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# Measures of Dispersion : Range and Standard Deviation

1. What were the name and type of measurement method used to measure Caring Practices in the Roch, Dubois, and Clarke (2014) study?

2. The data collected with the scale identiﬁed in Questions 1 were at what level of measurement? Provide a rationale for your answer.

3. What were the subscales included in the CNPISS used to measure RNs ’ perceptions of their Caring Practices? Do these subscales seem relevant? Document your answer.

4. Which subscale for Caring Practices had the lowest mean? What does this result indicate?

5. What were the dispersion results for the Relational Care subscale of the Caring Practices in Table 2 ? What do these results indicate?

6. Which subscale of Caring Practices has the lowest dispersion or variation of scores? Provide a rationale for your answer.

7. Which subscale of Caring Practices had the highest mean? What do these results indicate?

8. Compare the Overall rating for Organizational Climate with the Overall rating of Caring Practices. What do these results indicate?

9. The response rate for the survey in this study was 45%. Is this a study strength or limitation? Provide a rationale for your answer.

10. What conclusions did the researchers make regarding the caring practices of the nurses in this study? How might these results affect your practice?

## Measures of Dispersion : Range and Standard Deviation – Exercise 9

STATISTICAL TECHNIQUE IN REVIEW

Measures of dispersion , or measures of variability, are descriptive statistical techniques conducted to identify individual differences of the scores in a sample. These techniques give some indication of how scores in a sample are dispersed, or spread, around the mean. The measures of dispersion indicate how different the scores are or the extent that indi-vidual scores deviate from one another. If the individual scores are similar, dispersion or variability values are small and the sample is relatively homogeneous , or similar, in terms of these scores.

A heterogeneous sample has a wide variation in the scores, resulting in increased values for the measures of dispersion. Range and standard deviation are the most common measures of dispersion included in research reports. The simplest measure of dispersion is the range . In published studies, range is pre-sented in two ways: (1) the range includes the lowest and highest scores obtained for a variable, or (2) the range is calculated by subtracting the lowest score from the highest score. For example, the range for the following scores, 8, 9, 9, 10, 11, 11, might be reported as 8 to 11 (8–11), which identiﬁes outliers or extreme values for a variable. The range can also be calculated as follows: 11 − 8 = 3. In this form, the range is a difference score that uses only the two extreme scores for the comparison.

The range is generally reported in published studies but is not used in further analyses ( Grove, Burns, & Gray, 2013 ). The standard deviation ( SD ) is a measure of dispersion and is the average number of points by which the scores of a distribution vary from the mean. The SD is an important statistic, both for understanding dispersion within a distribution and for interpreting the relationship of a particular value to the distribution. When the scores of a distribution deviate from the mean considerably, the SD or spread of scores is large.

When the degree of deviation of scores from the mean is small, the SD or spread of the scores is small. SD is a measure of dispersion that is the square root of the variance. The equation and steps for calculating the standard deviation are presented in Exercise 27 , which is focused on calculating descriptive statistics.

### RESEARCH ARTICLE

Introduction Roch and colleagues (2014) conducted a two-phase mixed methods study ( Creswell, 2014 ) to describe the elements of the organizational climate of hospitals that directly affect nursing practice. The ﬁ rst phase of the study was quantitative and involved surveying nurses ( N = 292), who described their hospital organizational climate and their caring practices. The second phase was qualitative and involved a study of 15 direct-care regis-tered nurses (RNs), nursing personnel, and managers.

The researchers found the follow-ing: “Workload intensity and role ambiguity led RNs to leave many caring practices to practical nurses and assistive personnel. Systemic interventions are needed to improve organizational climate and to support RNs ’ involvement in a full range of caring prac-tices” ( Roch et al., 2014 , p. 229).

Relevant Study Results The survey data were collected using the Psychological Climate Questionnaire (PCQ) and the Caring Nurse-Patient Interaction Short Scale (CNPISS). The PCQ included a ﬁ ve-point Likert-type scale that ranged from strongly disagree to strongly agree , with the high scores corresponding to positive perceptions of the organizational climate.

The CNPISS included a ﬁ ve-point Likert scale ranging from almost never to almost always, with the higher scores indicating higher frequency of performing caring practices. The return rate for the surveys was 45%. The survey results indicated that “[n]urses generally assessed overall organizational climate as moderately positive ( Table 2 ).

The job dimension relat-ing to autonomy, respondents ’ perceptions of the importance of their work, and the feeling of being challenged at work was rated positively. Role perceptions (personal work-load, role clarity, and role-related conﬂict), ratings of manager leadership, and work groups were signiﬁcantly more negative, hovering around the midpoint of the scale, with organization ratings slightly below this midpoint of 2.5.

Caring practices were regularly performed; mean scores were either slightly above or well above the 2.5 midpoint of a 5-point scale. The subscale scores clearly indicated, however, that although relational care elements were often carried out, they were less frequent than clinical or comfort care” ( Roch et al., 2014 , p. 233).

Last Updated on February 11, 2019

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