8 Decisions, Power, Effect Size, and the Hybrid Model

Question 1

What is a type 1 error ?

Answer 1

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

Question 2

What is a type 2 error?

Answer 2

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

Question 3

What is mcritical ?

Answer 3

mcritical is the value that our sample mean must exceed in order for us to reject the null hypothesis.

Question 4

What is the formula for mcritical ?

Answer 4

mcritical=u0+zcritical(om)

Question 5

What is the formula to find z critical, when we have the value of mcritical ?

Answer 5

zcritical=(mcritical-u0)/om

Question 6

The proportion referred as ‘‘a’’ is …

Answer 6

above mcritical, which is 0.5. It is the probability of a type 1 error

Question 7

Any sample mean that exceeds mcritical is said to fall into the…

Answer 7

rejection region

Question 8

Any sample mean less than mcritical would produce zobs…

Answer 8

less than zcritical

Question 9

We use the symbol β to denote the probability of a…

Answer 9

type 2 error

Question 10

What is power ?

Answer 10

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.

Question 11

What is the formula for power ?

Answer 11

1-B

Question 12

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

Answer 12

1) above

2) below

Question 13

To find power or β, we simply convert mcritical to a…

Answer 13

z-score !

Question 14

What are the three factors that affect power ?

Answer 14

a, effect size and sample size

Question 15

as α increases, mcritical …

Answer 15

decreases

Question 16

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?

Answer 16

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.

Question 17

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?

Answer 17

The closer the criterion is to µ0, the more powerful the test. Therefore, a criterion of 30 would make for a more powerful test.

Question 18

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 =

…

Answer 18

±1.96,

Question 19

What is the formula to compute the effect size (δ) ?

Answer 19

δ=(u1-u0)/o

Question 20

Cohen’s δ is essentially a …

Answer 20

z-score !

Question 21

The regions to the right of mcritical represent …, and the regions to the left of mcritical represent…

Answer 21

1) power

2) B

Question 22

increasing sample size increases…

Answer 22

power

Question 23

What is U3 ?

Answer 23

The proportion of one distribution of scores that falls below (or above) the mean of a second distribution.

Question 24

Within the hybrid model, the significance level is referred to as…

Answer 24

a

Question 25

For Neyman and Pearson, this means that with repeated sampling from the same two distributions, α is…

Answer 25

the proportion of times the null hypothesis will be rejected incorrectly.

Question 26

What is the difference between p and a

Answer 26

1: p is a property of the data, occuring by chance when the null hypothesis is true. Computed AFTER the data was collected. associated with zobs
2: a is a property of the test. it is a probability that during an infinite series of tests, the statistic will surpass the criterion, when the null hypothesis is true. Specified BEFORE the data collection. associated with zcritical.