Question

5. As with many dried products, sun-dried tomatoes can exhibit an undesirable discoloration during the drying and storage process. A replicated 23 experiments were conducted in an effort to optimize color by considering storage time, temperature, and packaging type ("Use of Factorial Experimental Design for Analyzing the Effect of Storage Conditions on Color Quality of Sun- Dried Tomatoes," Sci. Res, and Essays, 2012: 477-489). In the following table, higher values of the response variable (based on chromaticity measurements) are associated with higher color quality: Color Quality Storage Storage Replication Replication Run time temp Packaging 2.40 2.38 2.42 2.38 11 11 + + + + + + 2.38 2.38 1.94 1.93 2.40 2.40 1.94 1.92 + + + + + a) Calculate all main effects and two-factor inter-action effects. b) Construct an ANOVA table and use it as a basis for deciding which factors appear to affect color quality (Use a = 0.01). c) Which settings (high or low) of the factors in part (b) lead to maximizing color quality?

Answer 1

5 het A time, B temperature & c Packaging Thus, we have 3 factors A, B & C at 2 levels each. (high & Cow). → 2088 Treatment combinations given by (1), a, b, c, ab, ac, bc & abc. From the given information we have; Run Treatment Rep 1 Rep 2 Total - Combination 2:38 2.40 - 4.78 2.38 - 4.78 2.42 2.40 4.82 2.31 2.29 4.60 2.38 2.40 ac 2.38 2.40 4.78 1.94 1.94 3.88 abc 1.93 1.92 3.85 Total (Rn) 18.12 18.15 36.27 The treatment contrast for main effects & Interacties effect is given by The main effects & interaction effects are calculated as follows a) A = (a + abt ag tabc - (1)- b-C - bc] 2- xn. there ne no. of replicates 22 of WN - 31 2.40 ab 4.78 be 8 + HOBO +4.78 + 3.85 - 4.78 -4.82 - 4.78 - 3.88 z -0.25 -0.03125

Illy B = 16+ ab + bct abc (1) -a-c-ac] 2 018 € 70/3/215/ -1.97 2-0.24625 AB 2 101) + ab + c + abc - a - b - ac - bc] 8 8 2 -0.25 2 -0.03125 Cz1c + ac + bc + abc - (1) - a - b - ab] 2 -1.69 2 0.21125_ _ AC: 1/0) + b + ac + abc - a-c - ab- bc 8 = 0.19 0.02375 BC = 1.0) + a + bc + abc - b - C - ab-ac) =1:64 2 0.21125_ A00 , lựa + b + c + abc - (1) - ab = ac - bc, 2 0.19 0.02375 (* also be Note: Treatment contrasts can found using Yates method

28 Total Ss. You - (06:27 2 82:8327 - (36.27)2 = 0.61314375 16 16 Emor SSz SSE = TSS - SSA-SSD - SSAB - SSC-SSAC - SSBC - SSAB - SS rep 2 0.00119375 ANOVA. take Sources dof SS MSS 2 ss/dof 0.00390625 0.00390625 0:24255625 0.24255625 O 00390625 0.00390625 0.178 506 2.5 0.178 506 25 0.00225625 0.00225625 . 0.178 5062.5 0.17850625 0.00225625 0.00225625 (2-1)21 0.0000 56 25 0.00005625 1 0.00119375 0.00001705 15 0.61314375 Fcal MSS/MSSerror 229.1055 718 14226.17302 229:1055718 10469.57478 132.3313783 10469.57478 132.331378 3 3.299120 С AC BC ABC eplication Ergon Tobal Le ai xx Note that the Feal values obtained quite absurd. The data is either faulty there is probably some calculation error which I am not able to figure out. However, the formulacs & the procedure is correct

Fbab F1, 7,0.01 = 12.25 : Feal > 12.25 t main & interaction effects All main & interaction effects appear to be significant