Statistics for the Behavioral Sciences by Frederick J. Gravetter, Larry B. Wallnau ISBN 10: 1305504917 ISBN 13: 9781305504912

SECTION 4.6 | More about Variance and Standard Deviation 121
scores have been multiplied by 2, these scores become X 5 82 and X 5 86. Now
the distance between scores is 4 points, twice the original distance. Multiplying
each score causes each distance to be multiplied, so the standard deviation also is
multiplied by the same amount.
IN THE LITERATURE
Reporting the Standard Deviation
In reporting the results of a study, the researcher often provides descriptive information
for both central tendency and variability. The dependent variables in psychology
research are often numerical values obtained from measurements on interval or ratio
scales. With numerical scores the most common descriptive statistics are the mean
(central tendency) and the standard deviation (variability), which are usually reported
together. In many journals, especially those following APA style, the symbol SD is used
for the sample standard deviation. For example, the results might state:
Children who viewed the violent cartoon displayed more aggressive responses
(M 5 12.45, SD 5 3.7) than those who viewed the control cartoon (M 5 4.22,
SD 5 1.04).
When reporting the descriptive measures for several groups, the findings may be
summarized in a table. Table 4.2 illustrates the results of hypothetical data.
TA B L E 4.2
The number of aggressive
behaviors for male
and female adolescents
after playing a violent or
nonviolent video game.
Males
Females
Type of Video Game
Violent
Control
M 5 7.72 M 5 4.34
SD 5 2.43 SD 5 2.16
M 5 2.47 M 5 1.61
SD 5 0.92 SD 5 0.68
Sometimes the table also indicates the sample size, n, for each group. You should
remember that the purpose of the table is to present the data in an organized, concise,
and accurate manner.
■ Standard Deviation and Descriptive Statistics
Because standard deviation requires extensive calculations, there is a tendency to get lost
in the arithmetic and forget what standard deviation is and why it is important. Standard
deviation is primarily a descriptive measure; it describes how variable, or how spread
out, the scores are in a distribution. Behavioral scientists must deal with the variability
that comes from studying people and animals. People are not all the same; they have
different attitudes, opinions, talents, IQs, and personalities. Although we can calculate
the average value for any of these variables, it is equally important to describe the variability.
Standard deviation describes variability by measuring distance from the mean. In
any distribution, some individuals will be close to the mean, and others will be relatively
far from the mean. Standard deviation provides a measure of the typical, or standard,
distance from the mean.
Describing an Entire Distribution Rather than listing all of the individual scores in
a distribution, research reports typically summarize the data by reporting only the mean