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Published byLambert Rodgers Modified over 9 years ago
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Ch. 26 Tests of significance Example: –Goal: Decide if a die is fair. –Procedure: Roll a die 100 times and count the number of dots. We observe 368 total dots in 100 rolls. Chance model: If the die is fair, Box model Average SD of box EVsum SEsum
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–So we expect the total (sum of dots) to be around 350 give or take 17, or so. –What is the chance of observing a total of 368? z= The chance of getting results as extreme as 368 (or more) is
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–Same situation by 1000 rolls and observe a total of 3680. Language: –Null hypothesis: Assume a specific chance process is at work (box model). –Alternative hypothesis: Another statement about the box. –Test statistic: Measures the difference between what is observed in the data and what is expected based on the null hypothesis.
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In our example, –Null hypothesis: The die is fair. –Alternative hypothesis: The die is “loaded” so as to favor higher numbers. P-value of a test = significance level –Probability/chance of getting a test statistic as extreme as, or more extreme than, the one based on observation.
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–Probability of observed result assuming the null hypothesis is true. (Not the probability that the alternative hypothesis is true.) –High p-value gives evidence supporting the null hypothesis. –Low p-value gives evidence against the null hypothesis. Using z is appropriate for “large” samples and when the probability histogram is approximately normal.
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Exercise C #7 p. 483 A results is said to be statistically significant if the p-value is less than 5% and highly significant if the p-value is less than 1%.
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