Student Center | Instructor Center | Information Center | Home

Statistics for the Behavioral Sciences, 4/e

Michael Thorne, Mississippi State University -- Mississippi State
Martin Giesen, Mississippi State University -- Mississippi State

Measures of Dispersion and Standard Scores

SPSS Exercises

USING SPSS—EXAMPLES AND EXERCISES

SPSS has several procedures that can provide measures of central tendency and dispersion. For example, Frequencies, Descriptives, or Explore can be used. Using a Compute statement, z scores can be calculated, or they can be obtained "automatically" as an option under the Descriptives procedure.

Example: We will use SPSS to obtain the three measures of central tendency (mean, median, and mode), measures of dispersion (range, variance, and standard deviation), and z scores for all test scores using the data in Problem 6. The steps are as follows:

Start SPSS, enter the data, and name the variable test.
We will use Frequencies to obtain the measures of central tendency and dispersion.
Go to Analyze>Descriptive Statistics>Frequencies.
Move test to the Variables box; uncheck "display frequency table" so the frequency distribution will not be calculated.
Click Statistics, select the measures of central tendency and dispersion that you want, and then click Continue>OK. This will give the descriptive statistics in the output Viewer window.
Next we will compute z scores using the Compute procedure. To do this we need to know the mean (symbolized by M = 74.3333 rather than X = 74.3333, as we symbolized it in the text) and standard deviation (s = 13.6403) from the output. The formula for any z score is z = (X – M)/s or z = (X – 74.3333)/13.6403. We will now put this formula in the Compute box.
From the Data Editor window, click Transform>Compute. Then enter "testz" in the Target variable box.
In the Numeric Expression box, move test in and use the keypad or type and edit so the expression appears as follows: (test – 74.3333)/13.6403.
Click OK. Check the Data Editor window and find the computed z scores.

Example: Repeat SPSS for the previous example using the Descriptives procedure. Although you will not be able to obtain the median and mode from this procedure, z scores can be computed automatically.

Click Analyze>Descriptive Statistics> Descriptives, move test into the Variables box, and click "Save standardized values as variables." This causes the z scores to be computed.
Click Options and select the desired descriptive statistics that are available, then click Continue>OK.
The output Viewer shows the descriptive statistics. The Data Editor should show another variable ztest showing the z scores again, differing only in the number of decimal places displayed.

SPSS Data Editor window showing z scores obtained using the Compute statement (first 20 cases).

SPSS Data Editor window showing z scores computed using the Compute statement and using the z-score output option for the Descriptives procedure.

Exercises Using SPSS

Using the data from Problem 2, use the SPSS Descriptives procedure to obtain the mean, standard deviation, variance, and z scores for each score.
Using the same data and the necessary statistics from the previous exercise, employ the SPSS Compute procedure to calculate z scores again for each score. Use correctz as the target variable name.

Click here to view the answers. (125.0K)

2003 McGraw-Hill Higher Education
Any use is subject to the Terms of Use and Privacy Notice.
McGraw-Hill Higher Education is one of the many fine businesses of The McGraw-Hill Companies.