## 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 subjected to mathematical operations. If a distribution has two scores that occur more frequently 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 distribution 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 tendency for ordinal-level data and for non-normally 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).

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

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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 subjected to mathematical operations. If a distribution has two scores that occur more frequently 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 distribution 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 tendency for ordinal-level data and for non-normally 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 “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 significant difference in activity tolerance from the first home visit (HV1) to the fourth home visit (HV4)? Was the null hypothesis accepted or rejected? Provide a rationale for your answer.

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 significantly 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 significant 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 significantly improved the nursing outcomes for these patients with HF? What implications for practice do you note from these study results?