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Posted on April 25th, 2014, by

Does socioeconomic status influence the probability of getting divorced?   You hypothesize that higher SES people are less likely to divorce. The mean SES for people who have never been divorced is 54.96.  For people who have been divorced one or more times, the mean SES is 50.54.  To see if this difference is significant, you ran a t-test in SPSS and got this output. What is the t-statistic?  Is the difference between means significant?  Should you accept or reject your hypothesis?

The results of t-test are 2.843 and 2.941 for assumed and not assumed equal values. Degrees of freedom are 936 and 393.666. The two-tailed significance is .005 and .003, and it appears that mean difference is equal (4.4129). Our hypothesis was that the difference between the number of divorced people among those with higher socioeconomic status and those who have lower socioeconomic status is significant. T-statistics has shown that this difference is not significant; therefore our hypothesis should be rejected. It means that although the number of divorced people among higher SES respondents is lower, this figure does not reflect the situation and should not influence conclusions about the dependence between socioeconomic status and being likely to divorce.

4.   (9 points) The Catholic religion is unfavorable towards divorce, so you hypothesize that being Catholic will lessen the chance of getting divorced.   To explore this relationship, you run a crosstab in SPSS with ever been divorced as the DV (rows) and Catholic as the IV (columns).  You ask for column percentages and a chi-square statistic.  Below is what you got (in an Excel table).  What does this table tell you about your hypothesis?

Before we take a chi-square test we may be disoriented by the figures provided in the Excel table. It shows us that the percentage of divorced is higher among non-Catholics, and we could conclude that there is an obvious relationship between being Catholic and not getting divorced. However, chi-square test does not rely on percents. It has demonstrated the result of 15.41, and probability is p<0.001. P is thus lower than standard 0.05 and therefore the hypothesis of relationship between being Catholic and getting divorced should be rejected. There is only 0.1% chance that these figures are dependent. In this way, we are to conclude that despite the fact that Catholic Church is unfavorable to divorces, belonging to this religion does not mean that a person will never get divorced.

5.   (12 points) By now you’ve looked at several other variables and are ready to do a regression analysis.  You hypothesize that regardless of SES and whether or not a person is Catholic attending religious services on a regular basis will reduce the likelihood of divorce.  You also want to account for age because people accumulate life experiences (including divorce) as they age. What kind of regression will you use, OLS or logistic?  Why?  Which IV is a control variable?  Please explain the final model, shown below, in words. (2-point BONUS: age was only borderline significant throughout the stepwise analysis. Why is it included in the final model?)

The final model has no adjusted R squared, but instead the results of the chi-square test are presented. It means that logistic regression would be more reasonable to apply because to take to account all the figures we have to check we need more complicated formulas than those used for ordinary least squares. OLS, as we know, is applicable when regressors are exogenous and no multicollinearity is mentioned. In our case variables are interdependent in several ways, that is why we cannot ignore errors which influence finite variances. Linear unbiased estimators can be calculated by OLS when we deal with homoscedastic and serially uncorrelated errors, not in our case. Our hypothesis was that when people actively attend religious service, they are less likely to get divorced. Unfortunately, this hypothesis has not been proved. As we see it from the table, the result of chi-square test for the variable of religious service attendance includes probability of less than 0.001. This figure signalizes that the hypothesis we have constructed has to be rejected.

In the meantime, if we turn out attention to the variable of age, we will see that it deals with the probability of p<0.10, so probably this is a factor that really influences the likelihood of getting divorced, therefore this indicator cannot be ignored or used just sideboard. Consequently, it seems to be true that getting older people change their attitudes to divorce and find it more rational or comfortable to solve problems in any other ways, but not getting divorced.

6.   (11 points) In the following table,  the dependent variable is income  and the independent variables are age, sex, and the highest y ear of school completed. Which method of analysis was used here? Please interpret the interaction effect.  (In other words, is the relationship between education and income different for men than it is for women? If so, how?)

The table under consideration probably deals with the logistic regression, and shows correlation between such factors as age, sex, and year of completing school. If we look at the results of the chi-test which are expressed in probability counted, we would be confident to conclude that age is not really connected with the income. However, for women the year of completing school is decisive (p<0.05), and it means that with years women are more likely to lose their jobs or other sources of income.

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