Quantitative Reasoning and Analysis

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4 Organization and Presentation of Information

In this chapter, basic methods of data description will be exhibited. This information will include frequency distributions, measures of central tendency, and measures of variability. Presentation can be made in the form of a table, chart, or graph.

Measures of Central Tendency and Variability To quickly produce a table with basic descriptive statistics about a variable or variables, select the following menus:

Analyze → Descriptive Statistics → Descriptives . . .

By clicking the “Options” button at the upper right-hand corner of the “Descriptives” dialog box, you will open another dialog box that will allow you to choose which basic descriptive information will be produced by SPSS Statistics:

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Leave check marks in the boxes next to those statistics you would like to request. You also have the option of choosing the display order; choose one of the four options. After clicking “Continue” in this dialog box and “OK” in the original one, you will be given the following SPSS Statistics output:

Note that the sample sizes along with the four measures that were selected for each variable have been presented in separate columns. Variables are listed in the rows of the table output.

Although this method of getting basic descriptive information is very quick and easy, it is possible to get more detailed descriptive information about variables in a data set.

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Note, for instance, that the previous method will not allow you to obtain the median. You can obtain information about measures of central tendency (including the median) and variability, and you can obtain actual frequency distribution tables using the following method.

Frequency Distributions Using the same variables as in the previous example, select the following menus:

Analyze → Descriptive Statistics → Frequencies . . .

The three selected variables, “age,” “educ,” and “tvhours,” are all scale variables. Therefore, frequency distribution tables for these variables would have too many categories and be too long to be of any real use. You must be cognizant of the level of measurement and categorization of variables before selecting tables. Therefore, make sure that the “Display frequency tables” box is unchecked. After removing the check mark, you will be presented with a pop-up box like this one:

Click “OK” to return to the “Frequencies” dialog box.

To choose which statistical information to request, click the “Statistics” button in the upper right corner of the “Frequencies” dialog box, and you will be presented with the following new dialog box:

Here, you can choose measures of central tendency (mean, median, and/or mode) and measures of variability. Quartiles are useful for computing the interquartile range. You can also select any percentile for computation as well, depending on your specific needs. On the basis of the above dialog boxes, the following output will be provided once you click “Continue” and then “OK” in the original dialog box:

Now, perform the same menu function with a different variable:

Analyze → Descriptives → Frequencies . . .

First, remove the variables that were there by using the arrow to send them back to the variable list or by clicking the “Reset” button. Note that if you click the “Reset” button, entries made in the “Statistics” portion of this box will also revert to default, so you would need to click the “Statistics” button and select the appropriate statistics.

Now, select “age2,” the recoded age dichotomy variable (we created this variable in

Chapter 2, “Transforming Variables”), and drag it into the “Variable(s)” area. Next, click the “Charts” button. You will be given a subdialog box as follows:

Choose the “Pie charts” radio button and “Frequencies.” (Of course, depending on your needs, and the level of measurement of your variable[s], you could select any of these types of charts.) Then click “Continue” and then “OK” in the original dialog box. The information below represents the output that SPSS Statistics will provide:

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This is only one way to obtain some of the chart and graph options; more detailed options and optimized interfaces to produce charts and graphs are explained in the next chapter. Your chart will likely appear in color and without data labels (percentages in each slice). Instructions for using these features are also addressed in Chapter 5, “Charts and Graphs.”

Now, suppose that you want to produce a frequency distribution for respondent’s age beyond just the dichotomy that was demonstrated in the previous example. It is not feasible to run the frequency command and use its menus using the variable “age” because a virtually useless table listing all ages in the data file would be generated.

To present a useful frequency distribution, it makes sense to divide the interval-ratio variable “age” into meaningful or otherwise appropriate categories. Take, for instance, the following example, in which “age” is divided into ranges according to decade. Bear in mind that the General Social Survey contains responses only from noninstitutionalized Americans 18 years of age and older. First, use the following menus to recode “age” into “agegroup” (see Chapter 2 for more details on recoding):

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Transform → Recode into Different Variables . . .

Select the original variable from the variable list on the left, and drag it into the “Numeric Variable → Output Variable” area. On the right side of the dialog box, name the new variable (here, the new name is “agegroup”) and provide a label if desired. Next, click the “Change” button to assign the new name you have entered. Now, click the “Old and New Values . . .” button. The following dialog box will be presented:

Here, enter the old values and ranges on the left in conjunction with the new value on the right, clicking the “Add” button after each pair of entries. For more details, review the recoding section of Chapter 2, “Transforming Variables.” After all of the old and

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new value changes have been added to the list, click the “Continue” button in this window and then the “OK” button in the “Recode into Different Variables” dialog box. The new variable will be displayed in the SPSS Statistics Data Editor window.

Click the Variable View tab and find the newly created variable. Because there are no decimals, change that to “0.” Also, there will be no values with more than one digit, so change the width to “1.” By recoding the variable, we have transformed it from a scale (ratio) variable into an ordinal variable, so select “ordinal” in the “Measure” column for the new “agegroup” variable.

In the “Values” cell, click the button with three dots. (You will need to click the “Values” cell in the agegroup row once first; then the button with the three dots will appear.) You will be given the following dialog box:

Enter the appropriate labels, as done in the example above. Then click “OK.” This will record the value labels onto the variable.

Next, request a frequency distribution for the newly structured variable. To do so, click the following menus:

Analyze → Descriptive Statistics → Frequencies . . .

When given the above dialog box, drag the variable of interest from the list on the left into the “Variable(s)” area. For a visual representation of the distribution, select the “Charts . . .” button, and see the dialog box that follows:

Click the radio button next to “Histograms,” and check the box for “Show normal curve on histogram.” This will produce a histogram with an overlay of a normal curve for reference. Click the “Continue” button here, and then click “OK” in the prior dialog box. SPSS Statistics will generate the following output, consisting of an easy-to- understand frequency table and a histogram:

Note that by inspecting the “Valid Percent” column, one can readily get a sense of the distribution, because of the manageable number of categories (rows) in the table. This same information is provided graphically in the histogram that follows:

Access the full 2014 data file and the 1972–2014 Cumulative Codebook at the student study site: study.sagepub.com/wagner6e.