#### ASSIGNMENT 5 ANALYZING THE RELATIONSHIP BETWEEN TWO CATEGORICAL VARIABLES

Open patient_data.sav in SPSS.   Test the following hypotheses.

1. Female patients are more bladder incontinent than male patients.
2. Whites are more bladder incontinent than minorities.
3. Patients with more frequent pain are more bladder incontinent.
4. Patients who are less able to get themselves in and out of bed are more bladder incontinent.

Print and save your output.  Write up your results using the examples below as a guide.  Be sure to (a) state the null hypothesis being tested, (b) identify and justify the statistical test(s) that are used, (c) present and discuss the values of all relevant statistics, (d) state your alpha level and indicate your decision regarding the null hypothesis, and (e) discuss the implications of your findings for the original hypothesis.  Include tables to support your narratives.  Turn in your write up and a printout of your output.

Example 1:

To determine whether social class affects support for welfare reform, I tested the null hypothesis that support for welfare reform is independent of social class.  A chi-square test of independence was used because such a test is appropriate for determining if the distribution of one categorical variable (support for welfare reform) is independent of the distribution of another categorical variable (social class).  However, since chi-square tells us little about the strength or direction of the association between the two variables, tau-b was also calculated.  Tau-b is appropriate because both variables are ordinal.  The analysis produced a chi-square of 19.69.  The probability of getting a chi-square this large if the null hypothesis of independence is true is .03.  Given that this probability falls below my alpha level of .05, I reject the null hypothesis that support for welfare reform is independent of social class.  Further, tau-b was calculated to be .37 indicating a moderate positive association between the variables, suggesting that as social class increases, support for welfare reform increases.  Based on these results, I find support for the original hypothesis that social class affects support for welfare reform.

Example 2:

To determine whether education level affects religious affiliation, I tested the null hypothesis that religious affiliation is independent of education level.  A chi-square test of independence was used because such a test is appropriate for determining if the distribution of one categorical variable (religious affiliation) is independent of the distribution of another categorical variable (education level).  However, since chi-square tells us little about the strength or direction of the association between the two variables, tau was also calculated.  Tau is appropriate because one of the variables is nominal (religious affiliation).  The analysis produced a chi-square of 8.3.  The probability of getting a chi-square this large if the null hypothesis of independence is true is .04.  Given that this probability falls below my alpha level of .05, I reject the null hypothesis that religious affiliation is independent of education level.  However, tau was calculated to be .09 indicating only a weak association between the variables.  Based on these results, I find limited support for the original hypothesis that education level affects religious affiliation.

Below is a sample bivariate table.

 Table 1 Distribution of Marital Status by Sex of Respondent Males Females Total Number Percent Number Percent Number Percent Never Married 61 12.3 78 7.8 139 9.3 Married 272 54.7 204 20.3 476 31.7 Widowed 119 23.9 648 64.6 767 51.1 Separated/Divorced 45 9.1 73 7.3 118 7.9 Total 497 100 1003 100 1500 100 Chi-squared = 21.7; p < .05.