A 2^3 factorial design was used to investigate the effect of three different ing
ID: 3028146 • Letter: A
Question
A 2^3 factorial design was used to investigate the effect of three different ingredients on the sale of chocolate chip cookies. An experiment was conducted in which the cookies were made using different quantities of these ingredients and the number of repeat customers (out of 100) was measured as a response. The study was conducted in three different markets to act as a replicate and the data is provided below. Estimate the main effects and interactions Using this analysis, indicate which factors are most relevant Suggest which levels of each of the factors will produce the best-selling cookiesExplanation / Answer
Consider 3 factors,Factor A vanilla,, Factor B Chocolate chips, and Factor C sugar.
The treatments given to the experimental units represented all combinations of the levels A,B,C are said to be in a 'factorial' argument.
The word 'treatment' refers to a combination of quantitiy of vanilla,Chocolate and sugar.
Afactorial design used to investigate the effect of 3 different ingredients on the sale of chocolate chip cookies.
Treatment
combination
To study the effects,the ANOVA table is derived in a manner similar to the derivation for other designs.The observed responses can be partitioned into parts representing the grand mean,the effect of the particular level of factor A, the error associated with the experimental unit, and the error associated with the measurement unit.
The sum of the squares of the deviations of the observed responses from the grand mean can be partitioned inot sums describing variability in the effects of A, experimental unit effects, and measurement unit effects.
Similar way can be adopted for the remaining B and C.
we will get the effect of each fator,from which we can conclde which is more relevent.
Treatment
combination
I A B AB C AC BC ABC Replicate1 Replicate2 Replicate3 total 1 + - - |+ - + + - 22 21 25 68 a + + - - - - + + 32 43 29 104 b + - + - - + - + 35 34 50 119 ab + + + + - - - - 55 47 46 148 c + - - + + - - + 44 41 38 123 ac + + - - + + - - 40 37 36 113 bc + - + - + - + - 60 50 54 164 abc + + + + + + + + 39 41 47 127Related Questions
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