【文章內(nèi)容簡介】 決策 Power越大，決策結(jié)果越可靠 不拒絕 H0 拒絕 H0 H0 是真 決策正確（概率＝ 1－ α ） I型錯誤（概率＝ α ） H0 是假 II型錯誤（ P＝ β ） 決策正確（ P＝ 1－ β ）＝ power 例 . 如果上例中我們希望檢測出的平均數(shù)差異是： （從以前的研究中知道）如果， 則 條。2. SAMPLE SIZE FOR DISCRETE VARIABLES Counts of the numbers of plants in a quadrat or the numbers of eggs in a nest differ from continuous variables in their statistical properties. The frequency distribution of counts will often be described by either the binomial distribution, the Poisson distribution or the negative binomial distribution (Elliott 1977). The sampling properties of these distributions differ, so we require a different approach to estimating sample sizes needed for counts.(1) Proportions and Percentages Proportions like the sex ratio or fraction of juveniles in a population are described statistically by the binomial distribution. All the anisms are classified into two classes, and the distribution has only two parameters: Proportion of types in the population Proportion of types in the populationIf sample size is above 20, we can use the normal approximation to the confidence interval:Where Observed proportion Value of Student’s tdistribution for n1 degrees of freedom Standard error of Thus the desired margin of error is Solving for n, the sample size required is where n=Sample size needed for estimating the proportion p d=Desired margin of error in our estimate As a first approximation for we can use We need to have an approximate value of p to use in this equation. Prior information, or a guess, should be used。 the only ruleofthumb is that when in doubt, pick a value of p closer to than you guess. This will make your answer conservative. As an example, suppose you wish to estimate the sex ratio of a deer population. You expect p to be about , and you would like to estimate p within an error limit of with . From equation(2) Counts from a Poisson DistributionSample size estimation is very simple for any variable that can be described by the Poisson distribution, in which the variance equals the mean. From this it follows thatorThus from equation,(1) assuming : where Sample size required for a Poisson variable Desired relative error (as percentage) Coefficient of variation =For example ,if you are counting eggs in starling nests and know that these counts fit a Poisson distribution and that the mean is about , then if you wish to estimate this mean with precision of (width of confidence interval), you have: nestsEquation (2) can be simplified for the normal range of relative errors as follows: For precision 3. STATISTICAL POWER ANALYSIS DecisionState of real world Do not reject null hypothesis Reject the null hypothesisNull hypothesis is Correct decision Type Ⅰ error actually true (probability =1 ) (probability = )Null hypothesis is Type Ⅱ error Correct decision actually false (probability = ) (probability =(1 )=power)Most ecologists worry about , the probability of a Type Ⅰ error, but there is abundant evidence now that we should worry just as much or more about ,the probability of a Type Ⅱ error (Peterman 1990。 Fairweather 1991). Power analysis can carried out before you begin your study (a priori, or prospective power analysis) or after you have finished (retrospective power analysis). Here we discuss a priori power analysis as it is used for the planning of experiments. Thomas (1997)discu