Power

Question 1

Draw a sampling distribution with the representation of Power/type 1 error and type 2 error regions. And equations if you can…

Answer 1

thanks

Question 2

x

Answer 2

x

Question 3

draw a diagram to show the factors affecting power

Answer 3

thanks

Question 4

what are p-values in regard to type X errors?

Answer 4

P values are type 1 error rates
We are prepared to accept a certain level of type 1 error – the risk is sufficiently low at .05 to say we’ll tolerate it.

Question 5

Minimum power ?

Answer 5

.8 or 80%

Question 6

what is Power?

Answer 6

The probability of correctly rejecting a false null hypothesis

Ð 1-B, where B is the probability of making a type 2 error.

Question 7

factors affecting power?

Answer 7

Ð Decreasing alpha level will decrease power
Ð Increasing alpha level will increase power, but increase type 1 error rates.
Ð Sample size
Ð Type of statistical test used
Ð Violation of assumptions of parametric tests will decrease power as alpha level is inaccurate (& p values cannot be guaranteed).
Ð Within design
Ð Effect size assuming H1 (mean difference between the groups)
Ð Using a 1 or 2 tailed test – where 1 increases power

Question 8

what is type 1 error?

Answer 8

Ð Falsely reject the null hypothesis / false positives

Ð (a: alpha) used for significance testing (i.e. p=.05 etc)

Question 9

what is type 2 error?

Answer 9

Ð Misses

Ð Occur with probability of B (beta)

Question 10

Power on a distribution?

Answer 10

Ð Power is the probability of correctly rejecting the null hypothesis (true + or, a hit)
The equation is (1-Beta) – it is the area outside the zone on the opposite side of the rejection level. Can increase in size with effect and N.

Question 11

Type 2 on a distribution?

Answer 11

Ð Type 2 error (missing effect that’s there) would be represented by the size of the triangle on the opposite side to Power.

Question 12

Type 1 on a distribution?

Answer 12

Ð Type-1 error is the opposite size triangle to this (same direction as power but not whole are under sampling distribution, just that triangle)

Question 13

what is the relationship between sample size and standard error?

Answer 13

Ð As sample size increases the standard error decreases - SE / sq rt of sample size
Ð it reduces the amount of variation you would get as more and more people = more precise
Ð related to central limit theorem
Ð Standard error is smaller (effectively making the difference larger)

Question 14

Sample size – Power – Effect size relation?

Answer 14

One can estimate one from two of the others (think Gpower) – NON-LINEAR CURVE

Ð As the effect size gets bigger we need fewer participants
Ð As sample size gets bigger so does power.

Question 15

3 things to calculate Power?

Answer 15

Ð You need a measure or estimate

1) effect size (guess intelligently)
2) sample size
3) Significance level - alpha (?) at 1 or 2 tails

Question 16

what is standard measure of effect size?

Answer 16

cohen’s d

Question 17

how to calculate cohens d?

Answer 17

d=(μ1 –μ2)/σ // Ð Has to be done before the experiment

Question 18

which ways are there to quantify d?

Answer 18

Ð Meta-analyses of the literature (average effect sizes across lots of experiments)
Ð Look at similar specific experiments and take the effect size
Ð Will vary as a function of statistical test used.

Question 19

Cohen’s Conventional Labels for EFFECT sizes ?

Answer 19

Not as good but: use Cohen’s Conventional Labels for EFFECT sizes (small .2 / med .5 / large .8)

Question 20

To calculate power we must first…

Answer 20

Ð Use d and sample size to calculate delta (: a non-centrality parameter)

Ð Key Note: The central distributions we use to test the null (as centered around the null, usually a value of 0, so non-central are ones shifted a certain amount (like effect size). So, if you can estimate , you can calculate power.

Question 21

second, to calculate power, we must…

Answer 21

delta =d*n [each group p number, better with equal]/2

Ð Then decide and use statistical table

Question 22

When we get a number for power we can say…

Answer 22

Ð IF power = .56 then we can say the researcher has 56% of correctly rejecting H0, if it is false to the extent expected.

Question 23

how do we calculate a priori sample size?

Answer 23

Ð This formula for delta can be rearranged to solve for n (the sample size needed to get certain power)
Ð To calculate sample size – n=2(delta/d)2
Ð In independent-groups design this refers to the sample size per group
Ð For unequal sample sizes, we use the smaller of the group n, or harmonic mean.
Ð Unequal sample sizes will result in less power

Question 24

why a priori not post hoc?

Answer 24

Power calculations for sample size and power needs to be done a priori – using observed power is biased as it uses the sample effect size, not the population effect size.

Question 25

how do you get a z score?

Answer 25

z = (x – μ) / σ