Post on 11-Jul-2020
transcript
Determination of Sample
Size
Dr.Deepak Langade
Objectives
List the factors influencing the sample size
Appreciate importance of incorrect sample
size in research
Calculate the sample size using
appropriate formulae
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
Correct () decisions and Types
of Errors (X) in hypothesis testing
X
X
Difference exists (H1) No Difference (H0)
Difference exists
(H1)
No Difference
Do not reject (H0)
TRUE Situation
CONCLUSION hypothesis test
(Power or 1-beta)
Type II error or
Beta error
Type I error or
Alpha error
Approach to sample sizeDetermine 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
Incorrect sample size
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
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
2
2
/2
2
difference
)Z(2
Zn
Formula for difference in
means
Sample size in each
group (assumes equal
sized groups)
Represents the desired
power (typically .84
for 80% power).
Represents the desired
level of statistical
significance (typically
1.96).
Standard deviation of
the outcome variable Effect Size (the
difference in
means)
Comparison of percentages
(two groups)
Alpha=0.05,
Beta=0.2, (power 80%)
n = 8 X p1q1 + p2q2
---------------
(p1-p2)2
2
21
2
/2
)(p
)Z)(1)((2
p
Zppn
Formula for difference in
proportions
Sample size in each
group (assumes equal
sized groups)
Represents the desired
power (typically .84
for 80% power).
Represents the
desired level of
statistical
significance
(typically 1.96).
A measure of
variability (similar to
standard deviation)
Effect Size (the
difference in
proportions)
Comparison of one mean only
Alpha=0.05,
Beta=0.2, (power 80%)
n = 8 X (S.D./M1-M0)2
Sample Size Example
Effect on sleep
Sleep Aid Example : 1 Sample
Study the effect of new sleep aid
1 sample test
Parameter – Sleep time after taking
the medication for one week
Two-sided test, α = 0.05, power =
90%
Difference = 1 (4 hours of sleep to 5)
Standard deviation = 2 hr
Sleep Aid Example
1 sample test
2-sided test, α = 0.05, 1-β = 90%
σ = 2hr (standard deviation)
δ = 1 hr (difference of interest)
2 2 2 21 / 2 1
2 2
( ) (1.960 1.282) 242.04 43
1
Z Zn
Effect of Difference
Change difference of interest from 1hr to 2 hr
n goes from 43 to 11
2 2
2
(1.960 1.282) 210.51 11
2n
Effect of Power
Change power from 90% to 80%
n goes from 11 to 8
(Small sample: start thinking about using the t distribution)
2 2
2
(1.960 0.841) 27.85 8
2n
Effect of S.D.
Change the standard deviation from 2
to 3
n goes from 8 to 18
2 2
2
(1.960 0.841) 317.65 18
2n
Sleep Aid Example: 2 Sample
2 2 2 21 / 2 1
2 2
2( ) 2(1.960 1.282) 284.1 85 170 total!
1
Z Zn
Original design (2-sided test, α = 0.05, 1-β = 90%, σ = 2hr, δ = 1 hr)
Two sample randomized parallel design
Needed 43 in the one-sample design
In 2-sample need twice that, in each group!
4 times as many people are needed in this design
Conclusion
2 2
1 / 2 1
2
4( )2
Z ZN
Changes in the detectable difference have HUGE impacts on sample size
20 point difference → 25 patients/group
10 point difference → 100 patients/group
5 point difference → 400 patients/group
Changes in α, β, σ, number of samples, if it is a 1- or 2-sided test can all have a large impact on your sample size calculation
Group Activity
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?
Task 1 - Answer
Aim – To see whether yoga is better than standard drug Rx in curing the pt.
Analysis type- comparison of proportion
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
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.
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 ?
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
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 ?
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, paired data
Parameters- fruit juice/day 5 vs 6 or 4
No. of groups-1
Given M1= 4 or 6, M0=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
Demonstration
Thank You !