The story of LFB and Foxy For this assignment, we're going to go back to meet up with LFB and Foxy and hear their story. As you'll recall, a few weeks ago they, Doggie, and Flopsy went on a mission to Otherland to steal some of their data. The mission was successful but LFB and Foxy went missing! In your assignment we get to see what happened to them. * * * LFB and Foxy are acting as lookout as Doggie and Flopsy enter the building. Standing on one side of the building, LFB is squinting through the darkness trying to see when she hears a rustle. Then another one, then another one, coming ever closer. Not wanting to raise the alarm prematurely, LFB holds still, but when she hears another rustle only meters from where she is, she whistles, giving the signal. Foxy dashes around the building as quickly as she can, just in time to see the bushes near LFB part. She catches a hasty glimpse as three very large shapes -- bears? dogs? something else? -- jump out at LFB. Startled, LFB whistles as loud as she can, but it is abruptly cut off by one of the animals covering her mouth. Forgetting her normal shyness, Foxy shouts "stop!" as loud as she can and charges at the two creatures. She growls at them, surprising herself, and they turn. She trembles: one of them is the largest bear she has ever seen, but it's too late to go back now. She growls again, and then the bear rushes at her and hits her and she is knocked unconscious. After a short and frightening journey through the dark, LFB and Foxy are put into a small, bright room. LFB is relieved to see Foxy start to stir after a moment — she hasn’t been hit that hard, then — and the two of them cuddle together in fear. The room they are in looks like a library, but it has very large chairs and books. LFB has to jump just to get down from the high sofa and reach the door handle. It is locked. After about a half an hour of worry, the door opens and seven people come in. The first is an enormous bear, larger than anybody LFB has ever seen; she suspects that is the main person who subdued them. He is followed by an owl, a small unicorn with a rainbow mane, a hippo, and a cute penguin carrying a snake. The entire group is trailed by what looks, to their astonishment, to be a sentient guitar (that's right, a musical instrument that can walk and talk). This is a very strange place, thinks LFB
Q2 [4% of total mark]
In 125 words or less, pick one of the kinds of reliability (e.g., test-retest, inter-rater, or internal consistency) and explain how you would evaluate these questions with respect to that kind of reliability. (Note that you can propose collecting more data if you need to). In your answer, clearly indicate what kind of reliability you have chosen, what it entails, and what your proposal involves.
Q3 [6% of total mark] It turns out that they gave the same answer to 38 of the 50 questions. (a) What is the probability that exactly 38 of the 50 answers would match if they were completely guessing? (b) What is the probability that 38 or more of the answers would match if they were completely guessing? (Hint: you’ll need to decide which of the distributions and arguments discussed on Week 5, Day 1 apply to this situation, and use R in the code chunk to make these calculations). Fill out the blanks in the answer spaces provided. * * * The Others confer a bit, and realise they were a bit silly to give Foxy and LFB yes/no questions, since chance performance is so high; as a result, they don’t do a great job of distinguishing whether they really were in agreement or not. They thus devise another test, this time with 50 multiple choice questions. Each of the questions has four possible answers (A through D). They have set it up so that adjacent answers are similar: this means that if (for example) LFB answered B and Foxy answered C, that those answers are closer to each other than if Foxy had answered D. The tibble dt, which has been loaded for you in the R Markdown document, contains answers to the questions LFB and Foxy were asked. Each row corresponds to one question. The four columns are as follows: question: the question number foxy: Foxy’s answer to that question (A, B, C, or D) lfb: LFB's answer to that question (A, B, C, or D) agree: “yes” if their answers were the same, “close” if they were within one, and “no” if further
Q4 [3% of total mark] Take dt and make a table showing how many questions LFB and Foxy give the same answer, close to the same answer, or not the same answer on. Assign this table to the variable agreementTable and make sure it is visible in your knitted document.
Q5 [7% of total mark] The research null hypothesis in this situation is that the amount of agreement between LFB and Foxy is what you would expect to see if they were just guessing in their answers to the questions. This corresponds to expecting 25% of the answers to be coded “yes”, 37.5% to be coded “close”, and 37.5% to be coded “no.” (You can work out for yourself why this is if you’re curious, but that’s not part of the question; just take it on faith if you like). Use the appropriate statistical test (i.e., one of the ones you learned in Week 6 or Week 7) to evaluate this hypothesis. Report on the results in 125 words or less. In your answer, don’t worry about including descriptive statistics but do include an explanation of which statistical test you used and what hypothesis is being tested, the appropriate stats reference, and the interpretation of this result: based on it, what should the Others conclude about whether Foxy and LFB were just guessing when they answered the questions?
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