I'm dealing with a question that has given me a peculiar result and I would like someone's opinion on how to deal this:

Say you have a population of $N=550$ objects: $N_1=75$ red and $N_2=475$ blue.

Given their $s_h^2$ 's and a required bound on a characteristic of interest, I was able to calculate the proper total sample size $n$ required, and used the formula to calculate each $n_h$.

The problem is that I ended up with a calculated $n_1>N_1$ because of the large difference in stratum sample variances. I've still used the calculated $n$, set $n_1=N_1$ and set $n_2=n-n_1$, but I don't think this will guarantee the required bound. What do I do?

  • $\begingroup$ You need to think in terms of variance reduction. One method of dealing with this is to further stratify $N_1$ into group that have homogeneity within the sub-strata and heterogeneity between the sub-strata. Also, you didn't provide the actual formula you used to compute your sample size so it' tough to say what you've done is actually a good approach. $\endgroup$ – StatsStudent Mar 10 at 14:31

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