Questions to Be Graded EXERCISE 26

grading. Alternatively, your instructor may ask you to use the space below for notes and submit your

Name: _______________________________________________________ Class: _____________________

Date: ___________________________________________________________________________________

1. Plot the frequency distribution for “Age at Enrollment” by hand or by using SPSS.

2. How would you characterize the skewness of the distribution in Question 1—positively skewed,

3. Compare the original skewness statistic and Shapiro-Wilk statistic with those of the smaller

dataset ( n = 15) for the variable “Age at First Arrest.” How did the statistics change, and how

would you explain these differences?

4. Plot the frequency distribution for “Years of Education” by hand or by using SPSS.

290 EXERCISE 26 • Determining the Normality of a Distribution

5. How would you characterize the kurtosis of the distribution in Question 4—leptokurtic, mesokurtic,

6. What is the skewness statistic for “Age at Enrollment”? How would you characterize the magnitude

of the skewness statistic for “Age at Enrollment”?

7. What is the kurtosis statistic for “Years of Education”? How would you characterize the magnitude

of the kurtosis statistic for “Years of Education”?

8. Using SPSS, compute the Shapiro-Wilk statistic for “Number of Times Fired from Job.” What

would you conclude from the results?

9. In the SPSS output table titled “Tests of Normality,” the Shapiro-Wilk statistic is reported along

with the Kolmogorov-Smirnov statistic. Why is the Kolmogorov-Smirnov statistic inappropriate

to report for these example data?

10. How would you explain the skewness statistic for a particular frequency distribution being low

and the Shapiro-Wilk statistic still being signifi cant at p < 0.05?

Calculating Descriptive Statistics

There are two major classes of statistics: descriptive statistics and inferential statistics.

Descriptive statistics are computed to reveal characteristics of the sample data set and to

describe study variables. Inferential statistics are computed to gain information about

effects and associations in the population being studied. For some types of studies,

descriptive statistics will be the only approach to analysis of the data. For other studies,

descriptive statistics are the fi rst step in the data analysis process, to be followed by inferential

statistics. For all studies that involve numerical data, descriptive statistics are

crucial in understanding the fundamental properties of the variables being studied. Exercise

27 focuses only on descriptive statistics and will illustrate the most common descriptive

statistics computed in nursing research and provide examples using actual clinical

data from empirical publications.

MEASURES OF CENTRAL TENDENCY

A measure of central tendency is a statistic that represents the center or middle of a

frequency distribution. The three measures of central tendency commonly used in nursing

research are the mode, median ( MD ), and mean ( X ). The mean is the arithmetic average

of all of a variable ’ s values. The median is the exact middle value (or the average of the

middle two values if there is an even number of observations). The mode is the most

commonly occurring value or values (see Exercise 8 ).

The following data have been collected from veterans with rheumatoid arthritis ( Tran,

Hooker, Cipher, & Reimold, 2009 ). The values in Table 27-1 were extracted from a larger

sample of veterans who had a history of biologic medication use (e.g., infl iximab [Remicade],

etanercept [Enbrel]). Table 27-1 contains data collected from 10 veterans who had

stopped taking biologic medications, and the variable represents the number of years that

each veteran had taken the medication before stopping.

Because the number of study subjects represented below is 10, the correct statistical

notation to refl ect that number is:

n 10

Note that the n is lowercase, because we are referring to a sample of veterans. If the

data being presented represented the entire population of veterans, the correct notation

is the uppercase N. Because most nursing research is conducted using samples, not populations,

all formulas in the subsequent exercises will incorporate the sample notation, n.

Mode

The mode is the numerical value or score that occurs with the greatest frequency; it does

not necessarily indicate the center of the data set. The data in Table 27-1 contain two

EXERCISE

27 