By Edward Bauer (Auth.)

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36 Experimental Design and the Analysis o f Variance To find F in the tables, use the column for / x (degrees o f freedom in the numerator) and the row for f 2 (degrees o f freedom in the denominator). 19. Hence, the null hypothesis is rejected and we can say that there is a high probability that the difference between treatments is significant. 6 B LO C K D E S IG N : T W O -W A Y C LA SS IF IC A T IO N To carry our illustration one step further let us synthesize a problem where we have three chemists each making a single analysis by three different methods o f analysis.

Both questions should be settled before the experiment is begun. This avoids wishful thinking from influencing the judgment o f the experimenter. ” Consequently, much o f the nomenclature o f experimental design may sound strange to a chemist. When we speak o f “ treatment” we mean some con­ dition such as pressure or temperature has been imposed on the subject o f the experiment. 3 TESTS O F SIG N IF IC A N C E A feature o f the statistically designed experiment, not inherent in the classic design, is the furnishing o f statistical proof that a signifi­ cant difference does or does not exist.

Testing the hypothesis against the data and accepting or rejecting it are matters o f judgment, and any way in which the judgment can be made objective, rather than subjective, will be o f service. A statistically designed experiment gives an estimate o f error that can be used as a standard by which the results o f the experiment can be measured. It is more efficient than the classic design in that it produces more usable information with less experimentation. 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.

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