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TRADE-OFF STUDY SAMPLE SIZE: HOW LOW CAN WE GO?

By Dick McCullough

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Table 2.

N=200
n=	100	75	50	25
	0.527451	0.320534	0.176183	0.092247
	0.474558	0.411911	0.255339	0.142685
	0.61104	0.3109	0.226798	0.11125
	0.563223	0.287369	0.223945	0.194286
	0.487692	0.398193	0.368615	0.205507
	0.483789	0.47338	0.229888	-0.09505
	0.524381	0.471472	0.288293	0.250967
	0.368708	0.274371	0.252346	0.169203
	0.446393	0.401521	0.245936	0.109158
	0.453217	0.389331	0.139375	0.184337

r=	0.494045	0.373898	0.240672	0.136459
n/N =	0.5	0.375	0.25	0.125

Sample Bias Study 2

To extend the concept further, a random sample of 200 was generated, a second sample of 100 was created where each member of the second sample was equal to a member of the first sample and a third sample of a random 100 was generated, independent of the first two.

For each of the three samples, the mean was calculated.� This process was replicated 13 times and the mean data are reported below (Table 3).

The absolute difference� (MAE) between the first two data sets is 0.147308 and the absolute difference between the first and third data sets is 0.218077.� By dividing the MAE for the first two data sets by the finite population correction factor (sqrt(1-n/N)), the MAEs become quite similar.

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