Getting Sample Size

SIMPLE SAMPLE SAMPLING

Getting a perfect sample is the most concern of every researcher; one might say 100 samples are enough but others needs a statistical proofs. But as for me a en able to achieved a perfect sample then the researcher doesn’t need to have a sample get the total population instead. However the role of sampling is important role in some of the principal steps in sample surveys choice of target population, determination of samples size and choice of sampling procedure.

The question of how large a sample should be is a difficult one. Sample size can be determined by various constraints. For example, the available funding may pre specify the sample size. When the research costs are fixed, a useful rule of the thumb is to spend about one half of the total amount for data collection and the other half for data analysis.

More technically, the required sample size is a function of the precision of estimated one wishes to achieve, the variability or variance, one expects to find in the population and the statistical level of significance one wishes to use.

The sample size n required to estimate populations mean µ with a given level of precision is:  

n= ( Z_∞/2*ð/e)²

Z_{∞/2 =} critical value of the Z variable obtained from the standard Normal Distribution

. ð = the standard deviation of the population

.e = with of the interval one willing to tolerate

Example:

For example to estimate mean earnings in a population with an accuracy of 100 Php per year , using 95% confidence interval and assuming that the standard deviation of earning in the population is 1,600 Php, the required sample size is:

.n = [ (1.96)(1600/100)]² = 983

One formula in getting sample size is the Slovin Formula; perhaps this is the most easiest way to get a sample, but much probably the most common.

Slovin Formula:

                        .n  = N/1+Ne²

Where   n  = sample size

             N = population size

            e² = margin of error desired

Example

            What should be the representative sample size if the population from which the sample will be taken is 10,000 and the desired margin of error is 2%?

.n = 10,000/ 1+ (10,000) (.02)²

     =   2,000

However we should take into consideration if this formula in finding the sample size cannot be used when the normal approximation of the population is poor or small. So if your total population is 100, 200 Slovin formula is not suggested.

Deciding on the sample size for qualitative inquiry can be even more difficult than quantitative because there are no definite rules to be followed. It will depend on what you want to know, the purpose of the inquiry, what is at stake, what will be useful, what will have credibility and what can be done with the available time and resources. With fixed a resource which is always the case, you can choose to study one specific phenomenon in depth with a smaller sample size or a bigger sample size when seeking the breadth. In purposeful sampling, the sample should be judge on the basis of the purpose and rationale for each study and the sampling strategy used to achieve the studies purpose. The validity, meaningfulness, and insights generated from qualitative inquiry have more to do with the information-richness of the cases selected and the observational/ analytical capabilities than with sample size.

There are more sampling formulas and strategies to follow in my succeeding blog. Hopefully could help in your research project. Fill free to comment anytime. So in finding an accurate sample size and if your statistician, adviser and technical consultant says or suggest that 100 is enough sample then follow by all means, the reason may be at the tip of their tongue.