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Unformatted text preview: Lecture 21: Power Analysis Power refers to the ability to avoid type2 errors. Sources of Information : Sokal & Rohlf p. 159169 otulsky Chapter 22 ** Peterman, R.M. 1990. Statistical power analysis can improve fisheries research and management. Canadian Journal of Fisheries & Aquatic Sciences 47: 215. [posted as pdf file on ACE] Errors in Hypothesis Testing Recall from our lectures on hypothesis testing that there are 2 types of errors that can be made: type1 and type2. Suppose we conducted an experiment in a situation where the null hypothesis is really true (but unknown to us, of course), but the experimental results by chance suggest that the H o is false and so we reject the H o . In this case, we have made a type1 error . A type1 error occurs when the outcome of an experiment (or observations) leads us to reject a true null hypothesis. i.e., when the data you collected happened (by chance) to lie unusually far from the hypothesized value (or the true population parameter). e guard against making too many type1 errors by establishing, a priori , a guideline that serves as a definition of rarity and against which we can evaluate the reliability of evidence (based on sample data). This guideline is commonly known as alpha or the significance level of a test . any scientists set an alpha rate of 0.05 – if the H o is true , they won’t incorrectly reject it on average more than 1 time in 20 (= 5% of experiments run). It is critically important that alpha be established before the data have been viewed . You should not set alpha after viewing the data, and you ust not adjust alpha in response to perceived patterns in the data. You can think of alpha as the average probability of a type1 error when the H o is true . Type2 Error A type2 error is made when the H o is really false, but your experiment failed to reject it. i.e., when the data you collected happened (by chance) to lie unusually close to the hypothesized value. or because the sample size is too low, or the amount of variability (scatter) of the data is too high relative to the sample size, to identify a significant difference even when a true difference exists. Protection against type2 errors is the domain of power analysis . Decision/Consequences (Probability) Situation Do not reject H o Reject H o o is true Correct (1  α ) Type1 error ( α ) o is false Type2 error ( β ) Correct (1  β ) (= power) Traditionally, hypothesis testing in the biosciences has placed most emphasis on management of the type1 error rate (rejecting true H o ’s). In recent years, increasing attention has been paid to the type2 error rate Æ the probability of failing to reject a false H o . Remember that a “not significant” outcome does not mean that the H o is true. It simply means that the data are not strong enough to convince you that the H o is not true!...
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 Winter '08
 Hall
 Power, Null hypothesis, Statistical hypothesis testing, Statistical significance, Statistical power

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