Studio 8

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Topics: T-tests, rejection regions
        R: coding

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Before class:
1. Post studio8.zip containing: studio8-sol.r (there is no studio8.r)

2. Students should download this zip file and unzip it in their 18.05 R directory.

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For class:
1. Use studio8-slides.pdf
2. Follow class script below.

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After class:
1. Post studio8-slides-all.pdf 

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Class script

Slide 1: Everyone should have downloaded and unzipped studio6.zip

Slides 2-4: Problem 1: Poll of heights
    -- divide the room into left and right halves 
    -- for each half, collect the height of each person
    -- while the class works problem 1 a staff member should compute the size, mean and variance of each group.
  DISCUSSION:
    -- Ask for arguments for and against the mean heights being the same. What if we divided by athletes vs non-athletes?
    -- Show slides 3,4 --no need to dwell on them, but spend a minute on the answers in 1c. The point is that all the tests make assumptions that must be justified by argument or other testing.

Slide 5: Problem 2: Students code and run the tests in R. 
    Code is in studio8-sol.r
      --The code has previous data. While they work someone should input the current data and run the code to see the answers.
      --The output of the code is prettiest if you source the file without echo. 
      --They will have studio8-sol.r ahead of time, but discourage peeking.
      --For groups having trouble you can point them to the code.
    DISCUSSION: 
      --It shouldn't be necessary to walk through the code. Remind them that the answers will be posted in studio8-sol.r.
      --Talk about p = 2*pt(-abs(t),df) 
      --Source the file and show them the output for problem 2
 
Slide 6 (paused slide with 2 parts): Binomial rejection regions
     --Either walk through choosing the region -- as close as possible 
       to 0.05 on each side -- or do it as a class discussion
     --Show part 2 of the slide with the region highlighted
        --Point out the the region is a range of values of x.
     --NOTE: there are different algorithms for choosing. The only strict 
         requirement is that the prob. of the rej. region is < or = alpha. 
         (In class 23 we'll choose by always taking the next smallest 
         available probability.) 
        THIS IS PROBABLY NOT WORTH talking about at this point.

Slide 7: Off-by-one errors
     The goal here is to explain the need for fiddly plus or minus 1's in the R code.
     Have them write the answers down. Then do the examples as call and response
     Ask about easy to make errors.
     DISCUSSION:
       --What we mean by off-by-one errors.

Slide 8: (paused slide with 2 parts): Problem 3. Binomial rej. regions using R
     -- Have them work.
     -- Push them to use R to check the probabilities using dbinom and/or pbinom
     -- SHOW part 2 of slide 8 with the rejection region.
     -- Show the output of the studio8-sol.r
          ** Explain what wide.left and wide.right are.
     -- Remind class that answers are in studio8-sol.r
     -- If it seems useful show them some of the code.

Slide 9: Problem 4: Left-handedness
     Might not have time for this
     -- Have all lefties raise hands. Count them.
        We already know the number of people in the room from the 
        class heights problem
     -- Have them use the data to do a one-sample test.
       DISCUSSION:  --we'll probably run out of time for this
        Show output of studio8-sol.r
        4(a) Can do an exact binomial test --rej. region like in problem 3
             Point out can do a z-test assuming normality
             Show output and MAYBE source code
        4(b) Assume sample is representative of MIT. --point out figure.
        4(c) Similar to (a)