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

124 CHAPTER 4 | Variability
Data from Experiment A
Data from Experiment B
Treatment 1 M 5 35 Treatment 1 M 5 35
3
Treatment 2 M 5 40
Treatment 2 M 5 40
3
f
2
f 2
1
1
33 34 35 36 37 38 39 40 41 42 X
10 20 30 40 50 60
X
FIGURE 4.8
Graphs showing the results from two experiments. In experiment A, the variability is small and it is easy to see the
5-point mean difference between the two treatments. In experiment B, however, the 5-point mean difference between
treatments is obscured by the large variability.
For each experiment, the data have been constructed so that there is a 5-point mean difference
between the two treatments: On average, the scores in treatment 2 are 5 points higher
than the scores in treatment 1. The 5-point difference is relatively easy to see in Experiment
A, where the variability is low, but the same 5-point difference is difficult to see in Experiment
B, where the variability is large. Again, high variability tends to obscure any patterns
in the data. This general fact is perhaps even more convincing when the data are presented
in a graph. Figure 4.8 shows the two sets of data from Experiments A and B. Notice that
the results from Experiment A clearly show the 5-point difference between treatments. One
group of scores piles up around 35 and the second group piles up around 40. On the other
hand, the scores from Experiment B (Figure 4.8) seem to be mixed together randomly with
no clear difference between the two treatments.
In the context of inferential statistics, the variance that exists in a set of sample data is
often classified as error variance. This term is used to indicate that the sample variance
represents unexplained and uncontrolled differences between scores. As the error variance
increases, it becomes more difficult to see any systematic differences or patterns that might
exist in the data. An analogy is to think of variance as the static that appears on a radio station
or a cell phone when you enter an area of poor reception. In general, variance makes it
difficult to get a clear signal from the data. High variance can make it difficult or impossible
to see a mean difference between two sets of scores, or to see any other meaningful patterns
in the results from a research study.
LEARNING CHECK
1. How is the standard deviation represented in a frequency distribution graph?
a. By a vertical line located at a distance of one standard deviation above the mean.
b. By two vertical lines located one standard deviation above the mean and one
standard deviation below the mean.
c. By a horizontal line or arrow extending from a location one standard deviation
above the mean to a location one standard deviation below the mean.
d. By a horizontal line or arrow extending from the mean for a distance equal to
one standard deviation.