Questions to Be Graded EXERCISE 26
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: _____________________
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,
negatively skewed, or approximately normal? Provide a rationale for your answer.
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
Copyright © 2017, Elsevier Inc. All rights reserved.
5. How would you characterize the kurtosis of the distribution in Question 4—leptokurtic, mesokurtic,
or platykurtic? Provide a rationale for your answer.
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?
Copyright © 2017, Elsevier Inc. All rights reserved. 291
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:
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.
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