Terminology

1s_b  = S.D. = 1 Between Laboratory Standard Deviation

1s_w  = 1 Within Laboratory Standard Deviation

1s% = C.V.= Coefficient of Variation = Standard Deviation divided by the Average = (1s / x) X 100

d2s = Difference 2 sigma = 1s X 2 √2

Between Lab 1sb  =	√	∑(xi - x )2      n-1
Within Lab 1sw  =	√	∑((xi - yi) - (x - y))2          2(n-1)

What it means

Your Z score is calculated by subtracting the average of all test data from your data and dividing by the between lab standard deviation of all test data for a given sample .

Z_score (Odd Sample) = (x_lab  -  x) / 1s_bx

The 3 sigma ellipse has two radii one parallel to the diagonal and one perpendicular to it.

The radius parallel to the diagonal is equal to 3 times the average of the between lab standard deviations for the odd and even samples.

3 X (1s_bx + 1s_by) / 2

The radius perpendicular to the diagonal is equal to 3 times the within lab standard deviation.

(3 x 1s_w)

References

1. Youden, W. J., "Statistical Aspects of the Cement Testing Program", Proceedings, American Society for Testing and Materials, Vol. 59, 1959, p. 1120.
2. Crandall, J. R. and Blaine, R. L., "Statistical Evaluation of Interlaboratory Cement Tests", Proceedings, American Society for Testing and Materials, Vol. 59, 1959, p. 1129.

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