In 1846, a group of 87 people (called the Donner Party) were heading west from Springfield, Illinois, for California. 16 The leaders attempted a new route through the Sierra Nevada and were stranded there throughout the winter. The harsh weather conditions and lack of food resulted in the death of many people within the group. Social scientists have used the data to study the theory that females are better able than men to survive harsh conditions.
a. Create a logistic regression model using Gender to estimate the probability of Survival.
b. Interpret the model in terms of the odds ratio. Use the Wald statistic to create a 95% confidence interval for the odds ratio.
c. Calculate and interpret the likelihood ratio test.
d. Test H0: β1 = 0 versus Ha: β1 ≠ 0 using both Wald’s test and the likelihood ratio test. State your conclusion based on these tests.
e. Report and interpret Somers’ D, Goodman-Kruskal gamma, or Kendall’s tau-a for this logistic regression model.
f. Create a two-way contingency table using Gender and Survival as row and column variables. Conduct a chi-square test for equal proportions (e. g., is the proportion of survival the same for males and females?). In addition, use this two-way table to create the odds ratio. How does the analysis of the two-way table compare to the logistic regression analysis?
g. D. K. Grayson states, “The differential fate of the members of the Donner Party lends strong support to the argument that females are better able than males to withstand conditions marked by famine and extreme cold.” While there is some evidence that Gender is associated with Survival, explain why the data cannot be used to show that being female causes a higher probability of survival.