Question

Four factors are thought to possibly influence the taste of a soft-drink beverage: type of sweetener (A), ratio of syrup to water (B), carbonation level (C), and temperature (D). Each factor can be run at two levels, producing a 2 design. At each run in the design, samples of the beverage are given to a test panel consisting of 20 people Each tester assigns a point score from 1 to 10 to the beverage. Total core is the response variable, and the objective is to find a formulation that maximizes total score. Two replicates of this design are run, and the results are shown in Table 13E.3. Analyze the data and draw conclusions Replicate Combination 188 172 179 185 175 183 190 175 200 170 189 183 201 181 189 178 195 180 187 178 180 178 180 168 193 178 181 188 188 ab bc ad bd cd bed abed 182 182

Answer 1

So first we have to sum the replicates and then make de contras so to make the contras ypu have to sum the elements for example you want the contras of AB you have to multiplicate the colum A*B* Total Replicas for each row and the total sum is the contras of each interection. then you make the effects and SS.

Type of swcctcncr ratio of syrup to water carbonation lever temperature Effects DATA replicate 1 Ireplicate 2 Total (sum the replicatesA B IC D Contrans 195 180 187 178 180 178 180 168 193 178 181 188 188 173 182 182 383 352 366 363 355 361 370 343 393 188 172 179 185 175 183 190 175 9.0625 1.3125 4.0625 2.6875 0.6875 0.5625 5.1875 3.9375 2.1875 0.1875 4.6875 1.6875 0.9375 0.9375 2.4375 657.03 13.78 132.03 57.78 3.78 2.53 215.28 124.03 38.28 0.28 175.78 22.78 7.03 7.03 47.53 145 -43 ас 1 11-1 170 189 183 201 181 189 178 370 371 389 354 371 360 75 27 15 acd hed abcd

Normal Plot of the Standardized Effects (response is REsulta, α 0.05) Effect Type Not Significant Significant 95 ■ A BD 1 90 AB Factor Na A. 80 70 60 50 40 20 10 Standardized Effect
you can see that only the factor A and the interections ABC, AB and ABD are significant, but for this exercise it´s not necessary to make this graphic it´s necessary only make the ANOVA

So if P <0.05 it is significant

Analysis of Variance Source Model DF Adj SS Adj MS F-Value P-Value 3.470.009 7.37 0.001 1 657.03 657.031 22.73 0.000 0.48 0.500 2.00 0.177 4.29 0.055 1.150.379 4.570.048 0.13 0.722 1.32 0.267 0.09 0.771 0.01 0.923 0.79 0.388 3.50 0.031 7.45 0.015 1 175.78 175.7816.08 0.025 0.24 0.629 0.24 0.629 1.64 0.218 1.64 0.218 151504.97 100.331 4852.63 213.156 Linear 1 13.78 13.781 1 57.78 57.781 1 124.03 124.031 2-Way Interactions 6 199.69 33.281 1 132.03 132.031 3.78 3.781 1 38.28 38.28:1 2.53 2.531 0.28 0.281 1 22.78 22.781 3-Way Interactions 4 405.12 101.281 1215.28 215.281 A" C A*D A*B*C A*B*D A*C* D B*C*D 7.03 7.031 7.03 7.031 4-Way Interactions 147.53 47.531 1 47.53 47.531 16462.50 28.906 A*B*C*D Error Total 31 1967.47 Model Summary