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Consider the following two questions:
1. Would you accept a gamble that offers a 10% chance to win $95 and a 90% chance to lose $5?
2. Would you pay $5 to participate in a lottery that offers a 10% chance to win $100 and a 90% chance to win nothing?
If you study the questions carefully, you will find that the two games are identical. Someone who is rational should give the same answer to both questions, but the reality is that the second question attracts more positive answers. This effect is called "framing". Some of the Stat 100 survey questions are designed to test this effect.
In Stat 100's fourth survey in Spring 2014, students were randomly assigned two versions of the same survey. The csv file of the survey data can be downloaded here and then loaded it to R using the following command.
survey <- read.csv("stat100_2014spring_survey04.csv")
The column variables are described on this webpage. Take some time to explore the data.
Before we study the framing effect, we want to make sure that the experiment was well-randomized and students in the two versions were as alike as possible.
a. Look at the 'gender' column. Perform a χ2 independence test to determine if there is any significant difference in the proportion of males and females in the two versions of the survey. Enter your results to 3 decimal places.
χ2 = , df = , p-value =
What do you conclude? There is a significant difference between the students in the two versions of the survey. Version 0 has more female students. There is no significant difference between the students in the two versions of the survey. There is a significant difference between the students in the two versions of the survey. Version 0 has more male students.
b. Look at the 'ethnicity' column. Perform a χ2 independence test to determine if there is any significant difference in the ethnic groups between the two versions. Enter your answers to 3 decimal places.
What do you conclude? There is no significant ethnicity difference between the students in the two versions of the survey. There is a significant ethnicity difference between the students in the two versions of the survey. Version 0 has significantly more Black students. There is a significant ethnicity difference between the students in the two versions of the survey. Version 0 has significantly less White students.
c. One question in the survey asked student's feeling toward the Affordable Care Act, a.k.a. Obamacare. In version 0, the question was
Version 0: What are your feelings toward the Affordable Care Act?
In version 1, the question was
Version 1: What are your feelings toward Obamacare?
Students' responses are in the column named 'healthCare' of the data frame. Perform a χ2 independence test to determine if there is any difference in the two versions. Enter yor answers to 3 decimal places.
What do you conclude? There is no significant difference between student's feeling toward Affordable Care Act/Obamacare in the two versions. There is a significant difference between student's feeling toward Affordable Care Act/Obamacare in the two versions.
d. Another question asked student's opinion on searching for the missing Malaysia Airlines Flight 370. In version 0, the question was
Version 0: Do you think that the American government should continue spending millions of dollars on searching for the missing Flight 370?
Version 1: Do you think that the American government should continue spending millions of dollars on searching for the 227 missing passengers on Flight 370?
Students' responses are in the column named 'flightSearch'. Peform a χ2 independence test to determine if there is any difference in the two versions. Enter yor answers to 3 decimal places.
What do you conclude? There is a significant difference between the two versions. There is no significant difference between the two versions.
e. In the same survey, a question asked student's view on abortion. In version 0, the question was as follows.
Which comes closest to your view on abortion: abortion should always be legal; should be legal most of the time; should be made illegal except in cases of rape,incest and to save the mother's life; or abortion should be made illegal without any exceptions?
In version 1, the wordings of the question are exactly the same, but the picture accompanied with the question is different:
Students' responses are in the column named 'abortion' of the data frame. Perform a χ2 independence test to determine if there is any difference in students' responses in the two versions. Enter your answers to 3 decimal places.
What do you conclude? There is no significant difference between the two versions. There is a significant difference between the two versions.
f. In the same survey, a question asked student's view on death penalty. In both versions, the wordings are the same: "Are you in favor of the death penalty for a person convicted of murder?" but the picture accompanied with the question is different. In the following two pictures, the left one (cute guy mugshot) was shown in version 0 and the right one (mean guy mugshot) was shown in version 1.
Students' responses to the question are in the column named 'deathPenalty'. Perform a χ2 independence test to determine if there is any difference in students' responses in the two versions. Enter your answers to 3 decimal places.
