By Edward Bauer (Auth.)

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1) becomes Xj « X + ( X t - X ) + ( X tJ - Xd- Transposing X (Xtj - * ) = - % ) + ( Xtj - * t ). 68). 2) states that the deviation o f any observation from the grand average is the sum o f the treatment average from the grand average plus the deviation o f the observation from the treatment average. 34 Experimental Design and the Analysis o f Variance In order to analyze the whole experiment these deviations must be added. However, as in the case o f the average deviation in Chapter 1, the sum o f the deviations would be zero, and to avoid this they must be squared, which gives rise to the fundamental equation o f the analysis o f variance.

Step 6. 0466. Step 7. The degrees o f freedom are: for pressure (n — 1) = 2 for temperature (n — 1) = 2; for catalyst (n — 1) = 2 for error (n — 1)(« — 2) = 2. Step 8. 11 Factorial Experiments Step 9. 49 Tests o f significance: catalyst Step 10. 0. 05 level o f significance was chosen, thisexperiment indicates that bothtemperature and pressure have a significant influence on the reaction. 01 level had been chosen, we would not have found any significant difference. As it is, the experimenter is taking five chances out o f 100 that the results o f this experiment are giving him false information.

An efficiently designed experiment should meet the following five criteria: 27 28 Experimental Design and the Analysis o f Variance (1) (2) (3) (4) (5) It should give an unbiased measure o f the main effects. It should provide an unbiased estimate o f the variability o f the main effects. When necessary, the experiment should furnish information as to possible interaction between the main effects. It should keep the unresolved experimental error as small as possible. It should give an estimate o f this error.