Power

Question 1

Type 11 error has a probability of beta what is the probability of power?

Answer 1

1-beta

Question 2

What is a type 1 error?

Answer 2

Reject the null hypothesis when it is true ( p = Alpha - 0.05)

Question 3

When null hypothesis is false and you reject the null hypothesis…describe what this is

Answer 3

Correct decision

P = 1 - beta

= power

Question 4

What is a type 11 error?

Answer 4

When the null is false but you don’t reject it…

P = beta

Question 5

Explain in terms of the null hypothesis what situation this would occur

A correct decision is made
P= 1- alpha

Answer 5

Null is true and you don’t reject the null

Question 6

What is a type 1 errors?

Answer 6

False positives

Is the conventional probability value (alpha) used for significance testing ( p = .05)

Question 7

What are type 11 errors

Answer 7

Misses

Occurs with a probability of beta

Question 8

What factors affect statistical power?

Answer 8

The probability of a type 1 error (alpha)
The effect size assuming h1 (e.g. Mean difference)
Sample size
Type of statistical test used
One or two tailed test

Question 9

What is the z critical value for a 1 tailed test?

Answer 9

1.65

Question 10

What is the z critical for a 2 tailed test?

Answer 10

1.96

Question 11

What happens to power when the significance level (alpha) is decreased?

Answer 11

Power decreases

Question 12

What happens to power when the significance level increases & what is a product of this?

Answer 12

Increase in power but also an increase in the probability of a type 1 error

Question 13

If the effect size between 2 means is increased what happens to power?

Answer 13

Power increases

Question 14

Increasing sample size will do what to power? (Remember central limit theorem)

Answer 14

Increase sample size reduces the sampling distribution of the mean (standard deviation) (random variation is reduced) so effect size increases and therefore power increases.

Question 15

If you reduce the variance between two means what happens to power?

Answer 15

Decreasing variance increases the effect size so increases power

Question 16

Discuss how the assumptions of parametric tests can influence power.

Answer 16

Violation of assumptions underlying parametric tests will often seriously reduce your power

• non- parametric tests may be more powerful in that circumstance.

Question 17

Why should we worry about power?

Answer 17

We are often interested in knowing he sample size needed to achieve an adequate level of power before we begin a study.

This often has important implications for planning time, resources etc when designing a study

To examine whether a completed statistical test had a fair chance of rejecting an incorrect h0.

Question 18

What do we need to know to estimate power?

Answer 18

Effect size

Sample size

Significance level (alpha) and whether 1 or 2 tailed test used

Question 19

What is the formula for cohens d?

Answer 19

D = (m1-m2/ sd)

Question 20

Where can we find the effect size from?

Answer 20

Previous research (use sample means and SDs obtained from previous studies)

Researcher estimate of important effect: a researcher decides on the minimum important difference between 2 means… Still need to estimate sd)

Using conventional labels of effect size magnitude for d originally provided by cohen

Question 21

What are cohens d effect sizes for t-test?

Answer 21

.8 = large
.5 = medium
.2 = small

Question 22

What is delta?

Answer 22

A noncentrality parameter… For power you a have to assume that h1 is true (in contrast to everything else which is assuming h0 is true, which is centred around the null hypothesis) so power is not centred around the null so it’s noncentral

Question 23

How do you calculate delta?

Answer 23

Delta = d * square root of n/2

Question 24

How do you calculate sample size?

Answer 24

n = 2(delta/d) squared

Question 25

What is the minimum power required

Answer 25

80 % but often people use 90%

Question 26

Unequal sample size will result in what to power?

Answer 26

Less power

With unequal sample size, we use the smaller of the group n

Question 27

When can you use power tests?

Answer 27

A priori and post hoc (e.g. determining sample size required)

Remember when testing whether there is a fair chance to correctly reject the null hypothesis population effect size should be used not sample effect size.

Question 28

What is observed power?

Answer 28

Post hoc power analyses using the sample estimate of the effect size.

Question 29

What is statistical power?

Answer 29

It’s the probability of correctly detecting an effect when it really is there.

Question 30

When you draw one of those distribution diagrams to represent power, if you know the population standard deviation (standard error) then what distribution is it? If you estimate the standard deviation from your sample what distribution is it?

Answer 30

Normal distribution & z test

T distribution and a one sample t test

Question 31

When you convert z scores to percentage of the curve ‘cumulative’ from the left (minus infinity) (x%) what is the name of the function you use?

Answer 31

Cumulative distribution function (CDF) - z to the -1

Question 32

What function do you use to convert percentage (x%) to z-score in spss?

Answer 32

Inverse distribution function (IDF) - z

The IDF is also known as the probit function

Question 33

When you have a participant ratio of 2:1 and you are calculating sample size, does this difference make a big impact?

Answer 33

Not too bad actually, you need some more participants but as the ratio gets larger many more are required