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mat2378-Chapter10 - MAT2378 Rafal Kulik Version 2009/Nov/23...

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MAT2378 Rafal Kulik Version 2009/Nov/23 Rafal Kulik
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MAT2378 Probability and Statistics for the Natural Sciences Chapter 10 Comments These notes cover material from Chapter 10. I’m planning to spend two lectures on this material. Pages 3-9 describe goodness of fit test (Section 10.1). Pages 10-12 describe 2 × 2 categorical tables (Section 10.2). Pages 13-14 describe independence in 2 × 2 categorical tables (Section 10.3). Rafal Kulik 1
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MAT2378 Probability and Statistics for the Natural Sciences Chapter 10 Categorical Data Analysis Consider the game of Two-Up: two coins are spun together, with 3 possible “outcomes”: both heads; both tails, or “evens”, where there is one head and one tail. Rafal Kulik 2
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MAT2378 Probability and Statistics for the Natural Sciences Chapter 10 If many games of Two-Up are played, and the number of heads recorded each spin, then the results will be a long sequence like 0,0,1,2,2,1,0,0,1,1,1,2,0,1,. . . If the coins are fair and spun independently, the number of heads (or equivalently the number of tails) should behave like a B (2 , 1 2 ) random variable, with probability distribution x 0 1 2 P ( X = x ) 1 4 1 2 1 4 and the proportion of 0’s, 1’s and 2’s in the sequence should be close to these. Rafal Kulik 3
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MAT2378 Probability and Statistics for the Natural Sciences Chapter 10 Checking that the game is in order As with any gambling game, it would always be of interest to verify that the game is being conducted fairly (i.e. that probabilities of various outcomes are as they should be). Various possible deviations might be one or both coins not fair; coins not spun independently.
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