By Edward Bauer (Auth.)

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13. 12. 14. 14 Analyst Step 4. 4 Tests o f significance. 63, L x A interaction obviously not significant; L x M interaction obviously not significant. 1106 ve+wm. 1221)/(4 + 2 + 2 + 4) = Ve. 0404 with 12 df. 75. 89. 89. 5, Conclusions: The differences between lots, methods, and analysts are significant. 12 N EST E D F A C T O R IA L E X PE R IM E N T It is often impossible or undesirable to do a complete factorial design in chemical work. For example, interlaboratory studies o f precision furnish data collected by different analysts on different instruments, so that we have Analysts a, b, and c using Instruments 1, 2, and 3 in one laboratory, studying the same methods as Analysts d, e, and f using Instruments 4, 5, and 6 in another laboratory.

Accuracy and precision of micro-analytical determina tions of carbon and hydrogen. Statistical study. Ind. Eng. , Anal. Ed. 11,660. 1 E X PE R IM E N T A L DESIG N Man has been designing experiments ever since he began asking questions about the world around him; hence, the design o f experi ments is nothing new. He has developed a systematic plan for attack ing problems, which has come to be known as the “ scientific method/’ Essentially, this method consists o f the following elements: (1) (2) (3) (4) (5) A problem is stated and defined.

3 V. 0 V. 6, which is a sum o f methods and analysts table. 8). 2; but because each figure is the sum o f two, we divide by twice the regular divisor. Step 1 Correction factor (180)2/(9 x 2) = 1800. Step 2. 33. Step 3. 42. 1800 1800 Step 4. 56. Step 5. Methods-analysts interaction. 90. Step 6. Total variance. 69. Step 7. 13. Step 8. Degrees o f freedom. 2. The degrees o f freedom for the error variance are ma(r — 1), and the total degrees o f freedom are mra — 1. 0 Methods: (m — 1) = 3 — 1 = 2; Analysts: (a — 1) = 3 — 1 = 2; M x A: Step 9.