Dear salames,

According your quarry your dependent variable is categorical so it is recommendation formula with example as :

If we use the stratified sample technique, the calculated sample size should be each of each stratum.

If researchers create the two strata and known two proportions about the population parameter then formula of calculating the sample size is

n={Z_((1-α)/2) √(2p ̅ q ̅ )+Z_((1-β) ) √(p_(1 ) q_(1+) p_(2 ) q_2 )}^2/(p_1-p_2 )^2

Where p ̅=(p_1+p_2)/2

Example 4:

In a pilot survey in a developing country, an epidemiologist compared a sample of adults who were suffering from a certain neurological disease with a sample of comparable control subjects who were free of the disease. Finding of the previous study 60% subjects with the disease and 50% of the controls were involved in fishing-related occupations. If the proportion of people involved in fishing-related occupations in the entire population is similar to that observed in the pilot survey, how many subjects should be included in a larger study in each of the two groups if the epidemiologist wishes to be 90% confident of detecting a true difference between the groups at the 5% level of significance?

Solution:

The level of significance is 5% which is standard normal deviate for α = Z_((1-α)/2)=1.96

And, 90% confidence to detecting a true difference; i.e. the standard normal deviate for β = Z_((1-β) )=1.28

The subjects who have the disease (p1) =0.60 and control (p2) = 0.50

p ̅=(p_1+p_2)/2 = 0.60+0.50/2=0.55

and finally sample size is

{1.96√(2×0.55×0.45)+1.28√(0.6×0.4+0.5×0.5)}^2/(0.6-0.5)^2

=517.51518

The required sample size would be 518 in each group.

Thank you Dr Govinda Prasad Dhungana