1. Determination of Sample Size
DR R.P. NERURKAR
Associate Professor
Dept. of Pharmacology
Good afternoon everybody, the topic given to me in this post-prandial session is statistical pitfalls and the time given for me to put you in to deep sleep is only 30 minutes and I hope that at least some of you are awake to listen to me at the end of my talk which will be followed by discussion and demo of user friendly statistical software. (next slide)
T.N. MEDICAL COLLEGE
B.Y.L NAIR HOSPITAL, MUMBAI
AYUSH Workshop
18th April 2006

2. Objectives At the end of this session participants should be able to
list the factors influencing the sample size
appreciate importance of incorrect sample size in research
calculate the sample size using appropriate formulae

3. Factors affecting sample size
Size of population
Resources – subjects, financial, manpower
Method of Sampling- random, stratified
Degree of difference to be detected
Variability (S.D.) – pilot study, historical
Degree of Accuracy (or errors)
- Type I error (alpha) p<0.05
- Type II error (beta) less than 0.2 (20%)
- Power of the test : more than 0.8 (80%)
Statistical Formulae
Dropout rate, non-compliance to Rx
What should be the sample size? Well, it depends upon many factors such as size of the population to whom the finding of study will be applied, Resources available such subjects under study (e.g. a rare disease such as pheochomocytoma) financial, manpower. In case of animal studies restrictions imposed by CPCSEA.
Degree of accuracy (or error)- Generally type I or alpha error should be less than 0.05 or 5%. Type II or beta error should be less than 0.2 or 20% and the power of the test should be more than 0.8 or 80%.
Next is variablity within or between the samples (Standard deviation- this can be obtained from pilot study or previous reported studies (historical). Degree of difference to be detected which may be clinically significant. Method of sampling whether randomised or stratified and well selected. And last is the statistical formulae. You have to decide only after taking into consideration all these points. (Next Slide)

4. Correct () decisions and Types of Errors (X) in hypothesis testing
TRUE Situation
Difference exists (H1)
No Difference (H0)
CONCLUSION hypothesis test  X
Type I error or
Alpha error
Difference exists (H1)
(Power or 1-beta)
No Difference
Do not reject (H0)
Type II error or
Beta error

5. Approach to sample size determination
Determine the expected difference
Find out the Standard deviations of both groups
Set alpha error to be tolerated viz. P = 0.05
Decide the power of the study desired viz. 80%, beta error 0.2
Select the appropriate formula
Calculate the sample size using the formula
Give allowance for drop-out rate
Give allowance for non-compliance of treatment if possible

6. Incorrect sample size will lead to
Wrong conclusions
Poor quality research (Errors)
Type II error can be minimized by increasing the sample size
Waste of resources
Loss of money
Ethical problems
Delay in completion

7. Formulae for Sample Size Comparison of means (two groups) (alpha=0
Formulae for Sample Size Comparison of means (two groups) (alpha=0.05, Beta=0.2, power 80%)
Between group comparison (Unpaired)
n = 16 X (S.D./M1-M2)2
Within group comparison (Paired)
n = 8 X (S.D.of differences/M1-M2)2

8. Formulae for Sample Size Comparison of percentages (two groups) (alpha=0.05, Beta=0.2, power 80%)
n = 8 X p1q1 + p2q2
(p1-p2)2

9. Formulae for Sample Size Comparison of mean of one group only (alpha=0
Formulae for Sample Size Comparison of mean of one group only (alpha=0.05, Beta=0.2, power 80%)
n = 8 X (S.D./M1-M0)2

10. THANK YOU Are you ready for group tasks?

11. Group Task 1 - Question
The cure rate of disease is 20% with a known drug treatment. It is claimed that yoga is better than the drug and a trial is to be conducted find out the truth. It is decided that a even 10% increase in cure rate would be clinically important. The alpha and beta were set at 0.05 and 0.2. The results will be analysed using Chi Square test. How many patients would be required for the trial?

12. Analysis type- comparison of percentage cure rate
GROUP TASK 1 – Answer
Aim – To see whether yoga is better than standard drug Rx in curing the pt.
Analysis type- comparison of percentage cure rate
Parameters- cure rate 20% vs 30%
No. of groups – 2
p1=20 q1=80, p2=30 q2=70
Set alpha=0.05, beta=0.2, Power=0.8
Statistical formula to be used
n = p1q1 + p2q2 X 8
(p1-p2)2
Ans. 296

13. Group Task No. 2 - Question
The mean(+SD) hospital stay of patients after a conventional surgical procedure (CP) is 12.3(+4.8) days. A modified procedure(MP) is to be tried to reduce the hospital stay. Two groups of patients will be undergoing either CP or MP. Their hospital stay will be compared using unpaired t test at p<0.05 with power of 80%. The minimum clinically important difference in the duration of hospital stay is expected to be 3. Calculate the sample size for each group ?

14. Analysis type- comparison of mean, unpaired data
GROUP TASK 2 - Answer
Aim – To see whether modified procedure reduces the hospital stay as compared to conventional proc
Analysis type- comparison of mean, unpaired data
Parameters- duration of hospital stay 12.3 vs 9.3
No. of groups-2
Given M1=12.3, M2=9.3, SD= 4.8
Set alpha=0.05, beta=0.2, Power=0.8
Statistical formula to be used
n = 16 X (S.D./M1-M2)2
Ans 40.96

15. Group Task 3 - Question
The mean fruit juice consumption in the population is 5 oz./day. Dennison and colleagues wanted to know whether mean juice consumption in 2 year old children is different from 5 oz./day – either more or less by1 oz/day. SD is 3 oz/day.
Calculate the sample size required ?

16. Analysis type- comparison of mean, unpaired data
GROUP TASK 3 - Answer
Aim – To see whether fruit juice consumption differs by 1 from the population (Normal standard) mean of 5oz./day
Analysis type- comparison of mean, unpaired data
Parameters- fruit juice/day 5 vs 6 or 4
No. of groups-1
Given M1= 4 or 6, Mo=5, SD= 3
Set alpha=0.05, beta=0.2, Power=0.8
Statistical formula to be used
n = 8 X (S.D./M1-M0)2
Ans 72