PS923 – Methods and Analysis in Behavioural Science
• Please use RMarkdown for the solution of this homework.
• For this homework, we will be using the same data as homework 3.
Past research has shown that people consistently believe that others are more easily manipulated by external influences than they themselves are – a phenomenon called the third-person effect (Davison, 1983). Cornwell and Krantz (2014) have investigated whether support for public policies aimed at changing behavior using incentives and other decision “nudges” is affected by this bias. To this end, they have asked participants to rate their support for various policies in different presentation formats. In their Study 2, participants were randomly assigned to one of four conditions, a second-person condition (“you”), a third-person condition (“people”), and two further control conditions. For example, one of the presented policies was taxes on fuel to discourage carbon dioxide emissions.
• In the in the second-person condition the policy was framed as follows:
The EPA is considering new fuel economy standards to reduce the release of harmful greenhouse gas emissions by increasing the price of gasoline. The theory is that when you need to pay more for gasoline, you will drive less to save money. Thinking about how you tend to make decisions, please answer the following questions about this policy:
• In the third-person condition, this policy was presented as follows:
The EPA is considering new fuel economy standards to reduce the release of harmful greenhouse gas emissions by increasing the price of gasoline. The theory is that when people need to pay more for gasoline, they will drive less to save money. Thinking about how people tend to make decisions, please answer the following questions about this policy:
• In the passive control condition the justification was presented in the passive voice (e.g., “The theory is that with the need to pay more for gasoline, there will be less driving to save money.”)
• In the no justification condition, the justification was completely removed from the policy description.
For each policy, participants were asked to indicate the degree (on scales from 1 to 7) to which they support such a policy (1 indicating “not at all” and 7 indicating “very strongly”), the degree to which they thought the policy was likely to achieve its intended goals (1 indicating “very unlikely” and 7 indicating “very likely”), and the degree to which they thought the policy would result in unintended consequences (with, again, 1 indicating “very unlikely” and 7 indicating “very likely”). Each participant provided responses for 8 of the 16 different scenarios.
The main hypothesis was that the third-person perspective will lead to higher support judgments than the second-person perspective. An additional research question was whether the level of the support of the third-person perspective or the second-person perspective differed from the more neutral (passive) and no-justification conditions.
The data of this study is available on Moodle as cornwell_krantz_2014_s2.csv and can be read in as follows.
library(-tidyverse-) d1 – read_csv(-cornwell_krantz_2014_s2.csv-) % %
condition, levels = 1:4, labels = c(-third-person-, -second-person-, -passive-, -no-justification-)
Relevant for the following tasks are the first six columns:
d1 % %
select(id:unintended) % % glimpse
## Rows: 2,400
## Columns: 6
## $ id dbl 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3,~
## $ condition fct no-justification, no-justification, no-justification, no-ju~
## $ scenario dbl 2, 5, 7, 8, 9, 10, 12, 14, 6, 7, 9, 10, 13, 14, 15, 16, 2, ~
## $ support dbl 7, 7, 6, 7, 4, 3, 7, 7, 3, 7, 6, 4, 4, 6, 6, 3, 5, 3, 3, 6,~
## $ achieve dbl 5, 7, 6, 7, 4, 3, 7, 6, 2, 5, 5, 4, 4, 4, 4, 2, 4, 5, 3, 6,~
## $ unintended dbl 1, 3, 1, 1, 7, 6, 4, 1, 6, 4, 4, 2, 3, 3, 3, 6, 6, 5, 4, 7,~
• id: participant identifier (i.e., each participant has a unique id)
• condition: perspective condition with mapping as shown in the code chunk above
• scenario: scenario identifier from 1 to 16 (for mapping see Appendix A of Cornwell and Krantz, 2014)
• support, achieve, and unintended: measurement on 7-point scale question as described above
Use the tidyverse for this task and answer the following questions:
• Count the number of observations (i.e., rows) for each of the participants. Do all participants have the same number of observations?
• Count the number of participants per condition.
• Create a tibble for which the first column is scenario and columns two to five each contain the number of times each scenario appeared in one of the conditions (i.e., column two to five each contain the number of times a scenario appeared for one condition).
Calculate three ANOVAs with IV condition and three different DVs, support, achieve, and unintended, using afex.
• What is the null-hypothesis of these ANOVAs?
• For which of the DVs do we find an effect of condition?
Produce a single composite score acceptability from the three variables support, achieve, and unintended. Create this such that higher values indicate a higher acceptability (i.e., support) for the respective policy (i.e., make sure to re-code variables as necessary).
Calculate an ANOVA with factor condition on the composite score acceptability. Calculate this ANOVA once using afex and once using the combination of lm and car::Anova(). Do the results agree? (They
Create a plot for each of the four ANOVAs calculated so far, using afex_plot. Combine these four plots into one figure (e.g., using cowplot::plot_grid()).
Apply the following contrasts to the ANOVA(s) with a significant effect of condition as well as the ANOVA with acceptability as DV. The contrasts should compare the means of the following conditions (or combination of conditions):
• Third person versus other conditions (i.e., mean of other conditions).
• Third person versus second person.
• Third person versus second and other.
• Second person versus other conditions.
• Three contrasts, each testing the no-justification versus one of the other conditions.
Please answer the following questions:
• Which of the contrasts are significant for the ANOVA(s) with a significant effect of condition?
• Does the pattern of significant contrasts change if you do not control for multiple testing compared to when using the Bonferroni-Holm method (i.e., adjust = -holm-)?
• Which contrasts do you think are the most relevant to the research questions listed on page 1 (potentially including contrasts other than those listed above)? Apply those to the significant ANOVAs using the Bonferroni-Holm method. Which substantive conclusions are justified, given these results?
• Apply the contrasts to the ANOVA on the acceptability scores. How would you interpret the results; which conclusions are justified?
Calculate the means and standard errors for the acceptability scores per condition (after aggregating the different observations per participant). Compare these values with the means and standard errors that are returned by emmeans for the ANOVA on acceptability scores. How can you explain the (small) differences?
A useful statistics book is by Thomas Baguley (2012): Serious Stats: A Guide to Advanced Statistics for the Behavioral Sciences. It does not (yet!) use afex, emmeans, the tidyverse, or ggplot2, but has several useful chapters that relate to the lectures:
• Statistical inference: Confidence intervals (ch. 3) and significance testing (ch. 4)
• Regression and ANOVAs: Chapters 5, 6, 12, and 13
• Sums of Squares and contrasts: Chapter 15
• Davison, W. P. (1983). The third-person effect in communication. The Public Opinion Quarterly, 47(1), 1–15.
• Cornwell, J. F. M., & Krantz, D. H. (2014). Public policy for thee, but not for me: Varying the grammatical person of public policy justifications influences their support. Judgment and Decision
Making, 9(5), 12. http://journal.sjdm.org/14/14625a/jdm14625a.pdf