# A Statistical Manual for Chemists by Edward Bauer (Auth.) By Edward Bauer (Auth.)

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Tests o f Significance: “ Positions in trays” obviously is not significant. It can be combined with Ve to give a new estimate o f error.

42 Source of variation Between treatments The mean square is the estimated variance for each source o f variation and is obtained by dividing sum o f squares by the degrees o f freedom. (7) The test o f significance is equal to or greater than F = F 0 01 in Table V III. 19. Table V III gives tables o f the F distribution, which is the distribu­ tion o f the ratio o f two variances. Table V I I I A gives critical values for F 0 05 ; these values would be exceeded by chance only five times in 100.

8308. 9 EXPECTED M E A N S Q U A R E (E M S ) C O M P O N E N T S Step 1. Designate the number o f levels in each main effect by some convenient letter. 2 if we designate methods by m, analysts by a, and replications by r, numerically: m = 3, a = 3, and r — 2. Step 2. Designate the variances by Vm for variance between methods, Va for variance between analysts, Vma for the interaction variance, Ve for the error variance. Step 3. Set up the following table: EMS Mean square Methods Ve + rVma + arVm Analysts Ve + rVma + mrVa M x A K + rVma Error K This is a table o f all possible components.