8.2 Design of experiments
When we inspect our dataset, we see that Flavor has 5 levels (raspberry, chocolate, strawberry, mango, vanilla), Packaging has 3 levels (homemade waffle, cone, pint), Light has 2 levels (low fat vs. not), and Organic has 2 levels (organic vs. not). The goal of a conjoint analysis is to estimate the extent to which each attribute level affects the rating of the ice cream. To do this, the ice cream manufacturer could create 5 \(\times\) 3 \(\times\) 2 \(\times\) 2 = 60 different ice creams and ask people to rate all of these. This will give the manufacturer a good estimate of the importance of each attribute and all their possible interactions. However, rating 60 ice creams is difficult for the participants and such a large study would be expensive for the manufacturer to fund. In practice, researchers in this situation will ask people to rate a subset of those 60 ice creams. In this section, we discuss how to select a subset (e.g., 10 ice creams) of all possible attribute level combinations (i.e., 60 ice creams) that will still allow us to get good estimates of the most important effects.
In the dataset, we already have the ratings for ten profiles, so the decision of which ice creams to test has already been made. However, let’s disregard the fact that we already have the data and consider the decisions that need to be made before collecting data. In other words, let’s discuss how we go from a full factorial (all 60 combinations) to a fractional design (less than 60 combinations).
The doe (design of experiments) function from the radiant package will help us decide on study designs. Radiant is an R package for business analytics. The following discussion of the doe function is based on Radiant’s discussion of this function.
install.packages("radiant")
library(radiant)To use doe we need to input the information about our attributes and their levels in a specific way:
# attribute1, attribute2, etc. are vectors with one element in which we first provide the name of the attribute followed by a semi-colon and then provide all the levels of the attributes separated by semi-colons
attribute1 <- "Flavor; Raspberry; Chocolate; Strawberry; Mango; Vanilla"
attribute2 <- "Package; Homemade waffle; Cone; Pint"
attribute3 <- "Light; Low fat; No low fat"
attribute4 <- "Organic; Organic; Not organic"
# now combine these different attributes into one vector with c()
attributes <- c(attribute1, attribute2, attribute3, attribute4)We can now ask for potential experimental designs:
summary(doe(attributes, seed = 123)) # Seed: fix random number generator, see explanation below## Experimental design
## # trials for partial factorial: 60
## # trials for full factorial : 60
## Random seed : 123
##
## Attributes and levels:
## Flavor: Raspberry, Chocolate, Strawberry, Mango, Vanilla
## Package: Homemade_waffle, Cone, Pint
## Light: Low_fat, No_low_fat
## Organic: Organic, Not_organic
##
## Design efficiency:
## Trials D-efficiency Balanced
## 9 0.105 FALSE
## 10 0.389 FALSE
## 11 0.411 FALSE
## 12 0.614 FALSE
## 13 0.542 FALSE
## 14 0.479 FALSE
## 15 0.762 FALSE
## 16 0.738 FALSE
## 17 0.748 FALSE
## 18 0.756 FALSE
## 19 0.644 FALSE
## 20 0.895 FALSE
## 21 0.848 FALSE
## 22 0.833 FALSE
## 23 0.790 FALSE
## 24 0.827 FALSE
## 25 0.787 FALSE
## 26 0.768 FALSE
## 27 0.759 FALSE
## 28 0.736 FALSE
## 29 0.702 FALSE
## 30 0.984 TRUE
## 31 0.952 FALSE
## 32 0.933 FALSE
## 33 0.928 FALSE
## 34 0.900 FALSE
## 35 0.871 FALSE
## 36 0.893 FALSE
## 37 0.866 FALSE
## 38 0.843 FALSE
## 39 0.836 FALSE
## 40 0.922 FALSE
## 41 0.899 FALSE
## 42 0.904 FALSE
## 43 0.882 FALSE
## 44 0.861 FALSE
## 45 0.949 FALSE
## 46 0.919 FALSE
## 47 0.912 FALSE
## 48 0.911 FALSE
## 49 0.891 FALSE
## 50 0.959 FALSE
## 51 0.939 FALSE
## 52 0.944 FALSE
## 53 0.925 FALSE
## 54 0.924 FALSE
## 55 0.906 FALSE
## 56 0.902 FALSE
## 57 0.884 FALSE
## 58 0.872 FALSE
## 59 0.855 FALSE
## 60 1.000 TRUE
##
## Partial factorial design correlations:
## ** Note: Variables are assumed to be ordinal **
## Flavor Package Light Organic
## Flavor 1 0 0 0
## Package 0 1 0 0
## Light 0 0 1 0
## Organic 0 0 0 1
##
## Partial factorial design:
## trial Flavor Package Light Organic
## 1 Raspberry Homemade_waffle Low_fat Organic
## 2 Raspberry Homemade_waffle Low_fat Not_organic
## 3 Raspberry Homemade_waffle No_low_fat Organic
## 4 Raspberry Homemade_waffle No_low_fat Not_organic
## 5 Raspberry Cone Low_fat Organic
## 6 Raspberry Cone Low_fat Not_organic
## 7 Raspberry Cone No_low_fat Organic
## 8 Raspberry Cone No_low_fat Not_organic
## 9 Raspberry Pint Low_fat Organic
## 10 Raspberry Pint Low_fat Not_organic
## 11 Raspberry Pint No_low_fat Organic
## 12 Raspberry Pint No_low_fat Not_organic
## 13 Chocolate Homemade_waffle Low_fat Organic
## 14 Chocolate Homemade_waffle Low_fat Not_organic
## 15 Chocolate Homemade_waffle No_low_fat Organic
## 16 Chocolate Homemade_waffle No_low_fat Not_organic
## 17 Chocolate Cone Low_fat Organic
## 18 Chocolate Cone Low_fat Not_organic
## 19 Chocolate Cone No_low_fat Organic
## 20 Chocolate Cone No_low_fat Not_organic
## 21 Chocolate Pint Low_fat Organic
## 22 Chocolate Pint Low_fat Not_organic
## 23 Chocolate Pint No_low_fat Organic
## 24 Chocolate Pint No_low_fat Not_organic
## 25 Strawberry Homemade_waffle Low_fat Organic
## 26 Strawberry Homemade_waffle Low_fat Not_organic
## 27 Strawberry Homemade_waffle No_low_fat Organic
## 28 Strawberry Homemade_waffle No_low_fat Not_organic
## 29 Strawberry Cone Low_fat Organic
## 30 Strawberry Cone Low_fat Not_organic
## 31 Strawberry Cone No_low_fat Organic
## 32 Strawberry Cone No_low_fat Not_organic
## 33 Strawberry Pint Low_fat Organic
## 34 Strawberry Pint Low_fat Not_organic
## 35 Strawberry Pint No_low_fat Organic
## 36 Strawberry Pint No_low_fat Not_organic
## 37 Mango Homemade_waffle Low_fat Organic
## 38 Mango Homemade_waffle Low_fat Not_organic
## 39 Mango Homemade_waffle No_low_fat Organic
## 40 Mango Homemade_waffle No_low_fat Not_organic
## 41 Mango Cone Low_fat Organic
## 42 Mango Cone Low_fat Not_organic
## 43 Mango Cone No_low_fat Organic
## 44 Mango Cone No_low_fat Not_organic
## 45 Mango Pint Low_fat Organic
## 46 Mango Pint Low_fat Not_organic
## 47 Mango Pint No_low_fat Organic
## 48 Mango Pint No_low_fat Not_organic
## 49 Vanilla Homemade_waffle Low_fat Organic
## 50 Vanilla Homemade_waffle Low_fat Not_organic
## 51 Vanilla Homemade_waffle No_low_fat Organic
## 52 Vanilla Homemade_waffle No_low_fat Not_organic
## 53 Vanilla Cone Low_fat Organic
## 54 Vanilla Cone Low_fat Not_organic
## 55 Vanilla Cone No_low_fat Organic
## 56 Vanilla Cone No_low_fat Not_organic
## 57 Vanilla Pint Low_fat Organic
## 58 Vanilla Pint Low_fat Not_organic
## 59 Vanilla Pint No_low_fat Organic
## 60 Vanilla Pint No_low_fat Not_organic
##
## Estimable effects from partial factorial design:
##
## Flavor|Chocolate
## Flavor|Strawberry
## Flavor|Mango
## Flavor|Vanilla
## Package|Cone
## Package|Pint
## Light|No_low_fat
## Organic|Not_organic
## Flavor|Chocolate:Package|Cone
## Flavor|Strawberry:Package|Cone
## Flavor|Mango:Package|Cone
## Flavor|Vanilla:Package|Cone
## Flavor|Chocolate:Package|Pint
## Flavor|Strawberry:Package|Pint
## Flavor|Mango:Package|Pint
## Flavor|Vanilla:Package|Pint
## Flavor|Chocolate:Light|No_low_fat
## Flavor|Strawberry:Light|No_low_fat
## Flavor|Mango:Light|No_low_fat
## Flavor|Vanilla:Light|No_low_fat
## Package|Cone:Light|No_low_fat
## Package|Pint:Light|No_low_fat
## Flavor|Chocolate:Organic|Not_organic
## Flavor|Strawberry:Organic|Not_organic
## Flavor|Mango:Organic|Not_organic
## Flavor|Vanilla:Organic|Not_organic
## Package|Cone:Organic|Not_organic
## Package|Pint:Organic|Not_organic
## Light|No_low_fat:Organic|Not_organic
## Flavor|Chocolate:Package|Cone:Light|No_low_fat
## Flavor|Strawberry:Package|Cone:Light|No_low_fat
## Flavor|Mango:Package|Cone:Light|No_low_fat
## Flavor|Vanilla:Package|Cone:Light|No_low_fat
## Flavor|Chocolate:Package|Pint:Light|No_low_fat
## Flavor|Strawberry:Package|Pint:Light|No_low_fat
## Flavor|Mango:Package|Pint:Light|No_low_fat
## Flavor|Vanilla:Package|Pint:Light|No_low_fat
## Flavor|Chocolate:Package|Cone:Organic|Not_organic
## Flavor|Strawberry:Package|Cone:Organic|Not_organic
## Flavor|Mango:Package|Cone:Organic|Not_organic
## Flavor|Vanilla:Package|Cone:Organic|Not_organic
## Flavor|Chocolate:Package|Pint:Organic|Not_organic
## Flavor|Strawberry:Package|Pint:Organic|Not_organic
## Flavor|Mango:Package|Pint:Organic|Not_organic
## Flavor|Vanilla:Package|Pint:Organic|Not_organic
## Flavor|Chocolate:Light|No_low_fat:Organic|Not_organic
## Flavor|Strawberry:Light|No_low_fat:Organic|Not_organic
## Flavor|Mango:Light|No_low_fat:Organic|Not_organic
## Flavor|Vanilla:Light|No_low_fat:Organic|Not_organic
## Package|Cone:Light|No_low_fat:Organic|Not_organic
## Package|Pint:Light|No_low_fat:Organic|Not_organic
## Flavor|Chocolate:Package|Cone:Light|No_low_fat:Organic|Not_organic
## Flavor|Strawberry:Package|Cone:Light|No_low_fat:Organic|Not_organic
## Flavor|Mango:Package|Cone:Light|No_low_fat:Organic|Not_organic
## Flavor|Vanilla:Package|Cone:Light|No_low_fat:Organic|Not_organic
## Flavor|Chocolate:Package|Pint:Light|No_low_fat:Organic|Not_organic
## Flavor|Strawberry:Package|Pint:Light|No_low_fat:Organic|Not_organic
## Flavor|Mango:Package|Pint:Light|No_low_fat:Organic|Not_organic
## Flavor|Vanilla:Package|Pint:Light|No_low_fat:Organic|Not_organic
##
## Full factorial design:
## trial Flavor Package Light Organic
## 1 Raspberry Homemade_waffle Low_fat Organic
## 2 Raspberry Homemade_waffle Low_fat Not_organic
## 3 Raspberry Homemade_waffle No_low_fat Organic
## 4 Raspberry Homemade_waffle No_low_fat Not_organic
## 5 Raspberry Cone Low_fat Organic
## 6 Raspberry Cone Low_fat Not_organic
## 7 Raspberry Cone No_low_fat Organic
## 8 Raspberry Cone No_low_fat Not_organic
## 9 Raspberry Pint Low_fat Organic
## 10 Raspberry Pint Low_fat Not_organic
## 11 Raspberry Pint No_low_fat Organic
## 12 Raspberry Pint No_low_fat Not_organic
## 13 Chocolate Homemade_waffle Low_fat Organic
## 14 Chocolate Homemade_waffle Low_fat Not_organic
## 15 Chocolate Homemade_waffle No_low_fat Organic
## 16 Chocolate Homemade_waffle No_low_fat Not_organic
## 17 Chocolate Cone Low_fat Organic
## 18 Chocolate Cone Low_fat Not_organic
## 19 Chocolate Cone No_low_fat Organic
## 20 Chocolate Cone No_low_fat Not_organic
## 21 Chocolate Pint Low_fat Organic
## 22 Chocolate Pint Low_fat Not_organic
## 23 Chocolate Pint No_low_fat Organic
## 24 Chocolate Pint No_low_fat Not_organic
## 25 Strawberry Homemade_waffle Low_fat Organic
## 26 Strawberry Homemade_waffle Low_fat Not_organic
## 27 Strawberry Homemade_waffle No_low_fat Organic
## 28 Strawberry Homemade_waffle No_low_fat Not_organic
## 29 Strawberry Cone Low_fat Organic
## 30 Strawberry Cone Low_fat Not_organic
## 31 Strawberry Cone No_low_fat Organic
## 32 Strawberry Cone No_low_fat Not_organic
## 33 Strawberry Pint Low_fat Organic
## 34 Strawberry Pint Low_fat Not_organic
## 35 Strawberry Pint No_low_fat Organic
## 36 Strawberry Pint No_low_fat Not_organic
## 37 Mango Homemade_waffle Low_fat Organic
## 38 Mango Homemade_waffle Low_fat Not_organic
## 39 Mango Homemade_waffle No_low_fat Organic
## 40 Mango Homemade_waffle No_low_fat Not_organic
## 41 Mango Cone Low_fat Organic
## 42 Mango Cone Low_fat Not_organic
## 43 Mango Cone No_low_fat Organic
## 44 Mango Cone No_low_fat Not_organic
## 45 Mango Pint Low_fat Organic
## 46 Mango Pint Low_fat Not_organic
## 47 Mango Pint No_low_fat Organic
## 48 Mango Pint No_low_fat Not_organic
## 49 Vanilla Homemade_waffle Low_fat Organic
## 50 Vanilla Homemade_waffle Low_fat Not_organic
## 51 Vanilla Homemade_waffle No_low_fat Organic
## 52 Vanilla Homemade_waffle No_low_fat Not_organic
## 53 Vanilla Cone Low_fat Organic
## 54 Vanilla Cone Low_fat Not_organic
## 55 Vanilla Cone No_low_fat Organic
## 56 Vanilla Cone No_low_fat Not_organic
## 57 Vanilla Pint Low_fat Organic
## 58 Vanilla Pint Low_fat Not_organic
## 59 Vanilla Pint No_low_fat Organic
## 60 Vanilla Pint No_low_fat Not_organicLook at the output under the header Design efficiency. It shows 52 rows. The rows represent experimental designs with different numbers of Trials or different numbers of ice creams (i.e., attribute level combinations) that would be tested. A better word for trial is profile. For each experimental design, it shows the D-efficiency of the design — a measure of how cleanly we will be able to estimate the effects of interest after running the experiment (higher scores are better) — and whether or not the design is balanced — whether each level is included in the same number of trials or profiles. Ideally, we’re looking for balanced designs with a high D-efficiency (above 0.80 is considered reasonable). We get two candidates, an experimental design with 60 profiles, which is just the full factorial design, or a design with 30 profiles. Let’s have a look at the design with 30 profiles:
summary(doe(attributes, seed = 123, trials = 30))## Experimental design
## # trials for partial factorial: 30
## # trials for full factorial : 60
## Random seed : 123
##
## Attributes and levels:
## Flavor: Raspberry, Chocolate, Strawberry, Mango, Vanilla
## Package: Homemade_waffle, Cone, Pint
## Light: Low_fat, No_low_fat
## Organic: Organic, Not_organic
##
## Design efficiency:
## Trials D-efficiency Balanced
## 30 0.984 TRUE
##
## Partial factorial design correlations:
## ** Note: Variables are assumed to be ordinal **
## Flavor Package Light Organic
## Flavor 1 0 0.000 0.000
## Package 0 1 0.000 0.000
## Light 0 0 1.000 -0.105
## Organic 0 0 -0.105 1.000
##
## Partial factorial design:
## trial Flavor Package Light Organic
## 1 Raspberry Homemade_waffle Low_fat Organic
## 4 Raspberry Homemade_waffle No_low_fat Not_organic
## 6 Raspberry Cone Low_fat Not_organic
## 7 Raspberry Cone No_low_fat Organic
## 10 Raspberry Pint Low_fat Not_organic
## 11 Raspberry Pint No_low_fat Organic
## 13 Chocolate Homemade_waffle Low_fat Organic
## 14 Chocolate Homemade_waffle Low_fat Not_organic
## 19 Chocolate Cone No_low_fat Organic
## 20 Chocolate Cone No_low_fat Not_organic
## 22 Chocolate Pint Low_fat Not_organic
## 23 Chocolate Pint No_low_fat Organic
## 26 Strawberry Homemade_waffle Low_fat Not_organic
## 28 Strawberry Homemade_waffle No_low_fat Not_organic
## 29 Strawberry Cone Low_fat Organic
## 32 Strawberry Cone No_low_fat Not_organic
## 33 Strawberry Pint Low_fat Organic
## 35 Strawberry Pint No_low_fat Organic
## 39 Mango Homemade_waffle No_low_fat Organic
## 40 Mango Homemade_waffle No_low_fat Not_organic
## 41 Mango Cone Low_fat Organic
## 42 Mango Cone Low_fat Not_organic
## 46 Mango Pint Low_fat Not_organic
## 47 Mango Pint No_low_fat Organic
## 49 Vanilla Homemade_waffle Low_fat Organic
## 51 Vanilla Homemade_waffle No_low_fat Organic
## 53 Vanilla Cone Low_fat Organic
## 56 Vanilla Cone No_low_fat Not_organic
## 58 Vanilla Pint Low_fat Not_organic
## 60 Vanilla Pint No_low_fat Not_organic
##
## Estimable effects from partial factorial design:
##
## Flavor|Chocolate
## Flavor|Strawberry
## Flavor|Mango
## Flavor|Vanilla
## Package|Cone
## Package|Pint
## Light|No_low_fat
## Organic|Not_organic
## Flavor|Chocolate:Package|Cone
## Flavor|Strawberry:Package|Cone
## Flavor|Mango:Package|Cone
## Flavor|Vanilla:Package|Cone
## Flavor|Chocolate:Package|Pint
## Flavor|Strawberry:Package|Pint
## Flavor|Mango:Package|Pint
## Flavor|Vanilla:Package|Pint
## Flavor|Chocolate:Light|No_low_fat
## Flavor|Strawberry:Light|No_low_fat
## Flavor|Mango:Light|No_low_fat
## Flavor|Vanilla:Light|No_low_fat
## Package|Cone:Light|No_low_fat
## Package|Pint:Light|No_low_fat
## Flavor|Chocolate:Organic|Not_organic
## Flavor|Strawberry:Organic|Not_organic
## Flavor|Mango:Organic|Not_organic
## Flavor|Vanilla:Organic|Not_organic
## Package|Cone:Organic|Not_organic
## Light|No_low_fat:Organic|Not_organic
## Flavor|Strawberry:Package|Pint:Light|No_low_fat
##
## Full factorial design:
## trial Flavor Package Light Organic
## 1 Raspberry Homemade_waffle Low_fat Organic
## 2 Raspberry Homemade_waffle Low_fat Not_organic
## 3 Raspberry Homemade_waffle No_low_fat Organic
## 4 Raspberry Homemade_waffle No_low_fat Not_organic
## 5 Raspberry Cone Low_fat Organic
## 6 Raspberry Cone Low_fat Not_organic
## 7 Raspberry Cone No_low_fat Organic
## 8 Raspberry Cone No_low_fat Not_organic
## 9 Raspberry Pint Low_fat Organic
## 10 Raspberry Pint Low_fat Not_organic
## 11 Raspberry Pint No_low_fat Organic
## 12 Raspberry Pint No_low_fat Not_organic
## 13 Chocolate Homemade_waffle Low_fat Organic
## 14 Chocolate Homemade_waffle Low_fat Not_organic
## 15 Chocolate Homemade_waffle No_low_fat Organic
## 16 Chocolate Homemade_waffle No_low_fat Not_organic
## 17 Chocolate Cone Low_fat Organic
## 18 Chocolate Cone Low_fat Not_organic
## 19 Chocolate Cone No_low_fat Organic
## 20 Chocolate Cone No_low_fat Not_organic
## 21 Chocolate Pint Low_fat Organic
## 22 Chocolate Pint Low_fat Not_organic
## 23 Chocolate Pint No_low_fat Organic
## 24 Chocolate Pint No_low_fat Not_organic
## 25 Strawberry Homemade_waffle Low_fat Organic
## 26 Strawberry Homemade_waffle Low_fat Not_organic
## 27 Strawberry Homemade_waffle No_low_fat Organic
## 28 Strawberry Homemade_waffle No_low_fat Not_organic
## 29 Strawberry Cone Low_fat Organic
## 30 Strawberry Cone Low_fat Not_organic
## 31 Strawberry Cone No_low_fat Organic
## 32 Strawberry Cone No_low_fat Not_organic
## 33 Strawberry Pint Low_fat Organic
## 34 Strawberry Pint Low_fat Not_organic
## 35 Strawberry Pint No_low_fat Organic
## 36 Strawberry Pint No_low_fat Not_organic
## 37 Mango Homemade_waffle Low_fat Organic
## 38 Mango Homemade_waffle Low_fat Not_organic
## 39 Mango Homemade_waffle No_low_fat Organic
## 40 Mango Homemade_waffle No_low_fat Not_organic
## 41 Mango Cone Low_fat Organic
## 42 Mango Cone Low_fat Not_organic
## 43 Mango Cone No_low_fat Organic
## 44 Mango Cone No_low_fat Not_organic
## 45 Mango Pint Low_fat Organic
## 46 Mango Pint Low_fat Not_organic
## 47 Mango Pint No_low_fat Organic
## 48 Mango Pint No_low_fat Not_organic
## 49 Vanilla Homemade_waffle Low_fat Organic
## 50 Vanilla Homemade_waffle Low_fat Not_organic
## 51 Vanilla Homemade_waffle No_low_fat Organic
## 52 Vanilla Homemade_waffle No_low_fat Not_organic
## 53 Vanilla Cone Low_fat Organic
## 54 Vanilla Cone Low_fat Not_organic
## 55 Vanilla Cone No_low_fat Organic
## 56 Vanilla Cone No_low_fat Not_organic
## 57 Vanilla Pint Low_fat Organic
## 58 Vanilla Pint Low_fat Not_organic
## 59 Vanilla Pint No_low_fat Organic
## 60 Vanilla Pint No_low_fat Not_organicUnder Partial factorial design (or fractional factorial design), we find the profiles that we could run in an experiment with 30 instead of 60 profiles. Under Partial factorial design correlations, we see that two attributes are correlated, namely Light and Organic (r = -0.105). This will always be the case in fractional factorial designs. It means that some combinations of attribute levels will be more prevalent than others. Only in a full factorial design will all attributes be uncorrelated or orthogonal.
A possible design with only 10 profiles would be unbalanced and would look like this:
summary(doe(attributes, seed = 123, trials = 10))## Experimental design
## # trials for partial factorial: 10
## # trials for full factorial : 60
## Random seed : 123
##
## Attributes and levels:
## Flavor: Raspberry, Chocolate, Strawberry, Mango, Vanilla
## Package: Homemade_waffle, Cone, Pint
## Light: Low_fat, No_low_fat
## Organic: Organic, Not_organic
##
## Design efficiency:
## Trials D-efficiency Balanced
## 10 0.389 FALSE
##
## Partial factorial design correlations:
## ** Note: Variables are assumed to be ordinal **
## Flavor Package Light Organic
## Flavor 1.000 0.121 0.000 0.000
## Package 0.121 1.000 0.000 0.000
## Light 0.000 0.000 1.000 0.309
## Organic 0.000 0.000 0.309 1.000
##
## Partial factorial design:
## trial Flavor Package Light Organic
## 4 Raspberry Homemade_waffle No_low_fat Not_organic
## 5 Raspberry Cone Low_fat Organic
## 20 Chocolate Cone No_low_fat Not_organic
## 21 Chocolate Pint Low_fat Organic
## 25 Strawberry Homemade_waffle Low_fat Organic
## 36 Strawberry Pint No_low_fat Not_organic
## 39 Mango Homemade_waffle No_low_fat Organic
## 46 Mango Pint Low_fat Not_organic
## 50 Vanilla Homemade_waffle Low_fat Not_organic
## 59 Vanilla Pint No_low_fat Organic
##
## Estimable effects from partial factorial design:
##
## Flavor|Chocolate
## Flavor|Strawberry
## Flavor|Mango
## Flavor|Vanilla
## Package|Cone
## Package|Pint
## Light|No_low_fat
## Organic|Not_organic
## Flavor|Chocolate:Package|Cone
##
## Full factorial design:
## trial Flavor Package Light Organic
## 1 Raspberry Homemade_waffle Low_fat Organic
## 2 Raspberry Homemade_waffle Low_fat Not_organic
## 3 Raspberry Homemade_waffle No_low_fat Organic
## 4 Raspberry Homemade_waffle No_low_fat Not_organic
## 5 Raspberry Cone Low_fat Organic
## 6 Raspberry Cone Low_fat Not_organic
## 7 Raspberry Cone No_low_fat Organic
## 8 Raspberry Cone No_low_fat Not_organic
## 9 Raspberry Pint Low_fat Organic
## 10 Raspberry Pint Low_fat Not_organic
## 11 Raspberry Pint No_low_fat Organic
## 12 Raspberry Pint No_low_fat Not_organic
## 13 Chocolate Homemade_waffle Low_fat Organic
## 14 Chocolate Homemade_waffle Low_fat Not_organic
## 15 Chocolate Homemade_waffle No_low_fat Organic
## 16 Chocolate Homemade_waffle No_low_fat Not_organic
## 17 Chocolate Cone Low_fat Organic
## 18 Chocolate Cone Low_fat Not_organic
## 19 Chocolate Cone No_low_fat Organic
## 20 Chocolate Cone No_low_fat Not_organic
## 21 Chocolate Pint Low_fat Organic
## 22 Chocolate Pint Low_fat Not_organic
## 23 Chocolate Pint No_low_fat Organic
## 24 Chocolate Pint No_low_fat Not_organic
## 25 Strawberry Homemade_waffle Low_fat Organic
## 26 Strawberry Homemade_waffle Low_fat Not_organic
## 27 Strawberry Homemade_waffle No_low_fat Organic
## 28 Strawberry Homemade_waffle No_low_fat Not_organic
## 29 Strawberry Cone Low_fat Organic
## 30 Strawberry Cone Low_fat Not_organic
## 31 Strawberry Cone No_low_fat Organic
## 32 Strawberry Cone No_low_fat Not_organic
## 33 Strawberry Pint Low_fat Organic
## 34 Strawberry Pint Low_fat Not_organic
## 35 Strawberry Pint No_low_fat Organic
## 36 Strawberry Pint No_low_fat Not_organic
## 37 Mango Homemade_waffle Low_fat Organic
## 38 Mango Homemade_waffle Low_fat Not_organic
## 39 Mango Homemade_waffle No_low_fat Organic
## 40 Mango Homemade_waffle No_low_fat Not_organic
## 41 Mango Cone Low_fat Organic
## 42 Mango Cone Low_fat Not_organic
## 43 Mango Cone No_low_fat Organic
## 44 Mango Cone No_low_fat Not_organic
## 45 Mango Pint Low_fat Organic
## 46 Mango Pint Low_fat Not_organic
## 47 Mango Pint No_low_fat Organic
## 48 Mango Pint No_low_fat Not_organic
## 49 Vanilla Homemade_waffle Low_fat Organic
## 50 Vanilla Homemade_waffle Low_fat Not_organic
## 51 Vanilla Homemade_waffle No_low_fat Organic
## 52 Vanilla Homemade_waffle No_low_fat Not_organic
## 53 Vanilla Cone Low_fat Organic
## 54 Vanilla Cone Low_fat Not_organic
## 55 Vanilla Cone No_low_fat Organic
## 56 Vanilla Cone No_low_fat Not_organic
## 57 Vanilla Pint Low_fat Organic
## 58 Vanilla Pint Low_fat Not_organic
## 59 Vanilla Pint No_low_fat Organic
## 60 Vanilla Pint No_low_fat Not_organicCompared to the design with 30 profiles, there are now more and stronger correlations between the attributes.
Note that the profiles are not exactly the same as those in the experiment that was used to collect the ice cream data. This is because, for unbalanced designs, there is some randomness involved in setting the actual attribute level combinations. That is also why we set seed = 123. seed is used to fix R’s random number generator. Setting it to a fixed number (123 or 456 or something else) will make sure that R generates the same output every time. Without setting the seed, doe with trials = 10 would not give the same fractional design every time you run it.
Also note that the radiant package installs an add-in that you can access via Addins (find this button on the right of the row below ‘File’ etc.) -> Start radiant (browser). This will open an app in your browser that will allow you to carry out the steps above in an intuitive visual interface. For help on this, check out Radiant’s discussion of their Design of Experiments module here.