. A percentage is calculated by dividing the smaller number, which would be a part of the whole, by the larger number, which represents the whole. The result of this calculation is then multiplied by 100%. For example, if 14 nurses out of a total of 62 are working on a given day, you can divide 14 by 62 and multiply by 100% to calculate the percentage of nurses working that day. Calculations: (14 ÷ 62) × 100% = 0.2258 × 100% = 22.58% = 22.6%. The answer also might be expressed as a whole percentage, which would be 23% in this example. 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% (Grove, Gray, & Burns, 2015). Cumulative percentages can also be used to deter-mine percentile ranks, especially when discussing standardized 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 75 th percentile. When reported as a percentile rank, the percentage is often rounded to the nearest whole number. Percentile ranks can be used to analyze ordinal data that can be assigned to categories that can be ranked. Percentile ranks and cumulative percentages might also 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 is presented as an example for 200 subjects: Income Level Frequency ( f ) Percentage (%) Cumulative % 1. $100,000 105%100% EXERCISE 6 60EXERCISE 6 • Understanding Frequencies and PercentagesCopyright © 2017, Elsevier Inc. All rights reserved. In data analysis, percentage distributions can be used to compare ﬁ ndings from different studies that have different sample sizes, and these distributions are usually arranged in tables in order either from greatest to least or least to greatest percentages ( Plichta & Kelvin, 2013 ). RESEARCH ARTICLE Source Eckerblad, J., Tödt, K., Jakobsson, P., Unosson, M., Skargren, E., Kentsson, M., & Thean-der, K. (2014). Symptom burden in stable COPD patients with moderate to severe airﬂ ow limitation. Heart & Lung, 43 (4), 351–357. Introduction Eckerblad and colleagues (2014 , p. 351) conducted a comparative descriptive study to examine the symptoms of “patients with stable chronic obstructive pulmonary disease (COPD) and determine whether symptom experience differed between patients with mod-erate or severe airﬂ ow limitations.” The Memorial Symptom Assessment Scale (MSAS) was used to measure the symptoms of 42 outpatients with moderate airﬂ ow limitations and 49 patients with severe airﬂ ow limitations. The results indicated that the mean number of symptoms was 7.9 ( ± 4.3) for both groups combined, with no signiﬁ cant dif-ferences found in symptoms between the patients with moderate and severe airﬂ ow limi-tations. For patients with the highest MSAS symptom burden scores in both the moderate and the severe limitations groups, the symptoms most frequently experienced included shortness of breath, dry mouth, cough, sleep problems, and lack of energy. The research-ers concluded that patients with moderate or severe airﬂ ow limitations experienced mul-tiple severe symptoms that caused high levels of distress. Quality assessment of COPD patients ’ physical and psychological symptoms is needed to improve the management of their symptoms. Relevant Study Results Eckerblad et al. (2014 , p. 353) noted in their research report that “In total, 91 patients assessed with MSAS met the criteria for moderate ( n = 42) or severe airﬂ ow limitations ( n = 49). Of those 91 patients, 47% were men, and 53% were women, with a mean age of 68 ( ± 7) years for men and 67 ( ± 8) years for women. The majority (70%) of patients were married or cohabitating. In addition, 61% were retired, and 15% were on sick leave. Twenty-eight percent of the patients still smoked, and 69% had stopped smoking. The mean BMI (kg/m 2 ) was 26.8 ( ± 5.7). There were no signiﬁ cant differences in demographic characteristics, smoking history, or BMI between patients with moderate and severe airﬂ ow limitations ( Table 1 ). A lower proportion of patients with moderate airﬂ ow limitation used inhalation treatment with glucocorticosteroids, long-acting β 2 -agonists and short-acting β 2 -agonists, but a higher proportion used analgesics compared with patients with severe airﬂ ow limitation. Symptom prevalence and symptom experience The patients reported multiple symptoms with a mean number of 7.9 ( ± 4.3) symptoms (median = 7, range 0–32) for the total sample, 8.1 ( ± 4.4) for moderate airﬂ ow limitation and 7.7 ( ± 4.3) for severe airﬂ ow limitation ( p = 0.36) . . . . Highly prevalent physical symp-toms ( ≥ 50% of the total sample) were shortness of breath (90%), cough (65%), dry mouth (65%), and lack of energy (55%). Five additional physical symptoms, feeling drowsy Understanding Frequencies and Percentages • EXERCISE 6Copyright © 2017, Elsevier Inc. All rights reserved. TABLE 1 BACKGROUND CHARACTERISTICS AND USE OF MEDICATION FOR PATIENTS WITH STABLE CHRONIC OBSTRUCTIVE LUNG DISEASE CLASSIFIED IN PATIENTS WITH MODERATE AND SEVERE AIRFLOW LIMITATION Moderate n = 42 Severe n = 49 p Value Sex, n (%)0.607 Women19 (45)29 (59) Men23 (55)20 (41)Age (yrs), mean ( SD )66.5 (8.6)67.9 (6.8)0.396Married/cohabitant n (%)29 (69)34 (71)0.854Employed, n (%)7 (17)7 (14)0.754Smoking, n %0.789 Smoking13 (31)12 (24) Former smokers28 (67)35 (71) Never smokers1 (2)2 (4)Pack years smoking, mean ( SD )29.1 (13.5)34.0 (19.5)0.177BMI (kg/m 2 ), mean ( SD )27.2 (5.2)26.5 (6.1)0.555FEV 1 % of predicted, mean ( SD )61.6 (8.4)42.2 (5.8) < 0.001SpO 2 % mean ( SD )95.8 (2.4)94.5 (3.0)0.009Physical health, mean ( SD )3.2 (0.8)3.0 (0.8)0.120Mental health, mean ( SD )3.7 (0.9)3.6 (1.0)0.628Exacerbation previous 6 months, n (%)14 (33)15 (31)0.781Admitted to hospital previous year, n (%)10 (24)14 (29)0.607Medication use, n (%) Inhaled glucocorticosteroids30 (71)44 (90)0.025 Systemic glucocorticosteroids3 (6.3)0 (0)0.094 Anticholinergic32 (76)42 (86)0.245 Long-acting β 2 -agonists30 (71)45 (92)0.011 Short-acting β 2 -agonists13 (31)32 (65)0.001 Analgesics11 (26)5 (10)0.046 Statins8 (19)11 (23)0.691 Eckerblad, J., Tödt, K., Jakobsson, P., Unosson, M., Skargren, E., Kentsson, M., & Theander, K. (2014). Symptom burden in stable COPD patients with moderate to severe airﬂ ow limitation. Heart & Lung, 43 (4), p. 353. numbness/tingling in hands/feet, feeling irritable, and dizziness, were reported by between 25% and 50% of the patients. The most commonly reported psychological symptom was difﬁ culty sleeping (52%), followed by worrying (33%), feeling irritable (28%) and feeling sad (22%). There were no signiﬁ cant differences in the occurrence of physical and psy-chological symptoms between patients with moderate and severe airﬂ ow limitations” ( Eckerblad et al., 2014 , p. 353). 62EXERCISE 6 • Understanding Frequencies and PercentagesCopyright © 2017, Elsevier Inc. All rights reserved. STUDY QUESTIONS 1. What are the frequency and percentage of women in the moderate airﬂ ow limitation group? 2. What were the frequencies and percentages of the moderate and the severe airﬂ ow limitation groups who experienced an exacerbation in the previous 6 months? 3. What is the total sample size of COPD patients included in this study? What number or fre-quency of the subjects is married/cohabitating? What percentage of the total sample is married or cohabitating? 4. Were the moderate and severe airﬂ ow limitation groups signiﬁ cantly different regarding married/cohabitating status? Provide a rationale for your answer. 5. List at least three other relevant demographic variables the researchers might have gathered data on to describe this study sample. 6. For the total sample, what physical symptoms were experienced by ≥ 50% of the subjects? Identify the physical symptoms and the percentages of the total sample experiencing each symptom.

Interpreting Line Graphs EXERCISE 7

69 Interpreting Line Graphs STATISTICAL TECHNIQUE IN REVIEW Tables and ﬁ gures are commonly used to present ﬁ ndings from studies or to provide a way for researchers to become familiar with research data. Using ﬁ gures, researchers are able to illustrate the results from descriptive data analyses, assist in identifying patterns in data, identify changes over time, and interpret exploratory ﬁ ndings. A line graph is a ﬁ gure that is developed by joining a series of plotted points with a line to illustrate how a variable changes over time. A line graph ﬁ gure 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 mean scores or values for a variable ( Grove, Burns, & Gray, 2013 ; Plichta & Kelvin, 2013 ). Researchers might include a line graph to compare the values for three or four variables in a study or to identify the changes in groups for a selected variable over time. For example, Figure 7-1 presents a line graph that documents time in weeks on the x -axis and mean weight loss in pounds on the y -axis for an experimental group consuming a low carbohydrate diet and a control group consuming a standard diet. This line graph illustrates the trend of a strong, steady increase in the mean weight lost by the experimental or intervention group and minimal mean weight loss by the control group. EXERCISE 7 FIGURE 7-1 ■ LINE GRAPH COMPARING EXPERIMENTAL AND CONTROL GROUPS FOR WEIGHT LOSS OVER FOUR WEEKS. Weight loss (lbs)Weeksy-axisx-axisControlExperimental10864201234 70EXERCISE 7 • Interpreting Line GraphsCopyright © 2017, Elsevier Inc. All rights reserved. RESEARCH ARTICLE Source Azzolin, K., Mussi, C. M., Ruschel, K. B., de Souza, E. N., Lucena, A. D., & Rabelo-Silva, E. R. (2013). Effectiveness of nursing interventions in heart failure patients in home care using NANDA-I, NIC, and NOC. Applied Nursing Research, 26 (4), 239–244. Introduction Azzolin and colleagues (2013) analyzed data from a larger randomized clinical trial to determine the effectiveness of 11 nursing interventions (NIC) on selected nursing out-comes (NOC) in a sample of patients with heart failure (HF) receiving home care. A total of 23 patients with HF were followed for 6 months after hospital discharge and provided four home visits and four telephone calls. The home visits and phone calls were organized using the nursing diagnoses from the North American Nursing Diagnosis Association International (NANDA-I) classiﬁ cation list. The researchers found that eight nursing interven tions signiﬁ cantly improved the nursing outcomes for these HF patients. Those interventions included “health education, self-modiﬁ cation assistance, behavior modiﬁ -cation, telephone consultation, nutritional counselling, teaching: prescribed medications, teaching: disease process, and energy management” ( Azzolin et al., 2013 , p. 243). The researchers concluded that the NANDA-I, NIC, and NOC linkages were useful in manag-ing patients with HF in their home. Relevant Study Results Azzolin and colleagues (2013) presented their results in a line graph format to display the nursing outcome changes over the 6 months of the home visits and phone calls. The nursing outcomes were measured with a ﬁ ve-point Likert scale with 1 = worst and 5 = best. “Of the eight outcomes selected and measured during the visits, four belonged to the health & knowledge behavior domain (50%), as follows: knowledge: treatment regimen; compliance behavior; knowledge: medication; and symptom control. Signiﬁ cant increases were observed in this domain for all outcomes when comparing mean scores obtained at visits no. 1 and 4 ( Figure 1 ; p < 0.001 for all comparisons). The other four outcomes assessed belong to three different NOC domains, namely, functional health (activity tolerance and energy conservation), physiologic health (ﬂ uid balance), and family health (family participation in professional care). The scores obtained for activity tolerance and energy conservation increased signiﬁ cantly from visit no. 1 to visit no. 4 ( p = 0.004 and p < 0.001, respectively). Fluid balance and family participation in professional care did not show statistically signiﬁ cant differences ( p = 0.848 and p = 0.101, respectively) ( Figure 2 )” ( Azzolin et al., 2013 , p. 241). The signiﬁ cance level or alpha ( α ) was set at 0.05 for this study. Interpreting Line Graphs • EXERCISE 7Copyright © 2017, Elsevier Inc. All rights reserved. FIGURE 2 ■ NURSING OUTCOMES MEASURED OVER 6 MONTHS (OTHER DOMAINS): Activity tolerance (95% CI − 1.38 to − 0.18, p = 0.004); energy conservation (95% CI − 0.62 to − 0.19, p < 0.001); ﬂ uid balance (95% CI − 0.25 to 0.07, p = .848); family participation in professional care (95% CI − 2.31 to − 0.11, p = 0.101). HV = home visit. CI = conﬁ dence interval. Azzolin, K., Mussi, C. M., Ruschel, K. B., de Souza, E. N., Lucena, A. D., & Rabelo-Silva, E. R. (2013). Effectiveness of nursing interventions in heart failure patients in home care using NANDA-I, NIC, and NOC. Applied Nursing Research, 26 (4), p. 242. 5.04.54.03.53.02.52.01.51.00.50MeanHV1HV2HV3HV4Fluid balanceFamily participationin professional careActivity toleranceEnergy conservation FIGURE 1 ■ NURSING OUTCOMES MEASURED OVER 6 MONTHS (HEALTH & KNOWLEDGE BEHAVIOR DOMAIN): Knowledge: medication (95% CI − 1.66 to − 0.87, p < 0.001); knowledge: treatment regimen (95% CI − 1.53 to − 0.98, p < 0.001); symptom control (95% CI − 1.93 to − 0.95, p < 0.001); and compliance behavior (95% CI − 1.24 to − 0.56, p < 0.001). HV = home visit. CI = conﬁ dence interval. 5.04.54.03.53.02.52.01.51.00.50MeanHV1HV2HV3HV4Compliance behaviorSymptom controlKnowledge: medicationKnowledge: treatment reg 72EXERCISE 7 • Interpreting Line GraphsCopyright © 2017, Elsevier Inc. All rights reserved. STUDY QUESTIONS 1. What is the purpose of a line graph? What elements are included in a line graph? 2. Review Figure 1 and identify the focus of the x -axis and the y -axis. What is the time frame for the x -axis? What variables are presented on this line graph? 3. In Figure 1 , did the nursing outcome compliance behavior change over the 6 months of home visits? Provide a rationale for your answer. 4. State the null hypothesis for the nursing outcome compliance behavior. 5. Was there a signiﬁ cant difference in compliance behavior from the ﬁ rst home visit (HV1) to the fourth home visit (HV4)? Was the null hypothesis accepted or rejected? Provide a rationale for your answer. 6. In Figure 1 , what outcome had the lowest mean at HV1? Did this outcome improve over the four home visits? Provide a rationale for your answer.

Copyright © 2017, Elsevier Inc. All rights reserved. 77

Questions to Be Graded EXERCISE 7 Follow your instructor ’ s directions to submit your answers to the following questions for grading. Your instructor may ask you to write your answers below and submit them as a hard copy for grading. Alternatively, your instructor may ask you to use the space below for notes and submit your answers online at http://evolve.elsevier.com/Grove/statistics/ under “Questions to Be Graded.”

What is the focus of the example Figure 7-1 in the section introducing the statistical technique of this exercise?

In Figure 2 of the Azzolin et al. (2013 , p. 242) study, did the nursing outcome activity tolerance change over the 6 months of home visits (HVs) and telephone calls? Provide a rationale for your answer.

State the null hypothesis for the nursing outcome activity tolerance.

Was there a signiﬁ cant difference in activity tolerance from the ﬁ rst home visit (HV1) to the fourth home visit (HV4)? Was the null hypothesis accepted or rejected? Provide a rationale for your answer.

In Figure 2 , what nursing outcome had the lowest mean at HV1? Did this outcome improve over the four HVs? Provide a rationale for your answer.

What nursing outcome had the highest mean at HV1 and at HV4? Was this outcome signiﬁ -cantly different from HV1 to HV4? Provide a rationale for your answer.

State the null hypothesis for the nursing outcome family participation in professional care.

Was there a statistically signiﬁ cant difference in family participation in professional care from HV1 to HV4? Was the null hypothesis accepted or rejected? Provide a rationale for your answer.

Was Figure 2 helpful in understanding the nursing outcomes for patients with heart failure (HF) who received four HVs and telephone calls? Provide a rationale for your answer. 10. What nursing interventions signiﬁ cantly improved the nursing outcomes for these patients with HF? What implications for practice do you note from these study results? Copyright © 2017, Elsevier Inc. All rights reserved. 79 Measures of Central Tendency : Mean, Median, and Mode

EXERCISE 8 STATISTICAL TECHNIQUE IN REVIEW Mean, median, and mode are the three measures of central tendency used to describe study variables. These statistical techniques are calculated to determine the center of a distribution of data, and the central tendency that is calculated is determined by the level of measurement of the data (nominal, ordinal, interval, or ratio; see Exercise 1 ). The mode is a category or score that occurs with the greatest frequency in a distribution of scores in a data set. The mode is the only acceptable measure of central tendency for analyzing nominal-level data, which are not continuous and cannot be ranked, compared, or sub-jected to mathematical operations. If a distribution has two scores that occur more fre-quently than others (two modes), the distribution is called bimodal . A distribution with more than two modes is multimodal ( Grove, Burns, & Gray, 2013 ). The median ( MD ) is a score that lies in the middle of a rank-ordered list of values of a distribution. If a distribution consists of an odd number of scores, the MD is the middle score that divides the rest of the distribution into two equal parts, with half of the values falling above the middle score and half of the values falling below this score. In a distribu-tion with an even number of scores, the MD is half of the sum of the two middle numbers of that distribution. If several scores in a distribution are of the same value, then the MD will be the value of the middle score. The MD is the most precise measure of central ten-dency for ordinal-level data and for nonnormally distributed or skewed interval- or ratio-level data. The following formula can be used to calculate a median in a distribution of scores. Median()()MDN=+÷12 N is the number of scores ExampleMedianscoreth:N==+=÷=31311232216 ExampleMedianscoreth:.N==+=÷=404012412205 Thus in the second example, the median is halfway between the 20 th and the 21 st scores. The mean ( X ) is the arithmetic average of all scores of a sample, that is, the sum of its individual scores divided by the total number of scores. The mean is the most accurate measure of central tendency for normally distributed data measured at the interval and ratio levels and is only appropriate for these levels of data (Grove, Gray, & Burns, 2015). In a normal distribution, the mean, median, and mode are essentially equal (see Exercise 26 for determining the normality of a distribution). The mean is sensitive to extreme

Copyright © 2017, Elsevier Inc. All rights reserved. 77 Questions to Be Graded EXERCISE 7 Follow your instructor ’ s directions to submit your answers to the following questions for grading. Your instructor may ask you to write your answers below and submit them as a hard copy for grading. Alternatively, your instructor may ask you to use the space below for notes and submit your answers online at http://evolve.elsevier.com/Grove/statistics/ under “Questions to Be Graded.” 1. What is the focus of the example Figure 7-1 in the section introducing the statistical technique of this exercise? 2. In Figure 2 of the Azzolin et al. (2013 , p. 242) study, did the nursing outcome activity tolerance change over the 6 months of home visits (HVs) and telephone calls? Provide a rationale for your answer. 3. State the null hypothesis for the nursing outcome activity tolerance. 4. Was there a signiﬁ cant difference in activity tolerance from the ﬁ rst home visit (HV1) to the fourth home visit (HV4)? Was the null hypothesis accepted or rejected? Provide a rationale for your answer. Name: _______________________________________________________ Class: _____________________ Date: ___________________________________________________________________________________ 78EXERCISE 7 • Interpreting Line GraphsCopyright © 2017, Elsevier Inc. All rights reserved. 5. In Figure 2 , what nursing outcome had the lowest mean at HV1? Did this outcome improve over the four HVs? Provide a rationale for your answer. 6. What nursing outcome had the highest mean at HV1 and at HV4? Was this outcome signiﬁ -cantly different from HV1 to HV4? Provide a rationale for your answer. 7. State the null hypothesis for the nursing outcome family participation in professional care. 8. Was there a statistically signiﬁ cant difference in family participation in professional care from HV1 to HV4? Was the null hypothesis accepted or rejected? Provide a rationale for your answer. 9. Was Figure 2 helpful in understanding the nursing outcomes for patients with heart failure (HF) who received four HVs and telephone calls? Provide a rationale for your answer. 10. What nursing interventions signiﬁ cantly improved the nursing outcomes for these patients with HF? What implications for practice do you note from these study results? Copyright © 2017, Elsevier Inc. All rights reserved. 79 Measures of Central Tendency : Mean, Median, and Mode EXERCISE 8 STATISTICAL TECHNIQUE IN REVIEW Mean, median, and mode are the three measures of central tendency used to describe study variables. These statistical techniques are calculated to determine the center of a distribution of data, and the central tendency that is calculated is determined by the level of measurement of the data (nominal, ordinal, interval, or ratio; see Exercise 1 ). The mode is a category or score that occurs with the greatest frequency in a distribution of scores in a data set. The mode is the only acceptable measure of central tendency for analyzing nominal-level data, which are not continuous and cannot be ranked, compared, or sub-jected to mathematical operations. If a distribution has two scores that occur more fre-quently than others (two modes), the distribution is called bimodal . A distribution with more than two modes is multimodal ( Grove, Burns, & Gray, 2013 ). The median ( MD ) is a score that lies in the middle of a rank-ordered list of values of a distribution. If a distribution consists of an odd number of scores, the MD is the middle score that divides the rest of the distribution into two equal parts, with half of the values falling above the middle score and half of the values falling below this score. In a distribu-tion with an even number of scores, the MD is half of the sum of the two middle numbers of that distribution. If several scores in a distribution are of the same value, then the MD will be the value of the middle score. The MD is the most precise measure of central ten-dency for ordinal-level data and for nonnormally distributed or skewed interval- or ratio-level data. The following formula can be used to calculate a median in a distribution of scores. Median()()MDN=+÷12 N is the number of scores ExampleMedianscoreth:N==+=÷=31311232216 ExampleMedianscoreth:.N==+=÷=404012412205 Thus in the second example, the median is halfway between the 20 th and the 21 st scores. The mean ( X ) is the arithmetic average of all scores of a sample, that is, the sum of its individual scores divided by the total number of scores. The mean is the most accurate measure of central tendency for normally distributed data measured at the interval and ratio levels and is only appropriate for these levels of data (Grove, Gray, & Burns, 2015). In a normal distribution, the mean, median, and mode are essentially equal (see Exercise 26 for determining the normality of a distribution). The mean is sensitive to extreme

Copyright © 2017, Elsevier Inc. All rights reserved. 77 Questions to Be Graded EXERCISE 7 Follow your instructor ’ s directions to submit your answers to the following questions for grading. Your instructor may ask you to write your answers below and submit them as a hard copy for grading. Alternatively, your instructor may ask you to use the space below for notes and submit your answers online at http://evolve.elsevier.com/Grove/statistics/ under “Questions to Be Graded.”

What is the focus of the example Figure 7-1 in the section introducing the statistical technique of this exercise?

In Figure 2 of the Azzolin et al. (2013 , p. 242) study, did the nursing outcome activity tolerance change over the 6 months of home visits (HVs) and telephone calls? Provide a rationale for your answer.

State the null hypothesis for the nursing outcome activity tolerance.

Was there a signiﬁ cant difference in activity tolerance from the ﬁ rst home visit (HV1) to the fourth home visit (HV4)? Was the null hypothesis accepted or rejected? Provide a rationale for your answer.

In Figure 2 , what nursing outcome had the lowest mean at HV1? Did this outcome improve over the four HVs? Provide a rationale for your answer.

What nursing outcome had the highest mean at HV1 and at HV4? Was this outcome signiﬁ -cantly different from HV1 to HV4? Provide a rationale for your answer.

State the null hypothesis for the nursing outcome family participation in professional care.

Was there a statistically signiﬁ cant difference in family participation in professional care from HV1 to HV4? Was the null hypothesis accepted or rejected? Provide a rationale for your answer.

Was Figure 2 helpful in understanding the nursing outcomes for patients with heart failure (HF) who received four HVs and telephone calls? Provide a rationale for your answer.

What nursing interventions signiﬁ cantly improved the nursing outcomes for these patients with HF? What implications for practice do you note from these study results?

Copyright © 2017, Elsevier Inc. All rights reserved. 79 Measures of Central Tendency : Mean, Median, and Mode EXERCISE 8 STATISTICAL TECHNIQUE IN REVIEW Mean, median, and mode are the three measures of central tendency used to describe study variables. These statistical techniques are calculated to determine the center of a distribution of data, and the central tendency that is calculated is determined by the level of measurement of the data (nominal, ordinal, interval, or ratio; see Exercise 1 ). The mode is a category or score that occurs with the greatest frequency in a distribution of scores in a data set. The mode is the only acceptable measure of central tendency for analyzing nominal-level data, which are not continuous and cannot be ranked, compared, or sub-jected to mathematical operations. If a distribution has two scores that occur more fre-quently than others (two modes), the distribution is called bimodal . A distribution with more than two modes is multimodal ( Grove, Burns, & Gray, 2013 ). The median ( MD ) is a score