PS296 Chapter Notes - Chapter 15: Standard Deviation, Type I And Type Ii Errors, Null Hypothesis
CHAPTER 15: POWER
-power is the probably of finding a significant difference if the effect that you are looking for is
real
-most applied statistical work is concerned primarily with minimizing the probably of a type I
error (alpha)/rejecting a true null hypothesis (finding a difference that is not there)
-type II/beta errors concern the problem of not finding a difference that is there (falsely
rejecting H1)
-power is defined as the probability of correctly rejecting a false H0
-power equals 1 – β
-if we say the power of a design is .65, we mean if the null hypothesis is false to the degree we
expect, the probability is .65 that the results of the experiment will lead us to reject H0
Factors affecting the power of a test:
1) alpha: the probability of a type I error
-if we increase alpha, our cutoff point moves to the left thus simultaneously decreasing
Beta and increasing power, although with a corresponding rise in the probability of a
type I error
-critical region is larger = more power
2) the true alternative hypothesis (H1)
-the chances of finding a difference depend on how large the difference actually is
3) the sample size
-as variance decreases, or n increases the overlap between the two distributions (mu0
Document Summary
Power is the probably of finding a significant difference if the effect that you are looking for is real. Most applied statistical work is concerned primarily with minimizing the probably of a type i error (alpha)/rejecting a true null hypothesis (finding a difference that is not there) Type ii/beta errors concern the problem of not finding a difference that is there (falsely rejecting h1) Power is defined as the probability of correctly rejecting a false h0. If we say the power of a design is . 65, we mean if the null hypothesis is false to the degree we expect, the probability is . 65 that the results of the experiment will lead us to reject h0. Factors affecting the power of a test: alpha: the probability of a type i error. If we increase alpha, our cutoff point moves to the left thus simultaneously decreasing.
