As shown in Table 1, the groups differed in terms of language skills and the type of job last held....

As shown in Table 1, the groups differed in terms oflanguage skills and the type of job last held. The intakeform asked the client to indicate languages used otherthan English. A total of 30% of the clients interviewedindicated they spoke, read, or wrote a language otherthan English; however, 55% of those not interviewedresponded that they used a language other than English.Some of the interviews were conducted in Spanish, butrespondents unable to be interviewed in either Spanishor English were not included in the interview sample.Clients unable to communicate in English would beexpected to hold blue-collar jobs relative to white-collarjobs. It is therefore not surprising that clients interviewedwere more likely to have been employed inlower skilled white-collar jobs compared to clients whocould not be interviewed.

Religion, Job Readiness, and Employment Outcomes: The Case of Latter-Day Saint EmploymentJohn P. Bartkowski, Vaughn R. A. Call, Tim B. Heaton and Renata ForsteResearch on Social Work Practice 2007; 17; 188

A contingency table from the research literatureThe table to the right, and as described below, is an example from the research literature used to describe key characteristics of the sample.

Contingency tables enable us to compare one characteristic of the sample, e.g. degree of religious fundamentalism, for groups or subsets of cases defined by another categorical variable, e.g. gender.

A contingency table, which SPSS calls a cross-tabulated table, is shown below. The columns contain the categories of the grouping variable. The rows contain the categories of the variable we are interested in comparing.

Each cell contains a count of the number of subjects who had both characteristics.

The column at the extreme right of the table contains the sum of the counts for each row. The row at the very bottom of the table contains the sum of the counts for each column.

04/21/23 Slide 2

Contingency tables in SPSS - 1

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Each cell in the table represents a combination of the characteristics associated with the two variables:

While a larger number of females were fundamentalist, we cannot tell if females were more likely to be fundamentalist because the total number of females (146) was different from the total number of males (107).

To answer the “more likely” question, we need to compare percentages.

42 females were fundamentalists.

29 males were also fundamentalists.


04/21/23 Slide 4

There are three percentages that can be calculated for a contingency table:• percentage of the total number of cases• percentage within each row• percentage within each column

A row percentage, i.e., 59.2% of fundamentalists were females.

A column percentage, i.e., 44.5% of females were moderates.

A total percentage, i.e., 15.4% of the sample were female and liberal.

Because this table contains an overwhelming amount of information, I prefer to compute percentages one at a time.


04/21/23 Slide 5

Each of the three percentages provide different information and answer a different question.

The percentage of the total number of cases is computed by dividing the number in each cell (e.g. 29, 42, etc.) by the total number of cases (253).

11.5% of the cases were both male and fundamentalist.

16.6% of the cases were both female and fundamentalist.


Second, the 100% total figure appears ONLY in the grand total cell beneath the table total of 253.

We have two visual clues that the table contains total percentages. First, the rows that the percentages are on are labeled “% of Total.”

04/21/23 Slide 6

The percentage within each row is computed by dividing the number in each cell (e.g. 29, 42) by the total for the row (71).

The label for the percentage tells us that it is computed within the category for fundamentalist.

The percentages in each row sum to 100% in the total column for rows (the row margin).

59.2% of the fundamentalists were female.


40.8% of the fundamentalists were male.

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The percentage of the total for each column is computed by dividing the number in each cell (e.g. 29, 36, and 42) by the total for the column (107).

The label for the percentage tells us that it is computed within the category for sex.

27.1% of the males were fundamentalists.

39.3% of the males were liberals.

The percentage in each column sums to 100% in the total row for columns (the column margin).


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The three percentages tell us:• the percent that is in both categories (total percentage)• the percent of each row that is found in each of the column

categories (row percentages)• the percent of each column that is found in each of the row

categories (column percentages)

The row and column percentages are referred to as conditional or contingent percentages. Our real interest is in conditional or contingent percentages because these tell us about the relationship between the variables.

The relationship between variables is defined by a distinct role for each: • the variable which is affected or impacted by the other is the

dependent variable• the variable which affects or impacts the other is the independent

variable

We assign the role to the variable. An independent variable in one analysis may be a dependent variable in another analysis.


04/21/23 Slide 9

A categorical variable has a relationship to another categorical variable if the probability of being in one category of the dependent variable differs depending on the category of the independent variable.

For example, if there is a relationship between social class and college attendance, the percentage of upper class persons who attend college will be different from the percentage of middle class persons who attend college. Attending college is the dependent variable and social class is the independent variable.

Given that we can represent this statistically with either the row or column percentages in a contingency table, my practice is to always put the independent variable in the columns and the dependent variable in the rows, and compute column percentages.

This order matches the order for many graphics where the dependent variable is on the vertical axis and the independent variable is on the horizontal axis.


04/21/23 Slide 10

Based on the column percentages, we can make statements like the following:

Males were most likely to be liberal (39.3%), while females were most likely to be moderate (45.5%).

Males were more likely to be liberal (39.3%) compared to females (26.7%).

This is not equivalent to the statement that liberals are more likely to be male or female.


We can also describe a relationship based on a comparison of odds. Odds are increasingly used to state findings when comparing groups. Odds are defined at the probability of being in one group divided by the probability of not being in that group.

First, we compute the odds separately for each category of the independent variable:

Odds are computed by dividing the number (or column percent) in one category of the row variable by the number (or column percent) in a second category of the row variable.04/21/23 Slide 11


The odds that a male would be a liberal rather than a fundamentalist are:

42 ÷ 29 = 1.45.

The odds that a female would be liberal rather than fundamentalist are:

39 ÷ 42 = 0.93.

04/21/23 Slide 12

Second, we compare the odds by computing the ratio between the two: 1.45 for males ÷ 0.93 for females = an odds ratio of 1.56.

We can now state the relationship between the two variables as: compare to females, males are 1.56 times more likely to be liberal rather than fundamentalist.

This could also be stated as: being male increases the odds of being liberal rather than fundamentalist by a factor of 1.56 or 56%. (1.56 – 1.0 = .56) and multiplying .56 by 100 to convert it to a percent.

If the odds ratio were 1.0, then both groups would be equally likely to be liberals rather than fundamentalists, and there would be no relationship.

We could have divided the odds for females by the odds for males (.93 ÷ 1.45 = .64) and stated that being female decreased the odds of being liberal versus fundamentalist by a factor of .64, or 36%. (.64 – 1.00 = .36) and multiplying .36 by 100 to convert it to a percent. Explaining decreases in odds is more awkward and less intuitive.


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Creating a Contingency Table in SPSS - 1

To compute a contingency table in SPSS, select the Descriptive Statistics > Crosstabs command from the Analyze menu.

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First, move the row variable fund to the Row(s) list box.

Third, click on Cells button to specify what should be printed in each cell of the table.

Second, move the column variable sex to the Column(s) list box.

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First, mark the check box for Column percentages.

Second, click on the Continue button to close the dialog box.

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After returning to the Crosstabs dialog box, click on the OK button to produce the output.

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The SPSS output provides us with two tables: the case processing summary which shows the number of valid and missing cases, and the crosstabulation table.

Contingency Table Homework Problems

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Contingency Table Homework Problems - 1

The problem includes a table to be completed from the statistical output, and narrative statements that might be included in a description of group comparisons of the sample.

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The column variable in the table (Sex) tells us the groups to be compared, Males and Females.

The notes provide information about the data set to use (GSS2000R.SAV), the variables for we will included in the contingency tables comparing groups (news, tvhours, compuse), and the directions for creating class intervals for the interval variable, tvhours.

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To create class intervals for tvhours, we can use the SPSS Visual Binning tool.

Select Visual Binning from the Transform menu.

We will create the binned variable for tvhours before continuing with the problem.

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First, move the variable tvhours to the Variables to Bin: list box.

Second, click on the Continue button to provide details to SPSS.

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First, click on the variable tvhours to move default information to the fields needed for the class intervals.

Second, add a name for the banded variable, e.g. tvhoursGroups.

Third, choose Excluded at the option for Upper Endpoints.

Finally, click on the Make Cutpoints button to enter the information needed to create the classes.

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First, the First Cutpoint Location is the upper bound of the first interval, i.e. the lower bound of 0 plus the interval width of 5, which equals 5.

Second, enter 5 as the Width for our intervals.

Third, click on the Number of Cutpoints text box. SPSS automatically computes the number of cut points (4) and the last cut point location (20).

Fourth, click on the Apply button to compute the intervals.

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SPSS lists the cut points in the grid and displays their positions (the vertical blue lines) in the histogram.

To add value labels showing the class intervals, click on the Make Labels button.

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SPSS adds value labels that specify the contents of each interval.

Click on the OK button to complete the creation of the tvhoursGroup variable.

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SPSS confirms your request with this dialog box. Click on the OK button to create the variable.

04/21/23 slide 28

Contingency Table Homework Problems - 10The first paragraph of the problem focuses on the number of cases available for the analysis.

The first sentence asks for the number of cases in the dataset.

Scrolling to the last row in the data set provides the answer.

04/21/23 slide 29


The last case in the data set is on row 270, so there are 270 cases in the dataset.

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The next sentence asks for the number of cases excluded because of missing data, and the number of cases that were missing data for each variable.

We can use an SPSS descriptive statistics table to list the number of missing cases for each variable.

The 270 cases in the data set is entered in the blank.

04/21/23 slide 31


To create the table of descriptive statistics, select Descriptives from the Analyze | Descriptive Statistics menu.

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First, move the four variables in the analysis to the Variable(s) list box.

Second, click on the OK button to produce the output.

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There were 159 cases that were valid for all variables. This means that the number excluded was the total number available minus the list wise valid n:

270 – 159 = 111

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Contingency Table Homework Problems - 16The 111 excluded cases is entered in the blank.

The next blank calls for the number of cases missing data for reading the newspaper.

04/21/23 slide 35


There were 165 valid cases for the variable news. This means that the number missing data for news was:

270 – 165 = 105

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Contingency Table Homework Problems - 18The 105 missing cases is entered in the blank.

The next blank calls for the number of cases missing data for watching TV.

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There were 165 valid cases for the variable tvhoursGroups. This means that the number missing data for tvhoursGroups was:

270 – 160 = 110

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Contingency Table Homework Problems - 20The 110 missing cases is entered in the blank.

The next blank calls for the number of cases missing data for computer use.

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There were 223 valid cases for the variable compuse. This means that the number missing data for compuse was:

270 – 223 = 47

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The 47 missing cases is entered in the blank.

The next blank calls for the number of cases missing data for the group variable, sex.

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There were 270 valid cases for the variable sex. This means that there were no missing data for sex was:

270 – 270 = 0

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The 0 missing cases is entered in the blank.

The next sentence calls for us to enter data from table 1, so we will complete table 1 before continuing.

SPSS’s crosstabulation procedure does not do listwise deletion when creating multiple contingency tables.

Since I want a crosstabulated table that uses the same cases for each row variable, I will explicitly do “listwise deletion” by excluding cases that are missing data for any variable.

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Contingency Table Homework Problems -25

In SPSS we exclude cases by specifying criteria for the cases that we want to include in the analysis.

Select the Select Cases from the Data menu.

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First, to specify the condition that will indicate the cases to include, mark the option button: If condition is satisfied.

Second, click on the If… button to specify the condition.

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The NMISS function counts the number of variables that have missing data for a case. If NMISS equals 0, the case has valid data for all of the variables and should be included in the analysis.

Click on the Continue button to close the dialog box.

SPSS includes function commands that perform specific calculations which we can use for creating new variables or for selecting cases.

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Having entered the condition, click on the OK button to complete the selection.

The condition we entered is printed to the right of the If button.

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SPSS marks the cases that will not be included with slashes through the case number.

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To compute a contingency table in SPSS, select the Descriptive Statistics > Crosstabs command from the Analyze menu.

Now that we have specifically included the cases that are not missing data for any variable, we create our crosstabs tables.

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First, move the row variables news, tvhoursGroups, compuse to the Row(s) list box.

Third, click on Cells button to specify what should be printed in each cell of the table.Second, move the

column variable sex to the Column(s) list box.

04/21/23 slide 50


First, mark the check boxes for Column percentages.

Second, click on the Continue button to close the dialog box.

We accept the default of including the count in each cell.

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After returning to the Crosstabs dialog box, click on the OK button to produce the output.

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The Case Processing Summary indicates that there are 159 cases in the analysis.

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The final part of the sentence asks for the number of males and females included in the analysis.

The number of cases in the analysis (159) is entered in the blank.

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The Total Row lists the number of males (60) and number of females in the analysis (99).

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The number of males (60) and number of females in the analysis (99) is entered in the blanks.

The number of males (60) and number of females in the analysis (99) is also entered in the table.

Next, we enter the percentages from the SPSS crosstabulation table into Table 1.

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We transfer the column percentages from the crosstabulation table into Table 1; for example, the percent of males who never read the newspaper is 5.0% and the percent of females who never read the newspaper is 16.2%.

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We transfer the column percentages from the crosstabulation table into Table 1; for example, the percent of males who watch less than 5 hours of TV is 75.0% and the percent of females who watch less than 5 hours of TV is 82.8%.

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We transfer the column percentages from the crosstabulation table into Table 1; for example, the percent of males who don’t use a computer is 40.0% and the percent of females who don’t use a computer is 41.4%.

04/21/23 slide 59


The next drop down menu ask us to select the modal group for reading the newspaper for males.

The category with the largest percentage for males is 38.3% for A few times a week.

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Contingency Table Homework Problems - 42The sentence is completed with a few times a week, and 38.3 is entered in the text box.

The introduction to the next statement depends on whether females have the same modal value or not.

We defer answering this question until we identify the mode for females.

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The next drop down menu ask us to select the modal group for reading the newspaper for females.

The category with the largest percentage for females is 34.3% for Everyday.

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Contingency Table Homework Problems - 44Since the modes are different, we select In contrast from the drop down menu.

The sentence is completed with everyday, and 34.3 is entered in the text box.

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The next sentence compares the percentage of males and females who read the newspaper less than once a week to identify which group is more likely.

The smaller percentage of males (8.3% vs. 15.2%) indicates that they are less likely to read the newspaper less than once a week.

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Contingency Table Homework Problems - 46Less likely is selected from the drop down menu, and the percentages for males (8.3) and females (15.2) are entered.

The next drop down menu ask us to select the modal group for watching TV for males.

The category with the largest percentage for males is 75.0% for Less than 5 hours per day.

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The sentence is completed with less than 5, and the modal percent of 75.0 is entered in the text box.



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The next drop down menu ask us to select the modal group for watching TV for females.

The category with the largest percentage for females is 82.8% for Less than 5 hours per day.

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Contingency Table Homework Problems - 49Since the modes are the same, we select Similarly from the drop down menu.

The sentence is completed with less than 5, and the modal percent of 82.8 is entered in the text box.

The next sentence compares the percentage of males and females who watch TV 5 to 9 hours a day to identify which group is more likely to do so.

The larger percentage of males indicates that they are more likely to watch TV 5 to 9 hours per week.

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Contingency Table Homework Problems - 50More likely is selected from the drop down menu, and the percentages for males (20.0) and females (11.1) are entered.

The next drop down menu ask us to select the modal group for computer use for males.

The category with the largest percentage for males is 60.0% for A used a computer.

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Contingency Table Homework Problems - 51The sentence is completed with used a computer, and the modal percentage of 60.0 is entered in the text box.



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The next drop down menu ask us to select the modal group for computer use for females.

The category with the largest percentage for females is 58.6% for used a computer.

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Since the modes are the same, we select Similarly from the drop down menu.

The sentence is completed with used a computer, and the modal percentage of 58.6 is entered in the text box.

The next sentence compares the percentage of males and females who don’t use a computer to identify which group is more or less likely to not use a computer.

The smaller percentage of males indicates that they are less likely to not use a computer.

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Less likely is selected from the drop down menu, and the percentages for males (40.0) and females (41.4) are entered.

All of the answers have been entered, so we submit the problem for grading.

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The green shading to the answers indicates that all have been answered correctly.

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Restoring All Cases to Dataset - 1

When we have completed one problem, we need to restore all cases to the data set in advance of the next problem.

If we do not restore the cases, they will continue to be omitted, resulting in incorrect calculations.

Select the Select Cases… command again from the Data menu.

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First, click on the All cases option button.

When the All cases option button is selected, the If condition will be disabled.

Second, click on the OK button to complete the command.

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The slash marks through the case numbers are cleared, indicating that all cases are available for the next analysis.

As shown in Table 1, the groups differed in terms of language skills and the type of job last held....

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