Errors and power Flashcards
What is a type I error
the probability of rejecting H0 when H0 is true
What the a type II error
the probability of NOT rejecting H0 when H0 is false
Is type I or type II worse?
Type I is worse
What is the probaility of a type I error
alpha
what is the probability of a type II error
beta
relationship of alpha and beta
if alpha goes up, beta goes down and vice versa
what is power
the probability of correctly rejecting H0 when H0 is false
what does power tell us about the strength of a test
the higher the power the better the test
Relationship between power and beta
power = 1 - B, B + power = 1
Chains (2)
- alpha goes up, so beta goes down, so power goes up and vice versa
- n goes up, beta goes down, power goes up and vice versa
Xbar decision rule
whether or not to reject H0 based on Xbar, for example reject if Xbar > 25, fail to reject if xbar < or equal to 25
Xbar*
what our decision rule will be based on. Formula is Xbar* = z* (sigma/root n) + mu0. make z* negative for a lower tail test
alpha beta tables
- place the decision rule in the first row ( ex. reject if xbar > 15 for alpha, do not reject if Xbar < or equal to 15 for beta)
- null and alternative hypothesis ( u0 for alpha, uA for beta)
- draw a picture and shade appropriately (alpha centered at u0, beta at uA) (mark xbar and shade towards tail)
- find shaded area (shaded area is alpha or beta respectively)
- conclude type I (alpha), type II (beta), and power (1-beta)
power and number lines
when given 2 uA’s in a question, draw a number line based on u0. The further away uA is from u0 means higher power. For example, if u0 = 5, and the first uA = 7 we find a power. If we change uA to 10, we dont know what the power is anymore, but we know is higher than when uA= 7
