In a metallurgy experiment it is desired to test the effect of four factors and their interactions on the concentration (percent by weight) of a particular phosphorus compound in casting material. The variables are A, percent phosphorus in the refinement; B, percent remelted material; C, fluxing time; and D, holding time. The four factors arc varied in a 24 factorial experiment with two castings taken at each factor combination. The 32 castings were made in random order. The following table shows the data and an ANOVA table is given in Figure. Discuss the effects of the factors and their interactions on the concentration of the phosphoruscompound.

Weight % of Phosphorus Compound Rep 2 Treatment Rep 1 Combination Total 30.3 28.5 24.5 25.9 24.8 26.9 24.8 22.2 31.7 24.6 27.6 26.3 29.9 28.6 31.4 58.9 (1) 59.9 50.1 53.1 48.2 50.7 52.6 47.1 65.2 50.8 58.2 54.1 57.6 a. 25.6 27.2 23.4 23.8 27.8 24.9 33.5 26.2 30.6 27.8 ab ac be abc ad bd abd cd 27.7 24.2 acd 51.0 26.8 bcd abcd 24.9 29.3 26.4 26.9 51.3 56.2 436.9 Total 428.1 865.0