Stat 301 - HW 7

Due midnight, Friday, March 10

Remember to put your name(s) inside each file and, if submitting together, join a HW group before you submit. Remember to show your work/calculations/computer details (even if not specifically asked) and to integrate this into the body of the solution.

1) To investigate an association between violent video games and aggressive behavior, British researchers Hollingdale and Greitemeyer (2014) randomly assigned 49 students from a university in the United Kingdom to play Call of Duty: Modern Warfare (a violent video game) and 52 students to play LittleBigPlanet 2 (a nonviolent/neutral video game). After 30 minutes of playing the video games, the subjects were asked to complete a marketing survey investigating a new hot chili sauce recipe. They were told they were to prepare some chili sauce for a taste tester and that the taste tester “couldn't stand hot chili sauce but was taking part due to good payment.” They were then presented with what appeared to be a very hot chili sauce and asked to spoon what they thought would be an appropriate amount into a bowl for a new recipe. The amount of chili sauce was weighed in grams after the participant left the experiment. The amount of chili sauce was used as a measure of aggression: the more chili sauce, the greater the subject’s aggression.

(a) Explain how and why random assignment was used in this study.

(b) Load the VideoAgression data into the Comparing Groups (Quantitative) applet (better yet, use the version from the pull-down menu, but note the direction of subtraction changes.) Screen capture the numerical and graphical summaries of the data comparing the two groups.  Summarize what you learn about the shapes, centers, and spreads of each group (= sample).

(c) In words, state appropriate null and alternative hypotheses to test whether there is an association between type of video games and level of aggression.

(d) Carry out a randomization test for these data. (Use 10,000 shuffles, might take a second 😊. Note: R won’t do the exact distribution for me because the sample size is too large!) Include a screen capture of the resulting null distribution with the p-value shaded.  Summarize the conclusions you would draw in terms of significance, causation, and generalizability.

(e) Do you think two-sample t-procedures are likely to be valid with these data?

(f) Use the pull-down menu to select the t-statistic. Report the observed value of the t-statistic for the actual study (this is unpooled if you want to verify its value) and use it to determine the simulation-based and the t-distribution-based p-values. Include a screen capture. How do they p-values compare?

(g) Calculate (you can use the applet) a 95% confidence interval for the difference in the treatment means. Carefully interpret your interval (Hint: What is the parameter?)

(h) Calculate the “independent samples” unpooled standard error for the difference in sample means. (Show your work.)

(i) Calculate the “independent samples” pooled standard error for the difference in sample means. (Show your work.)

(j) Give one reason why the pooled standard error might be a reasonable assumption here (e.g., how was the study conducted) and one piece of evidence that indicates it is not a reasonable assumption (Hint: An informal check of the equal variance assumption is the larger sample standard deviation is not more than twice the smaller sample standard deviation.)

(k) In randomization test, where we shuffle all existing observations across the two groups, another formula makes use of the finite population correction factor, the assumption of the null distribution, and the fact that the groups aren’t really independent. In particular, if all of the high scores are randomly assigned to one group, then all of the low scores must go to the other group, creating a larger difference between the groups.

But in our case, the correlation between the sample means (because of our assumptions in the simulation) is simply -1.

Note that I am calling these “sigmas” because I am going to treat these N = 101 observations (in each group) as the population.  . You can use Excel to calculate  using STDEV.P, the population standard deviation divides by the population size, rather than the sample size minus one.  Calculate this standard deviation. (Excel or some other online tool wouldn’t be a bad idea here either, but show your work!)

(l) Which of the 3 standard deviations best matches your simulation results in (d)?  Which SD largest?

Note:  Instead of using this very complicated standard deviation formula, we will trust in the t-distribution to make the right adjustments (uses a bigger denominator because has more of the bigger differences than might predict)!

Does 10 appear to be a plausible value for the increase in average aggression with more violent games?  In the applet, change the statistic back to the difference in group means and specify the hypothesized difference in “population means” as 10 (or -10 depending on direction of subtraction). Specify 1 as the number of shuffles as select the Plot radio button.

(m) Press Shuffle Responses and watch the animation. Explain in your own words what this animation is doing and why.  Explain how this matches our new null hypothesis.

Set the number of Shuffles to 1000 and regenerate the randomization distribution of the difference in sample means. Include a screen capture.

(n) How do the values of the mean and standard deviation compare to (d). Which change(s) and why/why not?

(o) Generate a two-sided p-value (include a screen capture). What conclusion do you draw in context?

(p) Is your conclusion in (o) consistent with your confidence interval in (g)?  Explain.

Demo Using the fancy new formula with our sleep deprivation/reaction time data where we did see a bit more of a difference between the initial formula and the simulation results.

Population standard deviation for all 21 subjects: 15.06

Does it better match the simulation results than the unpooled standard error formula?