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

By Dick McCullough

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Table 3.

	N=200	n=100	n=100
	11.075	11.18	9.54
	10.275	10.15	11.15
	10.85	11.15	10.62
	10.595	10.51	10.81
	9.99	9.92	10.88
	9.735	10.11	11.19
	10.555	11.3	11.43
	11.44	11.68	10.88
	10.41	10.33	9.37
	10.13	10.55	10.87
	10.34	9.84	11.23
	10.295	10.86	11.46
	10.855	10.88	9.95
	10.50346	10.65077	10.72154
MAE		0.147308	0.218077
MAE/sqrt(1-n/N)=		0.208325

Sample Bias Study 3

To continue the extension of the concept, 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.

The squared correlation was calculated for the first two samples and for the first and third samples.  This procedure was replicated 11 times.  The 11 squared correlations for the first two samples were averaged as were the 11 squared correlations for the first and third samples.

MPEs were caculated for both mean r-squares (Table 4).  The MPE for the first two sample is substantially smaller than the MPE for the first and third samples.  By dividing the MPE for the first two samples by the square of the finite population correction factor (1-n/N), the MPEs become quite similar.

Note that it is somewhat intuitive that the correction factor for the MPEs is the square of the correction factor for the MAEs.  MPE is a measure of squared error whereas MAE is a measure of first power error.

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