8 Decisions, Power, Effect Size, and the Hybrid Model Flashcards
What is a type 1 error ?
It occurs if the null hypothesis is rejected when it is true. This means that a sample was drawn from the distribution of scores specified by the null hypothesis, yet the statistic was statistically significant.
u0 REJECTED BUT TRUE
What is a type 2 error?
It occurs if the null hypothesis is retained when it is false. This means that a sample was not drawn from the distribution of scores specified by the null hypothesis, yet the null hypothesis was retained.
u0 RETAINED BUT FALSE
What is mcritical ?
mcritical is the value that our sample mean must exceed in order for us to reject the null hypothesis.
What is the formula for mcritical ?
mcritical=u0+zcritical(om)
What is the formula to find z critical, when we have the value of mcritical ?
zcritical=(mcritical-u0)/om
The proportion referred as ‘‘a’’ is …
above mcritical, which is 0.5. It is the probability of a type 1 error
Any sample mean that exceeds mcritical is said to fall into the…
rejection region
Any sample mean less than mcritical would produce zobs…
less than zcritical
We use the symbol β to denote the probability of a…
type 2 error
What is power ?
the proportion of the alternative hypothesis distribution above mcritical
the probability of rejecting the null hypothesis when it is false. Power is probability of correctly rejecting the null hypothesis.
What is the formula for power ?
1-B
1) power is the proportion of the distribution of means under H1… mcritical
2) and B is the proportion of the distribution of means under H1…mcritical
1) above
2) below
To find power or β, we simply convert mcritical to a…
z-score !
What are the three factors that affect power ?
a, effect size and sample size
as α increases, mcritical …
decreases
An acceptance procedure has been established in which µ0 = 20, µ1 = 30, and criterion = 22. If µ1 is the mean of the distribution associated with a manufacturing error, which error, Type I or Type II, is considered more costly in this procedure?
In this case, β < α because the criterion is closer to µ0 than µ1, so the probability of a Type II error is lower than the probability of a Type I error. Therefore, Type II errors are considered more serious, and efforts are made to avoid them.
An acceptance procedure has been established in which µ0 = 20 and µ1 = 60. If µ1 is the mean of the distribution associated with a manufacturing error, which criterion, 30 or 40, would make for a more powerful test?
The closer the criterion is to µ0, the more powerful the test. Therefore, a criterion of 30 would make for a more powerful test.
When we conduct a one-tailed test that predicts µ1 > µ0 and α = .05, zcritical = 1.645. For a two-tailed test with α = .05, zcritical =
…
±1.96,
What is the formula to compute the effect size (δ) ?
δ=(u1-u0)/o
Cohen’s δ is essentially a …
z-score !
The regions to the right of mcritical represent …, and the regions to the left of mcritical represent…
1) power
2) B
increasing sample size increases…
power
What is U3 ?
The proportion of one distribution of scores that falls below (or above) the mean of a second distribution.
Within the hybrid model, the significance level is referred to as…
a
