Microsoft Word research method fm doc

n = Z
2
 
σ
2
 / w
2
 
 
Example
: A health officer wishes to estimate the mean serum cholesterol in a population of 
men. From previous similar studies a standard deviation of 40 mg/100ml was reported. If he is 
willing to tolerate a marginal error of up to 5 mg/100ml in his estimate, how many subjects 
should be included in his study?
(
α =5%, two sided)
a) If the population size is assumed to be very large, the required sample size would be: 
n = (1.96)
2 
(40)
2
/ (5)
2
= 245.86 
≈ 246 persons 
- If the population size is, say, 2000, the required sample size would be 220 persons. 
b) If the investigator anticipates that 15% of the subjects will fail to comply with the intended 
study, the sample size required will be: 
n = (1/(1-0.15)) x 246 = 290 men 

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Research methodology 
50
NB:
σ
2
can be estimated from previous similar studies or could be obtained by conducting a 
small pilot study. 
Comparison of two proportions 
 
 
n (in each region) = (p
1
q
1
 + p
2
q
2
) (f(
α,β)) / ((p
1
 - p
2
)² 
α = type I error (level of significance) 
β = type II error ( 1-β = power of the study) 
power = the probability of getting a significant result 
f (
α,β) =10.5, when the power = 90% and the level of significance = 5% 
Eg. The proportion of nurses leaving the health service is compared between two regions. In 
one region 30% of nurses is estimated to leave the service within 3 years of graduation. In other 
region it is probably 15%.