Stratified sample size - sampling size, Operation Research

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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.

 

 


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