Slide 1Slide 2Slide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Slide 15Slide 16Slide 17Slide 18Slide 19Slide 20Slide 21Slide 22Slide 23Slide 24Slide 25Slide 26Slide 27Slide 28Slide 29Slide 30Slide 31Slide 32Slide 33Slide 34Slide 35Slide 36Slide 37Slide 38Slide 39Slide 40Slide 41Slide 42Slide 4301/13/19 Slide 1•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:01/13/19 Slide 2•Each cell in the table represents a combination of the characteristics associated with the two variables: 29 males were also fundamentalists.42 females were fundamentalists.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.01/13/19 Slide 3•There are three percentages that can be calculated for a contingency table:•percentage of the total number of cases•percentage of the total in each row•percentage of the total in each column•Each of the three percentages provide different information and answer a different question.01/13/19 Slide 4•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.We have two clues that the table contains total percentages. First, the rows that the percentages are on are labeled “% of Total.”Second, the 100% figure appears ONLY in the grand total cell beneath the table total of 253.01/13/19 Slide 5•The percentage of the total for 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 sums to 100% in the total column for rows (the row margin).40.8% of the fundamentalists were male.59.2% of the fundamentalists were female.01/13/19 Slide 6•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.The percentage in each column sums to 100% in the total row for columns (the column margin).27.1% of the males were fundamentalists.33.6% of the males were moderates.01/13/19 Slide 7•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.01/13/19 Slide 8•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.01/13/19 Slide 9•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 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.01/13/19 Slide 10•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.01/13/19 Slide 11•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.01/13/19 Slide 12•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%).01/13/19 Slide 13•Based on the column percentages, we can make statements like the following: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.01/13/19 Slide 14•We can also describe a relationship based on a comparison of odds. First, we compute the odds separately for each category of the independent variable:The odds that a female would be liberal rather than fundamentalist are 39 ÷ 42 = .93.The odds that a male would be a liberal rather than a fundamentalist are 42 ÷ 29 = 1.45.01/13/19 Slide 15•We compare the odds by computing the ratio between the two: 1.45 for males ÷ .93 for females = an odds ratio of 1.56.•We can now state the relationship between the two variables as: males are 1.56 times more likely to be liberal rather than fundamentalist, than are females. •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.01/13/19 Slide 16•If the odds ratio were 1.0, then both groups would be equally likely to be liberals rather than fundamentalists.•We could have divided the odds for females