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_organic

Look 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_organic

Under 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_organic

Compared 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.