making errors
1. when we perform a hypothesis test, we can make mistakes in two ways:
a. type 1 error
b. type II error
2. When Ho is false and we reject it, we have done the right thing.
- a test's ability to detect a false hypothesis is called the power of a test (wan
type I error
null hypothesis is true, but we mistakingly reject it
-false positive
-kid really is an A student (Ho) but you rejected it
-probability of our ? level (if operating at a 5% significance level, then you have a 5% chance of making a mistake (because for any
type II error
null hypothesis is false, but we fail to reject it
-false negative
-kid is not really an A student, but you failed to recognize it and reject that he was an A student
-we assign the letter ? to the probability of this mistake
Ho: patient doesn't have COVI
How often will a type I error occur?
Since a type I error is rejecting a true null hypothesis, the probability of a type I error is our ? level
-to decrease chances of committing a type I error, then decrease significance level by demanding stronger evidence (ex: by setting significance leve
People with type 2 diabetes are known to have about a 20.2% chance of suffering a heart attack within a seven-year period. According to a study of 4485 diabetes patients on Avandia, the risk found in the NEJM study was equivalent to a 28.9% chance of hear
Ho: P= 0.202 (safe)
Ha: P> 0.202 (unsafe)
Type I error: We believe it was unsafe when it really was safe (reject Ho and thought Ha was true when it wasn't)
Type II error: we failed to recognize it was unsafe when it really was unsafe (failure to reject Ho
A clean air standard requires that vehicle exhaust emissions not exceed specified limits for various pollutants. Many states require that cars be test annually to be sure they meet these standards. Suppose state regulators double-check a random sample of
Ho: meets standards
Ha: doesn't meet standards (license gets revoked)
a) we believed that standards were not met when it really was -> revoked their license when we shouldn't have
b) we failed to see that their standards were not met (so didn't revoke the
how to calculate chance of committing type II error (beta)
-harder to calculate because Ho was false and we failed to see it
example: reading program. if more than 80% students improve their reading scores then the school will implement the reading program. n=50
Ho: Reading program had no affect (p=0.8)
Ha: readi
power
1-?
-your ability to see Ho is false when it really is false -> correctly rejected the null hypothesis
-opposite of type II error (fail to reject Ho), so power and type II error are complimentary of each other
-we want a significance test that has a high
effect size
difference between truth and the lie
-bigger effect size -> bigger power
-smaller effect size -> smaller power
-lie is not that big, so you have a pretty good chance of getting away with that lie which is why ? (chance of missing that lie and making a mis
ways to increase power
1) increase ? (demand weaker evidence) -> decrease ? -> increase power
-when go from 5% significance to 10% significance then moving the rejection line and you double your power because if you don't demand such strong evidence then it is easier for you to
A lobbying group has been advocating a particular ballot proposal. One week before the election, they are considering moving some of their advertising efforts to other issues. If it the proposal has a support level of at least 55%, they will feel it's "sa
Ho: p=0.55 (not safe)
Ha: p > 0.55 (safe)
(a) Type I: we think it's safe to move $$ when it really wasn't
Type II: we failed to see it was safe to move $$
(b) 0.05
(c) Make two bell curves
-effect size: difference between truth and lie is 5% (0.6-0.55)
(1
A lobbying group has been advocating a particular ballot proposal. One week before the election, they are considering moving some of their advertising efforts to other issues. If it the proposal has a support level of not equal to 55%, they will feel it's
Ho: p=0.55
Ha: p does not equal 0.55
1) now, you're going to have two rejection lines
2) make two bell curves
(a) bell curve if Ho is true
-centered at 0.55 with spread of 0.0552
-now have two rejection lines so that pushes the rejection lines further out