PS296 Chapter Notes - Chapter 15: Type I And Type Ii Errors, Noncentrality Parameter, Null Hypothesis
Power Calculations for the One Sample t Test:
δ = dhat √n
-in this situation, δ is called the noncentrality parameter (degree to which the mean of the sampling
distribution under the alternative hypothesis departs from the mean of the sampling distribution
under the null hypothesis)
-experimenter can increase power by increasing n, but how large an n is needed? The answer
depends on the level of power that is acceptable
-read table e.5 backward to find what the value for δ is associated with the specified degree of
power
-ex for a power equal to .80, δ must equal 2.80
-thus we have δ and can solve for n using:
n = (δ / dhat)²
-with a power of .80, we still run a 20% chance of making a type II error
Power Calculations for Differences Between Two Independent Means:
-we want the difference between the two population means (mu1 – mu0) under H1 minus the
difference (mu1 – mu) under H0, divided by σ (σ²1 = σ²2 = σ²)
-however mu1-mu2 under H0 is 0, thus we can drop this term from our formula
d = mu1 – mu2 / σ
Document Summary
Power calculations for the one sample t test: In this situation, is called the noncentrality parameter (degree to which the mean of the sampling distribution under the alternative hypothesis departs from the mean of the sampling distribution under the null hypothesis) The answer depends on the level of power that is acceptable. Read table e. 5 backward to find what the value for is associated with the specified degree of power. Ex for a power equal to . 80, must equal 2. 80. Thus we have and can solve for n using: n = ( / dhat) . With a power of . 80, we still run a 20% chance of making a type ii error. Power calculations for differences between two independent means: We want the difference between the two population means (mu1 mu0) under h1 minus the difference (mu1 mu) under h0, divided by ( 1 = 2 = )
