By Edward Bauer (Auth.)
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Additional resources for A Statistical Manual for Chemists
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.
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. Statistical proof is not proof in the strict sense o f the term, but is a very high probability that a given hypothesis is true or false. A statistical hypothesis is an assumption about the population being tested.
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.