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A study concludes that one single trait that is a strong predictor of whether or not someone is a Donald Trump supporter is authoritarianism. Authoritarian personality is a state of mind or attitude characterized by belief in absolute obedience or submission to authority.
To see if the result holds for college students, we asked the same 4 questions as in the study in the Fall 2016 Stat 100 and Stat 200 survey 2:
For the following pairs of traits, which trait do you think is more important in raising children? independence or respect for their elders? curiosity or good manners? self-reliance or obedience? being considerate or being well-behaved?
A person with an authoritarian personality will prefer the second choices (respect for their elders, good manners, obedience and being well-behaved). In this problem, you are going to analyze the survey result.
Of 240 Stat 200 students who responded to the survey, only 30 are Trump supporters. So we won't have enough people to give decent statistics. Instead, we will look at the Stat 100 survey result, where there are 209 Trump supporters among 1240 students who responded to the survey. The survey data can be downloaded here and then loaded to R using the following command.
survey <- read.csv("Stat100_2016fall_survey02.csv")
The column variables are described on this webpage. The four questions related to authoritarianism are in columns 21–24. The "president" column (column 26) indicates which presidential candidates the student supports.
Here is how we can determine how authoritarian a person is. For the 4 questions, we assign 0 for the answers "independence", "curiosity", "self-reliance" and "being considerate". We assign 1 for the answers "respect for their elders", "good manners", "obedience" and "being well-behaved". We then add up the numerical values of the 4 questions and labeled it as AS (authoritarian score). A person who has strong authoritarian personality will have an AS = 4. Copy and paste the following R code that is used to calculate AS:
survey$AS <- as.integer(survey[[21]]=="respect for their elders") + as.integer(survey[[22]]=="good manners") + as.integer(survey[[23]]=="obedience") + as.integer(survey[[24]]=="well-behaved")
a. Calculate the average of the authoritarian score for the supporters of each presidential candidate. The supporters of which candidates have the highest average authoritarian score? Hillary Clinton Gary Johnson Jill Stein Donald Trump Other Unsure
b. Perform an F test to determine if the differences between the average AS among the groups are statistically significant. From the listed p-value, what do you conclude? All the group averages of AS are significantly different from one another. At least one group average of AS is significantly different from the rest. None of the group averages of AS is significantly different from one another.
Remember we read a previous study that indicated the authoritarianism is a strong predictor of being a Trump supporter. So to test this on college students, we collected data from our classes. Now we formulate the following null and alternative hypotheses and see if they hold up.
H01: There is no difference between the average AS of Donald Trump supporters and the average AS of Hillary Clinton supporters. HA1: The average AS of Donald Trump supporters is greater than the average AS of Hillary Clinton supporters.
H02: There is no difference between the average AS of Donald Trump supporters and the average AS of Gary Johnson supporters. HA2: The average AS of Donald Trump supporters is greater than the average AS of Gary Johnson supporters.
H03: There is no difference between the average AS of Donald Trump supporters and the average AS of Jill Stein supporters. HA3: The average AS of Donald Trump supporters is greater than the average AS of Jill Stein supporters.
H04: There is no difference between the average AS of Donald Trump supporters and supporters of candidates other than Trump, Clinton, Johnson and Stein. HA4: The average AS of Donald Trump supporters is greater than the average AS of supporters of candidates other than Trump, Clinton, Johnson and Stein.
H05: There is no difference between the average AS of Donald Trump supporters and the average AS of students who are unsure on which candidate to vote. HA5: The average AS of Donald Trump supporters is greater than the average AS of students who are unsure on which candidate to vote.
c. What tests should be done to test the hypotheses? One-sided multiple t-tests with Bonferroni correction. Two-sided multiple t-tests with Bonferroni correction. One-sided multiple t-tests without any correction. Two-sided multiple t-tests without any correction.
The following R command returns a table of the p-values for two-sided pairwise t-tests without any correction.
pairwise.t.test(survey$AS, survey$president, p.adjust="none")
For example, the number 0.572 in row "Jill Stein" and column "Gary Johnson" means that the p-value of the two-sided t-test between Jill Stein supporters and Gary Johnson supporters is 0.572.
d. Focus on the first column of the output, where the comparisons are between Donald Trump supporters and supporters of other candidates. What number should the p-values in the first column be multiplied to get the p-values appropriate for the tests in part (c)? 1/2 1 10 15 Some other number
Adopt a null cutoff α = 5%. Which of the following pairs show significant difference in the average of AS? (Select all that apply) Donald Trump - Unsure Donald Trump - Hillary Clinton Donald Trump - Other Donald Trump - Gary Johnson Donald Trump - Jill Stein
e. Now we want to know if there are any differences in the average AS among supporters of candidates other than Trump. So we look at the p-values in columns 2–5. This time we don't have any hypothesis as to which pairs of groups we think are different. We just want to find out if there are any differences among the other groups. What number should we multiply the p-values in columns 2–5 to account for Bonferroni correction?
The p-values in columns 2–5 should be multiplied by .
f. Which of the following pairs have significant different average AS? (Select all that apply) Gary Johnson - Other Gary Johnson - Unsure Hillary Clinton - Other Gary Johnson - Hillary Clinton Jill Stein - Unsure Hillary Clinton - Jill Stein Gary Johnson - Jill Stein Hillary Clinton - Unsure Jill Stein - Other Other - Unsure None of the groups is significantly different
g. What do you conclude? Is the authoritarian personality a good predictor of whether or not a Stat 100 student is a Donald Trump supporter? yes no
