| | Terminology: |
| | 1sb = S.D. = 1 Between Laboratory Standard Deviation |
| | 1sw = 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 = | √ |
| Within Lab 1sw = | √
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| ∑((xi - yi) - (x - y))2 |
| 2(n-1) |
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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 . |
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| Zscore (Odd Sample) = (xlab - x) / 1sbx |
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The 3 sigma ellipse has two radii one parallel to the diagonal and one perpendicular to it. |
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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 (1sbx + 1sby) / 2 |
| The radius perpendicular to the diagonal is equal to 3 times the within lab standard deviation. (3 x 1sw) |
| | The ellipse has an angle or tilt which is equal to the even sample between lab standard deviation divided by the odd sample between lab standard deviation. (1sby / 1sbx) |
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| References: |
| Statistical Aspects of the Cement Testing Program - Youden |
| Statistical Evaluation of Interlaboratory Cement Tests - Crandall & Blaine |
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