By Edward Bauer (Auth.)

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Square the sum o f the rows, divide by three, and subtract the correction. This gives the sum o f squares due to analysts. 4). Step 5. The degrees o f freedom for each variance are figured as follows: Methods = (m - 1) = 3 - 1 = 2, Analysts = (a -- 1 ) = 3 - 1 = 2 , Error = (m — 1)(a - - 1) = 2 x 2 = 4, Total = (ma - ■ Ο = ( 3 x 3 ) Step 6. 1 = 8. 4. 6 Block Design: Two-W ay Classification 39 On consulting tables o f the F distribution (Table V III), we find that both are highly significant. The “ between analysts” mean square has 2 df\ and the error mean square has 4 df.

Determination of the precision o f analytical control methods. Ind. Eng. , Anal. Ed. 15, 361. 2. Powers, F. W. (1939). 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.

1 is carried out as follows: (1) Calculate the correction by squaring the grand total and dividing by the total number o f analyses. 20 (2) Square the individuals and subtract the correction. This is the total sum o f squares. 42. 1, divide by the number o f observations and subtract the correction. This is the sum o f squares due to treatments. 86. (4) Subtract sum o f squares o f treatments from the total sum o f squares. 5 Block Design: One-W ay Classification 35 case the variation between analyses in each treatment.