For the following studies, think about everything that was done wrong in the ana
ID: 3314516 • Letter: F
Question
For the following studies, think about everything that was done wrong in the analysis. Then describe how you would do the analysis if you were in charge.
Researchers at Aperture Science Laboratory want to study whether a new chemical helps people complete puzzles faster. They collected 100 volunteers for the study. Everyone who identified as male (50 people) was given an injection of the new chemical, and everyone else was given a placebo. All subjects were then asked to solve a puzzle, and their times were recorded. Researchers used a paired t-test to determine if the subjects with the chemical performed faster.
Students at University of Winterhold study either Destruction Magic, Illusion Magic, or Healing Magic. The President of the University has noticed that 72% of Destruction Magic students and 78% of Illusion Magic students are graduating, while only 62% of Healing Magic students graduate. He does an ANOVA test to see if these means are equal. The test is significant, so he fires all his Healing Magic teachers.
Cerebrus is a powerful company that manufactures weapons. The CEO decides to do a poll to see if customers are likely to buy his new product, the Shepard 2.0. He mails a survey to every registered address on file. When he gets enough results, he does a t-test to see if more than 50% of customers will buy the product.
Star Fox is the captain of an elite squad of fighter pilots. He is concerned that one of his pilots, Slippy, is not keeping up. For the next 40 missions, Star Fox records the number of Bad Guy planes shot down by each of his 5 crew members (including himself and Slippy). He then makes a linear regression for each crew member over time. The slope for Slippy’s regression is negative, with a p-value of 0.32. Star Fox decides to kick Slippy out of the gang.
Kirby is growing some delicious tomatoes in his garden. He wants to see if his tomatoes are better than his neighbor Yoshi. In the Spring, Kirby steals the first 5 ripe tomatoes from Yoshi’s garden. He then compares the weights of these tomatoes to the 7 ripe tomatoes in his own garden. He does a 2-sample t-test, and finds that his tomatoes are indeed significantly heavier. Kirby eats all 12 tomatoes. Kirby is happy. It’s a good day to be Kirby.
Explanation / Answer
Problem 1)
Researchers at Aperture Science Laboratory want to study whether a new chemical helps people complete puzzles faster. They collected 100 volunteers for the study. Everyone who identified as male (50 people) was given an injection of the new chemical, and everyone else was given a placebo. All subjects were then asked to solve a puzzle, and their times were recorded. Researchers used a paired t-test to determine if the subjects with the chemical performed faster.
Problems:
a)
The test was performed on volunteers. It should have been performed on a randomly selected group of people.
b) Injection of the drug was given to males and placebo was given to females and others. It should have been a random selection of persons from the 100 selected persons to receive the injection of the drug.
c)
After the drug injection, all the subjects were asked to solve the puzzles, and their times were recorded. Paired sample t-test was used. This test is used for paired data that is generated before and after applying some kind of treatment.
The real procedure should be that we select randomly a small sample of 100 persons from the population. Ask them to solve puzzle and record timing. Then we would inject the drug to all the participants and ask them to solve puzzles again. Then we would record their timing. Now we can use the paired sample t-test and compare the means of timings before and after the treatments were applied to the sample. The significant difference in the two timings would suggest that there is a significant effect of the treatment.
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