Topic 6: Power

Question 1

What is a Type 1 error?

Answer 1

Rejecting the null hypothesis when it is true

Question 2

What is a Type 2 error?

Answer 2

Retaining the null hypothesis when it is false

Question 3

What is power conceptually?

Answer 3

The sensitivity of an experiment to detect a real effect of the independent variable on participants’ behaviour

Question 4

What is power statistically?

Answer 4

The probability of finding a significant difference - if the effect that you are looking for is real

Question 5

What is 1 - beta?

Answer 5

Probability of correctly rejecting a false null hypothesis

Question 6

What is 1 - alpha?

Answer 6

Probability of retaining the null hypothesis when it is true

Question 7

What defines the region of beta?

Answer 7

Beginning of alternative hypothesis near the null that overlaps with alpha

Question 8

What is beta?

Answer 8

A Type 2 error (falsely retaining the null)

Question 9

What is alpha?

Answer 9

A Type 1 error (falsely retaining the null)

Question 10

What happens if alpha shrinks - in regards to beta and to power?

Answer 10

Beta grows, therefore shrinking power

Question 11

What happens if alpha grows - in regards to beta and to power?

Answer 11

Beta shrinks, and power grows

Question 12

What are the four circumstances where you would test for power?

Answer 12

A priori: to find the desired sample size
A posteriori: if you retained the null but expected to reject it
If you retained the null and wanted to
If you rejected the null as expected

Question 13

What factors influence power?

Three major, 3 minor

Answer 13

Effect size, meaning:
- treatment effect (mean diff)
- variability
N, or n

Alpha level, directional vs non-directional, research design

Question 14

What is the problem with increasing sample size a posteriori?

Answer 14

It increases your chance of a Type 1 error (falsely rejecting the null)

Question 15

How is power computed?

Answer 15

Find d, then delta, then the table

Question 16

How is effect size calculated with an independent-samples design?

Answer 16

Cohen’s d, wherein the numerator is the difference between the two means, and the denominator is the pooled SD error (Sp)

Question 17

How is the sample size needed found from power and effect size?

Answer 17

Make sure you have d, and then use the table to find delta from the power and the alpha
Then solve for N

Question 18

What values of power are acceptable in behavioural sciences?

Answer 18

Excellent: 0.90
Acceptable: 0.50 - 0.70

Question 19

What is the relationship between effect size and power, in relation to variance and treatment effect?

Answer 19

A larger treatment effect (mean difference) results in a larger power
As variability grows larger, power grows smaller

Question 20

Why is related samples design more powerful than independent samples?

Answer 20

It reduces the variability caused by the bigger N in independent samples

Question 21

Why is related samples design more powerful than independent samples?

Answer 21

It reduces the variability caused by the bigger N in independent samples

Question 22

How does sample size influence power?

Answer 22

The larger the N = the smaller the variance = the larger the effect

Question 23

How does directionality of a hypothesis influence power?

Answer 23

One-tailed test: higher power, as long as the hypothesized direction is correct

Question 24

How is d found in a single samples design?

Answer 24

mean of the group - mean-null / SD

Question 25

How is delta found from d with an empirical population?

Answer 25

d times the square root of N

Question 26

How is d found in a related samples design?

Answer 26

mean difference - mean-null / SD of the sample of mean difference scores

Question 27

When is n divided in half to find delta?

Answer 27

For an independent samples design

Question 28

How is d found in an independent samples design?

Answer 28

mean-1 - mean-2 / pooled standard deviation

Question 29

What do you do if the ‘n’s of an independent samples design are unequal?

Answer 29

Either:
use the smaller n if the difference is small and the pop is large
Or - calculate the harmonic mean