Concepts

1power

Concepts

• Prospective power: conditional probability of reject the null given the null hypothesis is false. (29/(31+29)=.483)

• Retrospective power: conditional probability of reject the null given the null is rejected. (29/(2+29=.935)

H0 = T H0 = F Total

Fail to reject 38 31 69

Reject 2 29 31

Total 40 60 100

Concepts

• A priori power analysis the sample size N is computed as a function of

the required power level, the pre-specified significance level , and the population effect size to be detected with probability.

• Post hoc power analysis: the power is computed as a function of significance level, the population effect size parameter, and the sample size(s) used in a study.

Concepts

• Compromise power analyses both alpha and power are computed as functions of the effect

size, N, and an error probability ratio (beta/alpha). • Sensitivity analyses the critical population effect size is computed as a function of

alpha, power, and N. Sensitivity analyses is useful for evaluating published research. what is the minimum effect size the test was sufficiently sensitive to. before conducting a study to see whether, given a limited N, the size of the effect that can be detected is at all realistic .

Concepts

• Criterion analyses compute alpha, as a function of power, the effect size, and a given sample size. Criterion analyses are alternatives to post hoc power analyses after a study has already been conducted. They may be reasonable whenever the control of alpha is less important than the control of beta.

Example1

• A sample was taken from a normal distributed population, sample mean is 5, population standard deviation is 2, sample size is 20. calculate the power if the true mean is 6.5 (alpha = .05) with same sigma.

• Step 1: Impose 95%CI for mean=5• Step 2: Shift to the mean=6.5, get the beta.• Step 3: 1-beta = power

Example2

• A priori analysis: ANOVA: mean1=15, mean2=18, mean3=24;

sqrt(MSE) = 10, alpha = .05, power = 0.8 find N and f. (N = 72, f = .3742)• Post hoc analysis: ANOVA: mean1=15,

mean2=18, mean3=24; sqrt(MSE) = 13, alpha = .05, find power and f. (f = .2878, power = .5809)

Example3

• Random sampling: Given margin of error with 95% confidence,

find sample size: • For proportion, if there is no prior information

about p, set p = 0.5

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