Statistical Power.

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Presentation transcript:

Statistical Power

Statistical Power Definition: The probability that will reject a false null hypothesis

Decision process Population Decision H0 is true H0 is false Keep H0 Correct (1-a) Type II error (b) Reject H0 Type I error (a) (1-b) Power

Statistical inference m = 72 (1-b) b m = 69

Statistical inference m = 72 m = 70 b (1-b)

Statistical inference m = 72 m = 64 b (1-b)

Effect size (One group) Definition : It is the difference between the null hypothesis and the alternative hypothesis DI = 0.2 (small effect) DI = 0.5 (medium effect) DI = 0.8 (large effect) It gives us an idea of the magnitude of the difference that we want to detect. (Treatment effect)

Effect size (Two groups)

Effect size and power Example: To know the power we need to use a software like G*power.

Effect size and power

Factors influencing the power Signification level The magnitude of the treatment effect The variability within the population Sample size

Factors influencing the power Signification level The magnitude of the treatment effect The variability within the population Sample size The more a increases the more the power increases.

Factors influencing the power Signification level The magnitude of the treatment effect The variability within the population Sample size The higher the effect of treatment is the higher the power will be

Factors influencing the power Signification level The magnitude of the treatment effect The variability within the population Sample size The less variability in the population the higher the power will be

Factors influencing the power Signification level The magnitude of the treatment effect The variability within the population Sample size If n increases the power will increases.

Sample size estimation Type I and II errors Effect size