Determination of the Sample Size

Determination of the Sample Size

                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 research cost 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. In general the sample size depends on the nature of the analysis to be performed, the desired precision of the estimates one wishes to atchieve, the kind and number of comparisons that will be made, the number of variables that have to be examine simultaneously and how heterogeneous a universe is sampled.

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

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

                                          n=      ( )²

Z∞/2 = critical value of the Z variable obtained from the Standard Normal Distribution

ờ = standard Deviation of the population

e = width of the interval willing to tolerate

Example from 100 births per month .the researcher wants to know patients having vaginal adenosis which have a probability of 30/100 per month .

From the computed mean       Statistics

Mean		1.3000
Std. Deviation		.46057

 

From the exclusion criteria is expected that there would be 5 patients failed to be part of the sample since they failed to meet the criteria, so the required sample size is

n=   ( )²

( )^{2= 0.325}

Have you seen the sample size it small for a sample which is not suggested if we have small population?

The rule of 100

The 100 n samples is used if the key analysis of a randomized experiment consists of computing the averages and controls in a project and comparing differences, then the sample under 100 might be adequate , assuming that other statistical assumptions hold.

Here are some guidelines with regards to the minimum number of items needed for a representative sample:

1.     Descriptive studies – the minimum number of 100

2.     Co-relational studies – a sample of at least 50 is deemed necessary to establish the existence of a relationship.

3.     Experimental and Casual comparative studies – a minimum of 30 per group * sometimes experimental studies with only 15 items in each group can be defended if they are very tightly controlled.

*if the sample is randomly selected and is sufficiently large, an accurate view of the population can be had, provided that no bias enters the selection process.

Sampling Errors

1.     Is the error attributed to chance that is being made when selecting random samples to represent a given population under consideration.

2.     It is the expected change difference, variation or deviation between a random sample and the population.

3.     Does not result from measurement or computation errors, although these errors are attributed to inaccuracy.

So it is suggested that we used the Methods in Selecting the Sample

Non probability sampling

            Samples are drawn from the population based on the personal judgment of the researcher.

Types of Non-probability Sample

a.     Convenience Sample – A convenience sample results when the more convenient elementary units are chosen from a population for observation.

b.     Judgment sample – A judgment sample is obtained according to the discretion of someone who is familiar with the relevant characteristics of the population.

c.       Purposive Sample – Samples are drawn according to the purpose of the study.

Probability or Random Sampling

            This may be the most important type of sample. A random sample allows a known probability that each elementary unit will be chosen. For this reason it is sometimes referred to as a probability sample. These types of sampling are:

a.     Simple random Sampling- A simple random sampling is obtained by choosing elementary units is such away that each unit in the population has an equal chance of being selected. A simple random sample is free from sampling bias.

b.    Stratified random sampling – A stratified random sampling is obtained by independently selecting a separate simple random sample from each sub population or stratum. A population can be divided into different groups may be based on some characteristics or variable like income or education.

c.     Systematic Random Sampling – A systematic Random Sampling is obtained by selecting one unit on a random basis and choosing additional elementary units at evenly spaced intervals unit the desired units is obtained.

d.    Cluster Random Sample- A cluster sample is obtained by selecting clusters from the population on the basis of simple random sampling. The sample comprises a census of each random cluster selected.