W7: Power Calculations

Question 1

An important part of any experiment is to

Answer 1

choose an appropriate sample size to answer the RQ

Question 2

Experiments should include a sufficient number of participants to

Answer 2

address the RQ

Question 3

Experiments that have an inadequate number or excessively large number of participants are both wasteful in terms of - (3)

Answer 3

• participant and investigator time
• resources to conduct the assessment
• analytical efforts

Question 4

To choose a sample size, we use the idea of a

Answer 4

statistical power of a hypothesis test

Question 5

Statistical power of a hypothesis test is the probabilibty of

Answer 5

rejecting H0 given it is false

Question 6

What are the 2 errors we can make in a hypothesis test?

Answer 6

Type I and Type II

Question 7

What is a type I error? (False positive)

Answer 7

Rejecting H0 when it is true

Question 8

Example of type I error

Answer 8

the test result says you have coronavirus, but you actually don’t

Question 9

What is a type II error? (false negative)

Answer 9

Retaining H0 when it is false

Question 10

Example of a type II error (false negative)

Answer 10

the test result says you don’t have coronavirus, but you actually do

Question 11

The probabilibity of a Type II error is

Answer 11

β

Question 12

Power is

Answer 12

1 - β

Question 13

Power calculations chooses a sample size that ensures H0 has the highest power that is

Answer 13

highest probabilibty of rejecting H0 if it is false

Question 14

A power calculation we need to choose in advance (3)

Answer 14

what test we will use to answer RQ (e.g., ANOVA)
Choose the signifiance level (alpha) we will conduct hypothesis test - typically 5%
Choose smallest sample size that gives a particular value of power (commonly used values are 80% and 90%)

Question 15

One-sample t -test hypothesis for power

Answer 15

Question 16

One-sample t-test is when we are interested in

Answer 16

a continous variable in a single population

Question 17

Step 1 of Power Calculations is to calculate effect size

Effect size formula

Answer 17

Question 18

Step 1 of Power Calculations

Effect size formula components understood - (4)

Answer 18

σ’ = population SD
u0 = value under H0 - data
u1 = value that would be important clinically
E = effect size

Question 19

Step 1 of Power Calculations

Pick out values of u0, u1, E and σ’ from this question:

One-sample (3)

Answer 19

u1 = 100
u0 = 95
σ’ = 9.8

Question 20

Step 1 of Power Calculations

Pick out values of u2, u1, E and σ’ from this question

Two sample question - (2)

Answer 20

u2 - u1 = 14
σ’ = 20

Question 21

Step 1 of Power Calculations

Pick out values of u2, u1, E and σ’ from this question

Two sample question - (2)

Answer 21

u2 = 880
u1 = 900
σ’ = 50

Question 22

Step 2 of after calculating effect size is saying

for example if U1 and U0 was 100 and 95 and Effect size was 0.51 (2)

Answer 22

The effect size is the smallest meaningful difference in the mean

Here 95 vs 100, or 0.51 standard deviation units difference

Question 23

Step 3 after calculating effect size is calculating sample size

One-sample formula:

Answer 23

Question 24

Step 3 after calculating effect size is calculating sample size

Two sample formula

Answer 24

Question 25

Step 3 of calculating sample size (n)

z1-beta you would get from

Answer 25

question says they want 80% power so you would get z0.80

Question 26

Step 3 of calculating sample size (n)

getting z values

Answer 26

z1-alpha/2
calculate it then convert using table

Question 27

In two-sample t-test the assumptions are (2)

Answer 27

• continous outcome variable
• population SD is assumed to be common in both groups

Question 28

How can population SD be estimated in two-sample t test?

Answer 28

Using pooled SD

Question 29

In two-sample t-test, hypothesis of comparing a mean of continous outcome variale in 2 independent populations:

Answer 29

Question 30

When question says 95% confidence level its alpha is

Answer 30

5%

Question 31

Adjusting for drop out
Formula

Answer 31

Question 32

Suppose 10% of participants will drop out of sepsis experiment

We calculated in experiment n = 43

Two sample (4)

Answer 32

10% drop out means % retained is 90% and so

Number to recruit = 43/0.90

= 47.8 participants

So we need 48 participants per group

Question 33

When calculating sample size always round up

example

42.8
30.1

Answer 33

Therefore sample size of
43 people
31 people
will suffice

Question 34

At end of two sample independent t-test when calculating sample size you say

for example n = 43

Answer 34

So we need n = 43 people in each group, making 86 in total

Question 35

How could we reduce the required sample size for the experiment? (2)

Answer 35

Use paired instead of independent t-test
Reduce statistical power

Question 36

Paired Samples hypothesis

Answer 36

H0: ud = 0
H1: ud not equal to 0

Question 37

Paired-Samples formula for N

Answer 37

Question 38

Paired samples effect size

Answer 38