I have done a survey among 600 elderly living in old age homes. The sample size was estimated using prevalence of previous study and the sample was selected using cluster random sampling. 4 districts from the state was randomly selected and 150 samples was selected from each district. Can I generalise the finding for the all elderly (including elderly living with families) in the state?
Elderly living in 'old age homes,' and elder living 'with families' sounds like two different populations, or strata. Actually, if facilities are of different regulatory types, they could be different populations too. Or you could consider that they could all be different strata for one population. But regardless, you need data to show that either they are basicly identical, or perhaps you could just use stratified random sampling. (You could do your cluster sampling within each subpopulation or stratum. Here, I guess you might consider them more as subpopulations or different populations.)
That is, if you want to say that one population or one subpopulation/stratum is not fundamentally different from another, then you need data to analyze that claim. Otherwise, saying that one represents itself, and another, or others, is an unknown risk. You might make some arguments as to why you think that would be true, but I suppose you would call those arguments "subjective." This would likely be much more justifiable for some questions/variables of interest than others on a given survey.
In order to generalize the inferential results based on a sample, the sample has to satisfied the following remarks:
1. Research studies are usually carried out on sample of subjects rather than whole populations. The most challenging aspect of fieldwork is drawing a random sample from the target population to which the results of the study would be generalized. The key to a good sample is that it has to be typical of the population from which it is drawn. When the information from a sample is not typical of that in the population in a systematic way, we say that error has occurred.
2. In actual practice, the task is so difficult that several types of errors, i.e. sampling error, non-sampling error, Response error, Processing error,… In addition, the most important error is the Sampling error, which is statistically defined as the error caused by observing a sample instead of the whole population. The underlying principle that must be followed if we are to have any hope of making inferences from a sample to a population is that the sample be representative of that population. A key way of achieving this is through the use of “randomization”.
3.There several types of random samples, Some of which are: Simple Random Sampling, Stratified Random Sampling, Double-stage Random Sampling... Moreover, the most important sample is the simple random sample which is a sample selected in such a way that every possible sample of the same size is equally likely to be chosen. In order to reduce the sampling error, the simple random sample technique and a large sample size have to be developed.
4. The following factors are highly affected the sample size and need to be identified prior to draw the samples:
- Population Size,
- Margin of Error,
- Confidence Level (level of significance) and
- Standard of Deviation.
5. In order to reduce the sampling error, the sample size should be enough, and can be estimated by,
Necessary Sample Size = (z-score or t-value)2 * StdDev*(1-StdDev) / (margin of error)2 .
Regards,
Zuhair
This is two-stage cluster sampling. A random sample of four clusters was drawn from the state in the first stage of sampling. If the 150 elders chosen from each cluster in the second stage of sampling were chosen randomly too I think that the results can be generalized to cover all elders in the state. The level of probability, alpha, must however be stated.
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