Hi,

Probability proportional to size (PPS) sampling is a method of sampling from a finite population in which a size measure is available for each population unit before sampling and where the probability of selecting a unit is proportional to its size

Usually at least n = 30 to fulfil the CLT or c. 5% of each group :)

I would suggest that you look at Schaefer et all ELEMENTARY SURVEY SAMPLING.

PPS ISa subset of one of the methods suggested there but you

have other choices. Use the one that gives the best variance estimate as described in the text. Most statistics computer packages contain routines to do the calculations. Good luck, David Booth

the SRS sampling (Simple Random Sampling, ignoring stratifications) should approximately mirror the relative size of all strata. This would be recommended unless you want to read results by stratum. In this case you should oversample small strata and afterwards you should weight data for estimation. The weight should be the inverse of the inclusion probability. So, if your sample in a given stratum is double of what should be in an SRS sampling, the weight in that stratum should be half with respect to the weight (equal for all sampling units) in an SRS sampling.

You should have at least 30 cases per stratum to use t test appropriately, if you use it.

Ulderico Santarelli Thank you for your help, Wishing you the Best

Bhogaraju Anand Andrew Paul McKenzie Pegman Thank you 😊

Thank you

The stratified simple random sampling is used when you have groups. that is the population of N units divided into into subgroups called strata. A random sample of size n is taken from N, using Proportional or Nyman allocation to find the number of the sample units in each stratum. Fore more information you can see chapter 5 of W.G. Cochran's book Sampling Techniques.

Hi!

I suggest calculating a general sample size and then using stratified sampling. Stratified sampling achieves proportionality by its groups.

Mowafaq Muhammed Tawfeeq Al-kassab Andrea Freire-Pesántez Thank you for your help, Best wishes 🌼 🌼

The highest power is when the sample sizes are equal. When the sample sizes are unequal, you can work out the effective sample size by using the proportion on one group (p) as follows:

Effective sample size = N x (4(p x (1-p)))

where N is the total sample size and p is the proportion in one of the groups.

This shows you that when the split is 60/40 the loss of power is slight (4% loss), but at 90/10 the loss is drastic!

Ghazal Tanhaei -

It is not clear to me whether your question, or questions, are for proportions or for continuous data. The online calculator you chose appears to let you use either. (If you have more than one question, you would have to look at them individually, and pick the largest sample size needed for an important question.) Online calculators, however, are notoriously limited and subject to misuse. Pennsylvania State University has a great deal of online resources that would serve you better if you search on a term with "Pennsylvania State University" included in the search term. Then you could understand each topic better.

Note that you need to decide if you want a finite population correction factor.

You say that you have three groups of interest. If you were only interested in the overall result, you could use stratified random sampling and an optimal overall sample size, which you can research. But, here you appear to want a good result for each "group," so these groups should not be treated as strata, but as individual (sub)populations. Therefore, it looks like you are looking at simple random sampling for each group. Regardless, the standard deviation within each group could be different, and that, plus the fact that you say the population sizes are different means that the sample size in each group used to meet an expected, desired standard error in each case will all likely be different.

This all assumes simple random sampling. Also, in each case you need an estimate of "population" standard deviation (or, here, you need this for each subpopulation). If you cannot judge this from previous/other information, you might consider a "pilot study."

Cheers - Jim

PS - Ghazal, I just saw your note where you said you think you want stratified random sampling. No, that would not do what you want, as I explained in my response just above this one. Treat each group as a separate sample from a separate population, using simple random sampling in each case.

Dear James R Knaub and Ronán Michael Conroy

I'm surprised by the support I received in research gate, thank you so much for your contribution. I work with 3 supervisors, one of them was really keen to publish a paper on the results of this survey. The other 2 rightfully pointed out that similar work was published before. So, we are not gathering data from patients anymore. It's a shame, cause we spent so much time on designing the survey. Well, I hope this discussion becomes handy for anyone struggling with the same question.

Once again thank you for taking time to help me

Wishing you the best

Ghazal

Similar work? Did you come to similar conclusions?

James R Knaub

We are engineers and I guess a paper that's going to be published in a rehabilitation journal is not that interesting for them to spend time to apply for ethical approval.

Ghazal Tanhaei – oh-oh! Did you mean that you have gathered data but you haven't got ethical approval yet? In this case you can't actually get approval, because an ethics committee cannot give you approval to do something that you already did.

My feeling is with James R Knaub – every study is a study of the research question, but it cannot be the definitive study because each study has its own methodology, sampling frame, response rate etc etc. So your study has something to contribute, even if it's not dramatic.

When the population is divided into subgroups with different sizes, you can use stratified sampling to calculate the sample size of a survey. Stratified sampling is a method of sampling that involves dividing the population into subgroups or strata based on some characteristic that is important to the survey. The sample size for each stratum is calculated separately based on the size of the stratum and the desired level of precision.