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

FOCUS ON PROBLEM SOLVING 127
VAR00001
Valid N (listwise)
F I G U R E 4.9
The SPSS summary table showing descriptive statistics for the sample of n 5 8 scores in
Example 4.6.
2. Highlight the column label for the set of scores (VAR00001) in the left box and click the
arrow to move it into the Variable box.
3. If you want the variance and/or the range reported along with the standard deviation, click
on the Options box, select Variance and/or Range, then click Continue.
4. Click OK.
SPSS Output
We used SPSS to compute the range, standard deviation, and variance for the sample data in
Example 4.6 and the output is shown in Figure 4.9. The summary table lists the number of
scores, maximum and minimum scores, mean, range, standard deviation, and variance. Note
that the range and variance are included because these values were selected using the Options
box during data analysis. Caution: SPSS computes the sample standard deviation and sample
variance using n 2 1. If your scores are intended to be a population, you can multiply the
sample standard deviation by the square root of (n 2 1)/n to obtain the population standard
deviation.
Note: You can also obtain the mean and standard deviation for a sample if you use SPSS
to display the scores in a frequency distribution histogram (see the SPSS section at the end of
Chapter 2). The mean and standard deviation are displayed beside the graph.
FOCUS ON PROBLEM SOLVING
1. The purpose of variability is to provide a measure of how spread out the scores are in
a distribution. Usually this is described by the standard deviation. Because the calculations
are relatively complicated, it is wise to make a preliminary estimate of the standard
deviation before you begin. Remember that standard deviation provides a measure of the
typical, or standard, distance from the mean. Therefore, the standard deviation must have
a value somewhere between the largest and the smallest deviation scores. As a rule of
thumb, the standard deviation should be about one-fourth of the range.
2. Rather than trying to memorize all the formulas for SS, variance, and standard deviation, you
should focus on the definitions of these values and the logic that relates them to each other:
SS is the sum of squared deviations.
Variance is the mean squared deviation.
Standard deviation is the square root of variance.
The only formula you should need to memorize is the computational formula for SS.
3. A common error is to use n 2 1 in the computational formula for SS when you have
scores from a sample. Remember that the SS formula always uses n (or N). After you
compute SS for a sample, you must correct for the sample bias by using n 2 1 in the
formulas for variance and standard deviation.