#10
Due 36-309/749
Homework 3:00PM Wed 11/19/08
Turn in to BH 132L or Tuesday in class 1) SAT and testing (25 points, 5 each) A study was carried out to test the effects of three treatments (A, B and C) on the quantitative outcome of test score (not an SAT test). It was hypothesized that treatment A would work better for subjects who have higher math than verbal SAT scores, and the treatments B and C would work better for the other students. The data are in MV.sav. a) As a review, perform the appropriate analysis to test the hypothesis (ignoring gender). Consider the variable type for the two explanatory variables and the outcome when choosing a test. Turn in the F-statistic and p-value that best tests the hypothesis (but don't perform contrast testing, which we will skip now to avoid using too much of your time.) b) As a check on the adequacy of treatment randomization, perform a test to check if the distribution of treatment is the same for both males and females. Turn in the name of your test, the test statistic, the p-value, and your conclusion. c) Make a test of the independence of gender and which part of the SAT test a student did better on. Turn in the name of your test, the test statistic, the p-value, and your conclusion. d) Although it is not really interesting, to get practice at collapsing categories collapse treatments B and C, and turn in the new contingency table of treatment vs. gender. e) Turn in the p-value and what you conclude from a chi-square analysis of the data from part d. 2) Chi-square testing without raw data (25 points, 8+8+9) A study found these results (unless you are very clever, you'll need to create separate datasets for parts a and b): Open 34 30 Not Open 26 50 Agreeable 24 62 Not Agreeable 36 18
Extroverted Introverted
a) What is the p-value for testing independence between the personality traits of openness and extroversion/introversion? b) What is the p-value for testing independence between the personality traits of agreeableness and extroversion/introversion? c) Re-state the null hypothesis for part b in terms of probability distributions rather than independence.
3) Manipulating behavior (25 points, 5 each) Evil scientists want to manipulate people's cooperative behavior. In an experiment in which people must choose to cooperate or not, subjects are randomized to receive various monetary incentives to cooperate. For this problem, gender and the monetary incentive (dollars) are the explanatory variables, and "cooperate" is the outcome. The data for this problem and the next are in cooperate.sav.
a) Make and turn in a plot of fraction cooperating as a function of dollars following these instructions: Under Graph/ChartBuilder use the Grouped Scatter template. Right click on "cooperate" and select "scale" to use this as a quantitative variable for plotting purposes. Put cooperate on the y-axis, dollars on the x-axis, and as male the color. Under Element Properties change the Statistic for "cooperate" from "Value" to "Mean". Click Apply then OK to make the plot. View the plot in the Viewer, then open it in the Chart Editor. Add Fit Line at Subgroups. Double click on the y-axis to open the Properties, then go to Number Format and change the decimal places from 0 to 1, click Apply, and then set scale to have a major increment of 0.1, click Apply, then Close the Properties, then close the Chart Editor. b) Run logistic regression with dollars and "male" as the covariates (explanatory variables). Set "male" as Categorical with the "first" level as baseline (you must see "male(indicator(first))" in the box). Leave Method as "Enter". Turn on the HosmerLemeshow goodness-of-fit option. What is the prediction equation (using numeric estimates of parameters) for log odds of cooperating? c) What is the p-value for Hosmer-Lemeshow and what does it tell us? d) If the predicted log odds of cooperating are -0.111 for one gender and some number of dollars of incentive, what are the predicted log odds of cooperating for the same gender an incentive of one and ten more dollars? e) If the predicted odds of cooperating are 0.89 for one gender and some number of dollars, what are the predicted odds of cooperating for the same gender and one and ten more dollars? 4) Manipulating behavior continued (25 points, 5 each) Additional explanatory variables are available as indicator variables for male, introverted personality type, and business major (vs. all other majors). a) Perform the chi-square test of independence separately to see if cooperation is independent of each of the indicator variables. ...