Stratified Sample Size
The sampling study has depended much on the stratified sample to reduce the sampling error, samples size may have a number of strata or clusters. The researcher will have to deal within strata variability and within and between cluster variability in calculating the sample size. Since allocation of the population members into strata confines each sub samples variance within the range of values in each stratum the sampling error is reduced to a very nominal level the standard error has a determined affect on the sample size. The stratified sample size may be proportional of disproportional. While one stratum may contain 0.55% of the population size the other may contain 0.08% , 0.10% so on. The percentage may very as per requirements and situations. In case of stratified sampling only the size of the strum is used as guide for allocating the total sample. The size of stratified sampling may be calculated as below :
Ni = Ni /N -n
Where
n = Number of sample units from stratum
Ni = total number of units in stratum
N= total number of units the population
n = sample size desired
the advantage of proportional allocation is that it leads to an estimate which is computationally simple. For calculation the weighted estimates, the weighted calculation of each stratum is totalled.
Thus standard deviation of all the
x st= √∑W3 ∑ i 2 / ni
Where W i = weight of stratum i = Ni/N
standard deviation of the i stratum
The disproportional stratified sample may be a more desirable method if the standard deviation of the observation in each stratum is known. Thus the standard deviation of the mean of a disproportionate stratified sample.
σ = σ √ ( W )^{2} / n
The cost per observation did not enter into the formula for calculating the sample size although cost exerts a direct impact. If the cost per observation or variability is not the same for each stratum there is need of determining sample size by considering the precisions. Cost per observation b subgroup is considered for calculation of sample size.