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Sample size
Power
Random allocation
R.Raveendran
Why is sample size important?
Validity
Accuracy
Finance
Resources
Ethics
What factors will affect the
size of the sample?
Degree of difference
Type I error
Type II error
Variation of data
Drop out
Non-compliance
What methods can be used to
determine the sample size?
×
From previous studies ?
Nomograms & tables !
Arbitrary numbers
Formulas
Computer programs
How to calculate the sample size?
 Assess
the difference expected (0.5 kg)
 Find out the SD of groups (0.4)
 Set the level of significance (alpha - 0.05)
 Set the beta level (0.02)
 Select the appropriate formula (unpaired t)
 Calculate the sample size
u-v (diff/sd)/
 Give allowances for drop-outs & noncompliance
Power
Probability that a study can detect a difference
Priori power determination :
Power = 1 – beta
Beta or type 2 error is the chances of missing a
difference (false negative rate)
Posteriori power calculation :
Why?
How?
What is the implication?
Random Allocation
Each unit in a sample has equal
chance to be assigned a treatment
Treatment 1 Treatment 2
Simple
Block
Stratified
Cluster
3
4
5
7
8
1
2
6
9
10
Thank you
Degree of difference
The minimum difference that is clinically or practically
important
e.g. A drug reduces BP by 2 mm of Hg (120 to 118).
Is it clinically important?
What about 4 mm of Hg?
What about 6?
20?
10?
30?
40?
Implication – Large difference needs small sample size
Small difference needs large sample size
Type I and II errors
Question : Is the rice cooked?
Possible Results :
+ (Yes)
True
False
- (No)
True
False
Type I and II errors
Groups : Group A Vs B
Question : Is there a difference between
groups?
Possible Results :
+ (Yes)
- (No)
True
False
True
False
Type I error = False +
Type II error = False -
P Limit - 5%
P Limit - 20%
Power Calculation
Why?
To find out whether a negative result is TRUE or FALSE
How?
Using the formula or computer programs
What information is needed?
 The difference (0.5)
 Alpha (0.05)
 Sample size and SD both groups (5, 5 & 0.29, 0.33)
 Statistical test used (Unpaired t)
Implication? No power; redo the experiment / no diff.