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lecture22_2slides - Statistics 528 Lecture 22 Intro to...

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Statistics 528 - Lecture 22 1 Statistics 528 - Lecture 22 Prof. Kate Calder 1 Intro. to Hypothesis Tests Two of the most common types of statistical inference: 1. Confidence intervals Goal is to estimate (and communicate uncertainty in our estimate of) a population parameter. 2. Tests of Significance Goal is to assess the evidence provided by the data about some claim concerning the population. Statistics 528 - Lecture 22 Prof. Kate Calder 2 Basic Idea of Tests of Significance Example: Each day Tom and Heather decide who pays for lunch based on a toss of Tom’s favorite quarter. Heads - Tom pays Tails - Heather pays Tom claims that heads and tails are equally likely outcomes for this quarter. Heather thinks she pays more often.

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Statistics 528 - Lecture 22 2 Statistics 528 - Lecture 22 Prof. Kate Calder 3 Heather steals the quarter, tosses it 10 times, and gets 7 tails (70% tails). She is furious and claims that the coin is not fair. There are two possibilities: 1. Tom is telling truth – the chance of tails is 50% and the observation of 7 tails out of 10 tosses was only due to sampling variability. 2. Tom is lying – the chance of tails is greater than 50%. Statistics 528 - Lecture 22 Prof. Kate Calder 4 Suppose they call you to decide between the two possibilities. To be fair to both of them, you toss the quarter 25 times. Suppose you get 21 tails. What would you conclude? Why? => The coin is probably not fair. Even with sampling variability it is unlikely that a fair coin would result give such a high percentage of tails. (The actual probability of getting 21 or more tails in 25 tosses is 0.000455 if the coin is fair .)
Statistics 528 - Lecture 22 3 Statistics 528 - Lecture 22 Prof. Kate Calder 5 Moral of the story: an outcome that would rarely happen if a claim were true is good evidence that the claim is in fact not true. This is the idea behind Hypothesis Testing . Statistics 528 - Lecture 22 Prof. Kate Calder 6 A hypothesis is a statement about the parameters in a population; we will be making statements about in Section 6.2. A hypothesis test ( or significance test) is a formal procedure for comparing observed data with a hypothesis whose truth we want to assess. The results of a test are expressed in terms of a probability that measures how well the data and hypothesis agree.

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Statistics 528 - Lecture 22 4 Statistics 528 - Lecture 22 Prof. Kate Calder 7 Performing a Hypothesis Test 1. State Hypotheses State your research question as two hypotheses - the null and the alternative hypotheses. These hypotheses are written in terms of the population parameters. The null hypothesis ( H 0 ) is the statement being tested. This is assumed “true” and compared to the data to see if there is evidence against it. A null hypothesis that we will see often is that the mean μ is equal to some standard value. Usually, null hypotheses give a statement of “no difference” or “no effect.” Statistics 528 - Lecture 22
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lecture22_2slides - Statistics 528 Lecture 22 Intro to...

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