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What is the ideal sample size for a given population?
There is no "ideal" sample size for any given population, because polls and other statistical analysis forms depend on many factors, including what the survey is intended to show, who the target audience is, how much statistical error is permitted, and so on. The "Survey System" link, below, offers definitions and a couple of calculators to determine the best sample size for most purposes.
In an analysis of variance which is directly influenced by the size of the sample variances?
df within
In an analysis of variance is SS directly influenced by the size of the sample variances?
Yes it is.
How To get valid results small samples are sufficient?
I will assume the sample is random. In general, the larger the sample, the smaller the percentage error will be (the difference between percentages in the sample, and the percentages in the universe from whence the sample is taken). The percentage error tends to go down as the square root of the size of the sample.
How To Determine Sample Size?
I've included a couple of links. Statistical theory can never tell you how many samples you must take, all it can tell you the expected error that your sample should have given the variability of the data. Worked in reverse, you provide an expected error and the variability of the data, and statistical theory can tell you the corresponding sample size. The calculation methodology is given on the related links.
