In some papers I've seen the sample size formula for estimating proportions used as a magic one for obtaining "representative samples". In these cases they use the formula as if the estimated proportion were 0.5. I understand this formula is solely useful given the aim is to estimate a proportion. So, I wonder if there is some reasonable argument for this general use in surveys.
Rose -
Typically people may often use online calculators which are only good for proportions, simple random sampling without a finite population correction factor, and assume p=q=0.5, which is a "worst case" scenario. This is a big mistake which occurs when people do not understand how "formulas" are derived.
Best wishes - Jim
Rose -
If a stratified random sample can be used, that might reduce the overall sample size needed. However, if you want to publish for each stratum, then this will not be the case. There are various sample designs which will influence sample size needs, along with the standard deviations present.
Further, if you have auxiliary data for a model-assisted approach, that could help substantially. Also, a strictly model-based (prediction-based) approach may often be helpful.
Also note that the kind of data does matter. Continuous data are not the same as proportions.
So, there is no one single "sample size formula" which applies to "any kind of survey."
Cheers - Jim
ideal for cross-sectional surveys
Methods depend on designs and outcome variables
The use of .5 is a "worst case scenario" in the sense that this is the maximum variation for a proportion, but I don't think this is a "big mistake." That would only make sense if you had a better estimate for the proportionate split, and most sample estimators let you enter that if you have it (i.e., they use .5 as a default).
The result of using the maximum variation is that it gives you a "conservative" sample size. So, if your split is less than 50-50, the larger sample size will give you a more precise estimate.
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