W7: Power Calculations Flashcards
An important part of any experiment is to
choose an appropriate sample size to answer the RQ
Experiments should include a sufficient number of participants to
address the RQ
Experiments that have an inadequate number or excessively large number of participants are both wasteful in terms of - (3)
- participant and investigator time
- resources to conduct the assessment
- analytical efforts
To choose a sample size, we use the idea of a
statistical power of a hypothesis test
Statistical power of a hypothesis test is the probabilibty of
rejecting H0 given it is false
What are the 2 errors we can make in a hypothesis test?
Type I and Type II
What is a type I error? (False positive)
Rejecting H0 when it is true
Example of type I error
the test result says you have coronavirus, but you actually don’t
What is a type II error? (false negative)
Retaining H0 when it is false
Example of a type II error (false negative)
the test result says you don’t have coronavirus, but you actually do
The probabilibity of a Type II error is
β
Power is
1 - β
Power calculations chooses a sample size that ensures H0 has the highest power that is
highest probabilibty of rejecting H0 if it is false
A power calculation we need to choose in advance (3)
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%)
One-sample t -test hypothesis for power
One-sample t-test is when we are interested in
a continous variable in a single population
Step 1 of Power Calculations is to calculate effect size
Effect size formula
Step 1 of Power Calculations
Effect size formula components understood - (4)
σ’ = population SD
u0 = value under H0 - data
u1 = value that would be important clinically
E = effect size
Step 1 of Power Calculations
Pick out values of u0, u1, E and σ’ from this question:
One-sample (3)
u1 = 100
u0 = 95
σ’ = 9.8
Step 1 of Power Calculations
Pick out values of u2, u1, E and σ’ from this question
Two sample question - (2)
u2 - u1 = 14
σ’ = 20
Step 1 of Power Calculations
Pick out values of u2, u1, E and σ’ from this question
Two sample question - (2)
u2 = 880
u1 = 900
σ’ = 50
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)
The effect size is the smallest meaningful difference in the mean
Here 95 vs 100, or 0.51 standard deviation units difference
Step 3 after calculating effect size is calculating sample size
One-sample formula:
Step 3 after calculating effect size is calculating sample size
Two sample formula
Step 3 of calculating sample size (n)
z1-beta you would get from
question says they want 80% power so you would get z0.80
Step 3 of calculating sample size (n)
getting z values
z1-alpha/2
calculate it then convert using table
In two-sample t-test the assumptions are (2)
- continous outcome variable
- population SD is assumed to be common in both groups
How can population SD be estimated in two-sample t test?
Using pooled SD
In two-sample t-test, hypothesis of comparing a mean of continous outcome variale in 2 independent populations:
When question says 95% confidence level its alpha is
5%
Adjusting for drop out
Formula
Suppose 10% of participants will drop out of sepsis experiment
We calculated in experiment n = 43
Two sample (4)
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
When calculating sample size always round up
example
42.8
30.1
Therefore sample size of
43 people
31 people
will suffice
At end of two sample independent t-test when calculating sample size you say
for example n = 43
So we need n = 43 people in each group, making 86 in total
How could we reduce the required sample size for the experiment? (2)
Use paired instead of independent t-test
Reduce statistical power
Paired Samples hypothesis
H0: ud = 0
H1: ud not equal to 0
Paired-Samples formula for N
Paired samples effect size
