statics

CROSSTABS MODULE 1

We are going to begin doing bivariate analysis. Please carefully read Chapter 7 of the Adventures in Criminal Justice Research textbook.

The first technique we will develop is a procedure known as CROSSTABS. This procedure is very useful for analyzing the effect of an independent variable upon a dependent variable. The CROSSTABS procedure makes it possible for us to analyze two variables simultaneously in a table format. The first step is to determine which of the two variables that we want to analyze is the independent variable and which the dependent variable is. To do this it is often helpful to think in terms of which variable is “fixed” and which is “not”. For example, if we were attempting to determine if a person’s SEX influences their view on CAPITAL PUNISHMENT, I think it is logical to assume that SEX is the fixed variable in that a person’s SEX is predetermined. Following the logic we would specify SEX as the independent variable and hypothesize that opposition or support for CAPITAL PUNISHMENT will vary based upon an individual’s biological SEX. To examine this working hypothesis , let’s do a CROSSTABS procedure using the GSS dataset.

Step 1 – Initiating the CROSSTABS procedure

After accessing the GSS dataset you need to click ANALYZE – DESCRIPTIVES – CROSSTABS in that order. You are now looking at the CROSSTABS screen where you will select variables, request information to be contained in each cell of the table, and eventually request certain statistical procedures.

Step 2 – Choosing the variables for analysis

We are examining the working hypothesis that opposition and support for CAPITAL PUNISHMENT will vary as a function of SEX. It is important to develop a working habit for CROSSTABS regarding the placement of the independent and dependent variables in the table. The standard placement is to put the dependent variable in the ROW and the independent variable in the COLUMN. To do this we will select the variable SEX and click on the arrow adjacent to the box for COLUMN. Then we will select the variable CAPPUN and click on the arrow adjacent to the box for ROW.

You have now told SPSS to create a table that compares the responses to the question regarding SEX to the responses to the question assessing support or opposition for CAPITAL PUNISHMENT (CAPPUN). To run this procedure you click OK and SPSS produces the following table.

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You can see from this table that 1,356 individuals answered both of these questions. 606 Males and 750 Females answered both of these questions. 899 respondents favor the death penalty for murder and 457 oppose the death penalty for murder. 439 males favor the death penalty and 167 oppose it. 460 females favor the death penalty and 290 oppose it.

The information in the table appears to support the working hypothesis that views about CAPITAL PUNISHMENT vary as a function of SEX.

But there is much more that we can do to make our assessment of the working hypothesis more forcefully.

Step 3 – Controlling the information contained in the cells of the table.

To enhance the information presented in our table we need to go back to the CROSSTABS screen, ensure that the correct variables are selected and in the desired positions, and then click the CELLS button. When we do this we will be looking at the Cell Display screen.

Let’s start by adding one dimension to the table, COLUMN PERCENTAGES. Click on COLUMN – CONTINUE – OK to produce the following table.

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This table provides us with the same information as before only this time SPSS has calculated the percentage of Males and Females in each cell of the table. For example, 439 Males favor the death penalty. That is 72.4% of the 606 Males represented in this table. 167 Males oppose the death penalty, or 27.6% of the 606 Males represented in this table. 460 Females favor the death penalty, or 61.3% of the 750 Females represented in this table. 290 Females oppose the death penalty, or 38.7% of the Females represented in this table.

The information in the table appears to support the working hypothesis that views about CAPITAL PUNISHMENT vary as a function of SEX. In addition, we can also say that although the majority of Females and Males support the death penalty that a higher percentage of Females oppose the death penalty than do males.

Let’s enhance our table again by adding ROW PERCENTAGES. Go back to the Cell Display screen and make sure that the check marks for both ROW and COLUMN are displayed and then request the output by clicking CONTINUE followed by OK. You will now see the following output.

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This table displays all the information of the prior table, but with the added dimension of providing row percentages. 439 Males favor the death penalty, or 48.8% of the 899 people who favor the death penalty. 460 Females favor the death penalty, or 51.2% of the 899 people who favor the death penalty. We can see from this that support for the death penalty is close to equally distributed between Males and Females.

167 Males oppose the death penalty, or 36.5% of the 457 people opposing the death penalty. 290 Females oppose the death penalty, or 63.5% of the 457 people opposing the death penalty. Of those people opposing the death penalty, the overwhelming majority are Female.

Now let’s enhance our table one additional time by including TOTAL PERCENTAGES. Go back to the Cell Display screen and make sure that the check marks appear for ROW, COLUMN, and TOTAL and then request SPSS to generate the output. When you do, the following table will appear.

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This table displays all the information contained in the prior table plus TOTAL percentages. 439 Males favor the death penalty, or 32.4% of the 1,356 people represented in this table. 167 Males oppose the death penalty, or 12.3% of the 1,356 respondents represented in this table. 460 Females favor the death penalty, or 33.9% of the 1,356 respondents represented in this table. 290 Females oppose the death penalty, or 21.4% of the 1,356 respondents represented in this table. 899 people favor the death penalty, or 66.3% of the 1,356 respondents represented in this table. 457 people oppose the death penalty, or 33.7% of the 1,356 respondents represented in this table. 606 Males are represented in this table, or 44.7% of the 1,356 respondents represented in this table. 750 Females are represented in this table, or 55.3% of the 1,356 respondents represented in this table.

I hope through this example you are able to appreciate the sheer volume of information that can be obtained using the CROSSTABS procedure.

Now let’s more systematically examine our original working hypothesis .

Step 4 – Evaluating our working hypothesis

To evaluate our working hypothesis we use a simple statistic called Epsilon. Epsilon summarizes the percentage differences comparing Males and Females in terms of support and opposition of the death penalty. With our dependent variable in the ROWS of the table, we will find the absolute difference between the COLUMN percentages (% within RESPONDENTS SEX) by subtracting the larger percentage from the smaller percentage. Using the data in our tables, the Epsilon for FAVOR THE DEATH PENALTY is 11.1% (72.4% - 61.3% = 11.1%). The Epsilon for OPPOSE THE DEATH PENALTY is 11.1% (38.7% - 27.6% = 11.1%). Of those favoring the death penalty, a higher percentage is Male. Of those opposing the death penalty, a higher percentage is Female.

The Epsilon analysis of the table supports our working hypothesis that support and opposition for the death penalty will vary as a function of SEX.

You may have the question, How can I tell if the data in the table do not support a working hypothesis ? The answer to that question is the following. If the Epsilons for the table are zero or approaching (near to) zero, then the data does not support the working hypothesis . In this table, if there had been very little difference across Males and Females in support for, or opposition against, the death penalty, then I would conclude that support and opposition for the death penalty does not vary as a function of sex.