Power

Question 1

define Power

Answer 1

the probability of correctly rejecting a false h0, probability that we do the right thing

1-B

Question 2

Draw the table for the Decision rule, but insert power

Answer 2

h0 true, retain h0 = correct retention (1-a)

h0 true, reject h0 = type 1

h0 false, retain h0 = type 2

h0 false, reject h0 = correct rejection (1-B)

Question 3

draw a normal distribution for when h0 is true, include where cases of decision rule table apply.

Answer 3

1-a takes up majority of

where Zc cut off is, from that point on is where a is

include where null hypothesis mean lies on x-axis

Question 4

draw a normal distribution for when h0 is false, include where cases of the decision rule table apply.

Answer 4

overlapping normal distributions, before Zc cut off is where B lies (type II error), after cut off is where 1-B

include where null and alternative hypothesis means are on x-axis

Question 5

Five Factors that affect Statistical Power (1-2/5)

Answer 5

1. size of a

• it moves the critical statistic, which makes the borders of the 1-B and B smaller or larger

2. Directionality of h1

• (1 tailed or 2 tailed)
• 2 tailed is only applicable in this course

Question 6

Five Factors that affect Power (3/5)

Answer 6

3. Size of Effect

y = u1-u0/ o

• also referred to as Cohen’s d

the bigger the effect, the easier it is to detect (i.e. more power)

• psych research is more variable than other sciences, we are looking for effects that are more nuanced

a bigger effect size means more of the alternative hypothesis is going to lie past the Zc
- higher chance of 1-B

Question 7

Five Factors that affect Power (4-5)

Answer 7

4. size of o
   - size of standard dev
5. size of n

both 4 and 5 effect the size of the standard error, as if we look back at the standard error formula it includes them both

large oM vs small oM = larger or flatter distribution

• as o increases, oM increases, and power decreases
• as n increases, oM decreases, and power increases

Question 8

Principles of calculating power

Answer 8

we cannot find the exact power because this requires knowing the effect size which depends on the true population lean (which we don’t know)

• we draw samples which makes estimates with uncertainty
• calculate power for a specific effect size nominated by experimenter (the minimum effect size that would be considered important)

Question 9

Cohen’s (1988) Rule of Thumb

Answer 9

when the researcher doesn’t know enough about their DV to identify an effect size, they may use this.

• small effect size - .2
• medium effect size - .5
• large effect size - .8

Cohen recommends power of .8 for nominated effect size, power beyond the critical boundary

• today researchers tend to go for .9

Question 10

Note on Power

Answer 10

Note: gamma (γ) expresses the distance between μ0 and μ1 in units of standard deviation. When dealing with sampling distributions, we want to work with the distance between μ0 and μ1 in units of standard error σM, which is known as delta