answers to practice final exam

1 Simon Fraser University Department of Political Science FALL 2014 QUANTITATIVE METHODS IN POLITICAL SCIENCE Final Exam Time allowed TWO Hours Candidates must NOT write anything until the start of the examination period is announced Answer ALL questions on this examination sheet For full marks show all work Numbers in square brackets at the end of each question indicate the number of marks available for the question. Total Marks: 100 + 10 bonus points No electronic devices capable of storing and retrieving text, including electronic dictionaries, may be used. Calculators are permitted but graphing calculators are not. DO NOT open examination paper until instructed to do so

2 1. There are four hurdles we need to overcome in order to demonstrate a causal relationship between ? and ? . Which hurdle might we use bivariate hypothesis testing to overcome? [2] Is there covariation between X and Y? ( Half points for “the third” ) 2. List the three parts of a research design: [3] i) hypothesis/hypotheses ii) method of data collection iii) method of analysis 3. In a recent survey of 1000 randomly sampled British adults 18 years and older, 56% of respondents supported the nationalisation of utilities such as gas and electricity. Calculate a 95% confidence interval for the proportion of British adults supporting the nationalization of utilities. [5] 𝑠𝑒 = √ 𝑃(1−𝑃) 𝑁 = √ 0.56×0.44 1000 = 0.0157 95%𝐶𝐼 = 𝑃 ± 1.96 × 𝑠𝑒 95%𝐶𝐼 = 0.56 ± 1.96 × 0.0157 95%𝐶𝐼 = 0.56 ± 0.0308 (0.529, 0.591) 95%𝐶𝐼 = 𝑃 ± 2 × 𝑠𝑒 95%𝐶𝐼 = 0.56 ± 2 × 0.0157 95%𝐶𝐼 = 0.56 ± 0.0314 (0.529, 0.591) 4. You run a regression and the total sum of squares (TSS) is reported as 20 and the residual sum of squares (RSS) is reported as 10. Calculate the R -squared value: [4] ? 2 = ??? − ??? ??? = 20 − 10 20 = 0.5

4 5 continued Equation Equation A = ∑ (? 1,𝑖 − ? ̅ 1 )(? 𝑖 − ? ̅ ) 𝑁 𝑖=1 ∑ (? 𝑖 − ? ̅ 1 ) 2 𝑁 𝑖=1 Equation B = ∑ (? 𝑖 − ? ̅ )(? 𝑖 − ? ̅ ) 𝑁 𝑖=1 𝑁 Equation C = √ ∑ 𝜇̂ 𝑖 2 𝑁 𝑖=1 𝑁 Equation D = ? ̂ 1 𝜎 ̂ ? 𝜎 ̂ ? Equation E = √ ∑ 𝜇̂ 𝑖 2 𝑁 𝑖=1 𝑁 − 2 Match the quantity you wish to calculate with the correct equation. In each case ? and ? are continuous variables. iii. The covariance between ? and ? [2] a. Equation A b. Equation B c. Equation C d. Equation D e. Equation E iv. Standardizing the estimate of ? 1 in ? 𝑖 = ? + ? 1 ? 1,𝑖 + 𝜇 𝑖 [2] a. Equation A b. Equation B c. Equation C d. Equation D e. Equation E

5 6. There is evidence that minority governments at the federal level in Canada are more responsive to the public than majority governments in their policy priorities. However, there is also evidence that this relationship is less true for minority government that are popular the in the polls. Is the relationship between minority government status and responsiveness moderated or mediated by popularity in the polls ? [2] a) moderated b) mediated 7. Calculate the mean, median, mode and variance, and standard deviation of the following five values. Use the table and show all work. ? ? 𝑖 − ? ̅ (? 𝑖 − ? ̅ ) 2 8 5.8 33.64 3 0.8 0.64 -5 -7.2 51.84 8 5.8 33.64 -3 -5.2 27.04 ? ̅ = ____2.2_____ [2] 𝑠 2 = ____29.36___ [3] Median = ___3___ [1] 𝑠 = _____5.42____ [2] Mode = ____8___ [1] Half marks for using 𝑁 − 1 ? ̅ = ∑ ? 𝑖 𝑁 𝑖=1 𝑁 = 8 + 3 − 5 + 8 − 3 5 = 11 5 = 2.2 Median: -5, -3, 3, 8, 8 𝑠 2 = ∑ ( ? 𝑖 − ? ̅ ) 2 𝑁 𝑖=1 𝑁 = 33.64 + 0.64 + 51.84 + 33.64 + 27.04 5 = 534 5 = 29.36 𝑠 = √ 𝑠 2 = √29.36 = 5.42

7 12. Which of the following is a correct definition of R -squared from the linear regression: ? 𝑖 = ? + ?? 𝑖 + 𝜇 𝑖 ? [2] a) The proportion of variance in Y explained by variance in X b) The proportion of variance in μ explained by variance in X c) The proportion of variance in Y not explained by variance in X d) The proportion of variance in X explained by variance in Y 13. A survey of 1000 Canadians asked respondents to rate the Harper government on a 0 to 10 scale. The average amongst women was 3 with a standard deviation of 0.5. The average amongst men was 4 with a standard deviation of 1.5. 48 percent of the respondents were men and 52 percent were women. Calculate the 95 percent conference interval for the difference of means. [6] Hint, the standard error for a difference of means is: 𝑠𝑒(𝜇 2𝑚 − 𝜇 4𝑚 ) = √ 𝜎 2𝑚 2 𝑁 2𝑚 + 𝜎 4𝑚 2 𝑁 4𝑚 (𝜇 2𝑚 − 𝜇 4𝑚 ) ± 1.96 × √ 𝜎 2𝑚 2 𝑁 2𝑚 + 𝜎 4𝑚 2 𝑁 4𝑚 1 ± 1.96 × √ 1.5 480 + 3 520 1 ± 1.96 × 0.0719 1 ± 0.141 (0.86, 1.14) (𝜇 2𝑚 − 𝜇 4𝑚 ) ± 2 × √ 𝜎 2𝑚 2 𝑁 2𝑚 + 𝜎 4𝑚 2 𝑁 4𝑚 1 ± 2 × √ 1.5 480 + 3 520 1 ± 2 × 0.0719 1 ± 0.143 (0.86, 1.14) 14. Which of the following is a probabilistic model? [2] a) 𝐸(?|? 𝑖 ) = ? + ?? 𝑖 b) ? 𝑖 = ? + ?? 𝑖 c) ? 𝑖 = ? + ?? 𝑖 d) None of the above 15. Why might we standardize the coefficients in a linear regression? [2] We standardize coefficients in a linear regression so that they are in the same units. We do this when we want to compare the magnitudes of the coefficients.

8 16. For this question, consider the following cross tabulation: Candidate Male Female Row total McCain 49.46% 41.55% 44.97% Obama 50.54% 58.45% 55.03% Column total 100% 100% 100% Using the above cross tabulation and the column totals in the table below, calculate the expected frequencies for the cells indicated by the ‘?’ under the assumption that the two variables are independent: [8] Candidate Male Female Row total McCain ? ? 1434 Obama ? ? 1755 Column total 1379 1810 3189 0.4497 × 1379 = 620.14 0.5503 × 1379 = 758.86 0.4497 × 1810 = 813.96 0.5503 × 1810 = 996.04 17. A null hypothesis is chosen such that it must be true/false (select one) if the research hypothesis is true/false (select one). [2] 18. You have data on the average life expectancy (in years) of citizens in 20 democratic countries and the average life expectancy of citizens in 15 non-democratic countries. You calculate the difference in means (life expectancy in democratic countries – life expectancy in non-Democratic countries). You get a value of 5 years and a p -value for the difference of means of 0.1. Which of the following can you conclude (circle all that apply)? [3] a) There is a 0.1 probability that the null hypothesis is true b) There is a 0.1 probability of observing a difference of 5 years or greater if the null hypothesis is true c) There is a 0.1 probability of observing a difference of 5 years or greater if the null hypothesis is false d) There is a 0.1 probability that the null hypothesis is false

10 22 . For the next set of questions, consider the following results from regressing the number of yearly fatalities in revolutionary wars on seven independent variables: Table 1. Predictors of the number of fatalities in revolutionary wars 1965-1999 Coefficient Religious conflict 0.187*** Religious homogeneity -0.098** Ethnic homogeneity 0.115*** Infant mortality 0.141*** Contagion, all conflict 0.032 Contagion, ethnic conflict -0.89 Polity score -0.66 𝑁 = 888 , ? 2 = 0.071 , *** p<0.001, ** p<0.01 Variable key Religious conflict : 1 if the conflict is a religious conflict and 0 otherwise. Religious homogeneity : index ranging from 0 to 1 with higher values indicating higher religious homogeneity and lower values indicating lower religious homogeneity. Ethnic homogeneity : index ranging from 0 to 1 with higher values indicating higher ethnic homogeneity and lower values indicating lower ethnic homogeneity. Infant mortality : number of deaths of children less than one year of age per 1000 live births. Contagion, all conflict : number of bordering states with violent conflicts. Contagion, ethnic conflict : number of bordering states with violent ethnic conflicts. Polity score : a democracy score ranging from -10 to +10, with lower scores meaning greater autocracy and higher scores meaning greater democracy The dependent variable is a five-point scale of the number of yearly fatalities: 0 – less than 100 1 – 100 to 1,000 2 – 1,000 to 5,000 3 – 5,000 to 10,000 4 – more than 10,000 i. What can you conclude regarding the null hypothesis that the number of fatalities in religious conflicts is no greater than that in non-religious conflicts? [3] We can reject the null hypothesis [1] at the 0.05 significance level [1], controlling for the other variables in the model [1] ii. What is the direction and magnitude of the effect of the revolutionary war being a religious conflict? [3] The direction is positive in that the expected value for the number of fatalities is greater when the revolutionary war is a religious conflict than when it is not, controlling for the other variables in the model. The expected value for the number of fatalities is 0.187 greater for religious conflicts, on the 0-4 scale, controlling for the other variables in the model.

11 iii. There is a piece of information missing from these reported results that you would need to predict the number of fatalities for a given set of values for the independent variables. What is the missing piece of information? [2] a) Intercept b) Standard Errors c) Exact P -values d) Adjusted ? 2 e) Root mean squared error iv. What can you conclude about how well this model fits the data? [3] The R squared value is 0.071. This suggests the model does not fit the data well. 23. In order to estimate the correlation between Ethnic homogeneity and Religious homogeneity, you calculate a correlation coefficient. The correlation coefficient is 0.6 and the p -value is 0.005. What do you conclude about the statistical significance, direction and magnitude of correlation between Ethnic homogeneity and Religious homogeneity? [4] We can reject the null hypothesis that the correlation is 0, at the 0.05 significance level OR The correlation is statistically significant at the 0.05 significance level The direction of the correlation is positive. The magnitude of the correlation is moderately big and/or some reference to the fact that the correlation coefficient takes values between -1 and 1. 24. What concern might this correlation raise for the regression results in Table 1? [2] We might be concerned that we have high multicollinearity. This is a concern because it produces larger standard errors (than if there was no multicollinearity).

13 ii. Is the effect of TV watching when the individual feels another terrorist attack is very likely different than the effect of TV watching when the individual feels another terrorist attack is not very likely? Explain how you came to this conclusion? [3] Yes, we can reject the null hypothesis that the interaction variable between TV watching and terrorism threat is 0, at the 0.05 significance level iii. Which coefficient gives you the estimated effect of TV watching when individuals feel zero threat of terrorism (0 on the Terrorism Threat variable)? [3] The coefficient on the TV watching variable Bonus Question [Bonus 10] In a recent survey of 1000 randomly sampled British adults 18 years and older, 65% of male respondents supported the nationalisation of utilities such as gas and electricity. 47% of female respondents supported the nationalisation of utilities. Calculate a 95% confidence interval for the difference in the proportion of British men and women supporting the nationalization of utilities. The students are not told the sample sizes for men and women, so they must make some sort of assumption. Any reasonable assumption is acceptable. I will work with the assumption that the sample is 50 percent male and 50 percent female. 95%𝐶𝐼(𝑝 𝑚 − 𝑝 𝑓 ) = (𝑝 𝑚 − 𝑝 𝑓 ) ± 1.96 × 𝑠𝑒 (𝑝 𝑚 − 𝑝 𝑓 ) = 0.65 − 0.47 = 0.18 𝑠𝑒 = √ 𝜎 𝑚 2 𝑁 𝑚 + 𝜎 𝑓 2 𝑁 𝑓 = √ 𝑝 𝑚 (1−𝑝 𝑚 ) 𝑁 𝑚 + 𝑝 𝑓 (1−𝑝 𝑓 ) 𝑁 𝑓 = √ 0.65(1−0.65) 500 + 0.47(1−0.47) 500 = 0.031 95%𝐶𝐼(𝑝 𝑚 − 𝑝 𝑓 ) = 0.18 ± 1.96 × 0.031 = 0.18 ± 0.061 = (0.119, 0.241)