Multivariate exploration of the questionnaire and typology of the surveyed people The results are provided by the EnQuireR package July 28, 2010
Contents 1 Quick overview of the questionnaire
3
2 Multivariate exploration of the questionnaire 2.1 Graphical representations of the questionnaire . . 2.2 Highlights on the two principal axes of variability 2.2.1 First axis . . . . . . . . . . . . . . . . . . 2.2.2 Second axis . . . . . . . . . . . . . . . . .
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3 Typology on the individuals 3.1 Choice of the number of clusters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Simultaneous comparison of the clusters with respect with the most relevant variables 3.2.1 Number of individuals by cluster for the variable savoured.alone . . . . . . 3.2.2 Number of individuals by cluster for the variable frequency.eat.chocolate . 3.2.3 Number of individuals by cluster for the variable When . . . . . . . . . . . 3.2.4 Number of individuals by cluster for the variable frequency.buy.chocolate . 3.2.5 Number of individuals by cluster for the variable keep.chocolate . . . . . . 3.2.6 Number of individuals by cluster for the variable Where . . . . . . . . . . 3.2.7 Number of individuals by cluster for the variable handle.lack.of.chocolate . 3.2.8 Number of individuals by cluster for the variable savoured.with.people . . 3.2.9 Number of individuals by cluster for the variable sex . . . . . . . . . . . . 3.2.10 Number of individuals by cluster for the variable inspires.relaxation . . . . 3.3 Automatic description of each cluster . . . . . . . . . . . . . . . . . . . . . . . . . .
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List of Figures 1 2 3 4 5 6 7 8 9 10 11 12 13 14
Representations of the individuals and of the categories on axes 1 and 2 . . . . . . Representation of the individuals using density curbs and enhanced representation of the categories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Number of clusters chosen by the analyst; representation of the individuals according to their cluster . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Centers of gravity with confidence ellipses; representation of the individuals according to their cluster with density curbs . . . . . . . . . . . . . . . . . . . . . . . . . Number of individuals per cluster . . . . . . . . . . . . . . . . . . . . . . . . . . . . Variable savoured.alone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Variable frequency.eat.chocolate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Variable When . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Variable frequency.buy.chocolate . . . . . . . . . . . . . . . . . . . . . . . . . . . . Variable keep.chocolate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Variable Where . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Variable handle.lack.of.chocolate . . . . . . . . . . . . . . . . . . . . . . . . . . . . Variable savoured.with.people . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Variable sex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
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15
Variable inspires.relaxation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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1
Quick overview of the questionnaire
The analysis was performed on 120 individuals described by 13 variables: •
frequency.buy.chocolate ten )
( never ,
often ,
rarely ,
sometimes ,
very of-
•
frequency.eat.chocolate ( many times a day , many times a week , never , once a month , once a week )
•
handle.lack.of.chocolate ( absolutely , pretty much , sometimes , almost never , never )
•
kind.chocolate ( almond chocolate , black chocolate , lined chocolate , milk chocolate , white chocolate )
•
kind.brands ( discount , retailer , upmarket , well-known )
•
buy.fair.chocolate ( never , rarely , sometimes , often , always )
•
Where ( bed , dining room , others , outside , TV , work )
•
When ( after meal , after work , before sleep , snack , working )
•
side.drink ( alcohol , coffee , juices , nothing , tea , water , with milk )
•
savoured.alone ( disagree , slightly disagree , neither agree nor disagree , slightly agree , agree )
•
savoured.with.people ( disagree , slightly disagree , neither agree nor disagree , slightly agree , agree )
• •
cooking chocolate ,
keep.chocolate ( cupboard , fridge ) eaten.without.other.food ( disagree , slightly disagree , neither agree nor disagree , slightly agree , agree )
Moreover, the dataset contained 0% of missing values.
3
2
Multivariate exploration of the questionnaire
2.1
Graphical representations of the questionnaire
The following results are obtained by performing a Multiple Correspondence Analysis (MCA) on the previous 13 variables. This method provides two important graphical displays, a representation of the individuals (surveyed people) and a representation of the categories (answers given by the surveyed people). The first two main axes of variability explain 11.36% of the information contained in the dataset (6.06% for the first factorial axis and 5.3% for the second one). In some cases the analyst may want to introduce supplementary quantitative variables.
MCA factor map 2.0
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MCA factor map
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frequency.buy.chocolate_very often handle.lack.of.chocolate_never
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handle.lack.of.chocolate_absolutely eaten.without.other.food_disagree dining room savoured.alone_slightly disagree others inspires.relaxation_yes almond chocolate handle.lack.of.chocolate_pretty much snack frequency.buy.chocolate_sometimes inspires.energy_yes coffee with milk juices inspires.escape_yes eaten.without.other.food_slightly disagree
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inspires.comfort_yes savoured.with.people_agree eaten.without.other.food_neither nothing agree nor disagree 25−35 buy.fair.chocolate_often basic inspires.voluptuousness_yes TV milk chocolate buy.fair.chocolate_sometimes frequency.buy.chocolate_often savoured.with.people_disagree daily retailer inspires.relaxation_no handle.lack.of.chocolate_almost after meal never Man inspires.escape_no inspires.weakness.for.sweet.things_no blackinspires.pleasure_yes chocolate inspires.energy_no well−known inspires.guilt_no savoured.with.people_slightly agree bed savoured.alone_slightly inspires.voluptuousness_no Woman 15−25 agree many times a inspires.weakness.for.sweet.things_yes week savoured.alone_disagree handle.lack.of.chocolate_sometimes once a month savoured.alone_neither agree nor disagree ● inspires.pleasure_no savoured.with.people_neither agree nor disagree buy.fair.chocolate_rarely noble cupboard buy.fair.chocolate_never once a weekdisagree frequency.buy.chocolate_rarely savoured.with.people_slightly teainspires.comfort_no eaten.without.other.food_slightly agree upmarket inspires.guilt_yes
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Figure 1: Representations of the individuals and of the categories on axes 1 and 2
MCA factor map
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35−45 many times a day frequency.buy.chocolate_very often handle.lack.of.chocolate_never
fridge work working eaten.without.other.food_agree inspires.comfort_yes eaten.without.other.food_neither nothing agree nor disagree inspires.voluptuousness_yes TV frequency.buy.chocolate_often savoured.with.people_disagree inspires.relaxation_no Man handle.lack.of.chocolate_almost never inspires.escape_no inspires.weakness.for.sweet.things_no well−known savoured.with.people_slightly agree bed inspires.voluptuousness_no Woman inspires.weakness.for.sweet.things_yes 15−25 many times a week once a month savoured.alone_neither agree agree nor disagree ● savoured.with.people_neither nor disagree cupboard frequency.buy.chocolate_rarely inspires.comfort_no upmarket handle.lack.of.chocolate_absolutely eaten.without.other.food_disagree dining room savoured.alone_slightly disagree inspires.relaxation_yes almond chocolate handle.lack.of.chocolate_pretty much snack frequency.buy.chocolate_sometimes coffee inspires.escape_yes eaten.without.other.food_slightly disagree
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savoured.alone_agree
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Figure 2: Representation of the individuals using density curbs and enhanced representation of the categories
4
2.2 2.2.1
Highlights on the two principal axes of variability Characterization of the first factorial axis
The most meaningful variables characterizing the first factorial axis are: •
frequency.eat.chocolate
•
handle.lack.of.chocolate
•
frequency.buy.chocolate
•
side.drink
•
When
•
kind.chocolate
•
keep.chocolate
•
eaten.without.other.food
•
buy.fair.chocolate
•
savoured.alone
•
Where
The most meaningful categories characterizing the positive side of the first axis are: •
handle.lack.of.chocolate_absolutely – Contribution: 13.91 – V-Test: 7.84 – Frequency in the population: 15 %
•
frequency.eat.chocolate_never – Contribution: 9.31 – V-Test: 6.01 – Frequency in the population: 3.33 %
•
frequency.buy.chocolate_rarely – Contribution: 10.92 – V-Test: 7.16 – Frequency in the population: 20 %
•
alcohol – Contribution: 6.49 – V-Test: 4.96 – Frequency in the population: 0.83 %
•
frequency.buy.chocolate_never – Contribution: 2.65 – V-Test: 3.19 – Frequency in the population: 2.5 %
•
white chocolate – Contribution: 3.17 5
– V-Test: 3.48 – Frequency in the population: 1.67 % •
buy.fair.chocolate_always – Contribution: 2.94 – V-Test: 3.35 – Frequency in the population: 1.67 %
•
working – Contribution: 2.77 – V-Test: 3.5 – Frequency in the population: 15 %
•
savoured.alone_agree – Contribution: 2.71 – V-Test: 3.35 – Frequency in the population: 9.17 %
•
fridge – Contribution: 2.51 – V-Test: 3.27 – Frequency in the population: 11.67 %
The most meaningful categories characterizing the negative side of the first axis are: •
frequency.eat.chocolate_many times a week – Contribution: 5.42 – V-Test: -5.82 – Frequency in the population: 40 %
•
frequency.buy.chocolate_often – Contribution: 2.53 – V-Test: -3.87 – Frequency in the population: 36.67 %
•
frequency.eat.chocolate_many times a day – Contribution: 0.92 – V-Test: -1.92 – Frequency in the population: 5.83 %
•
frequency.buy.chocolate_very often – Contribution: 1.96 – V-Test: -2.89 – Frequency in the population: 11.67 %
•
tea – Contribution: 1.29 – V-Test: -2.45 – Frequency in the population: 19.17 % 6
•
handle.lack.of.chocolate_almost never – Contribution: 2.1 – V-Test: -3.41 – Frequency in the population: 32.5 %
•
handle.lack.of.chocolate_never – Contribution: 1.54 – V-Test: -2.53 – Frequency in the population: 10 %
•
nothing – Contribution: 0.02 – V-Test: 0.37 – Frequency in the population: 51.67 %
•
handle.lack.of.chocolate_sometimes – Contribution: 1.19 – V-Test: -2.44 – Frequency in the population: 25 %
•
frequency.buy.chocolate_sometimes – Contribution: 0.3 – V-Test: -1.26 – Frequency in the population: 29.17 %
2.2.2
Characterization on the second factorial axis
The most meaningful variables characterizing the second factorial axis are: •
handle.lack.of.chocolate
•
frequency.buy.chocolate
•
side.drink
•
kind.chocolate
•
When
•
eaten.without.other.food
•
keep.chocolate
•
frequency.eat.chocolate
•
savoured.with.people
•
savoured.alone
•
kind.brands
•
Where
•
buy.fair.chocolate
The most meaningful categories characterizing the positive side of the second axis are: 7
•
handle.lack.of.chocolate_never – Contribution: 12.99 – V-Test: 6.88 – Frequency in the population: 10 %
•
frequency.buy.chocolate_very often – Contribution: 10.82 – V-Test: 6.34 – Frequency in the population: 11.67 %
•
white chocolate – Contribution: 9.41 – V-Test: 5.6 – Frequency in the population: 1.67 %
•
alcohol – Contribution: 6.05 – V-Test: 4.47 – Frequency in the population: 0.83 %
•
eaten.without.other.food_agree – Contribution: 3.77 – V-Test: 4.02 – Frequency in the population: 23.33 %
•
fridge – Contribution: 3.54 – V-Test: 3.62 – Frequency in the population: 11.67 %
•
savoured.with.people_agree – Contribution: 3.85 – V-Test: 3.75 – Frequency in the population: 10 %
•
TV – Contribution: 2.62 – V-Test: 3.64 – Frequency in the population: 35 %
•
before sleep – Contribution: 2.67 – V-Test: 3.01 – Frequency in the population: 3.33 %
•
frequency.eat.chocolate_many times a day – Contribution: 3.03 – V-Test: 3.25 – Frequency in the population: 5.83 % 8
The most meaningful categories characterizing the negative side of the second axis are: •
snack – Contribution: 3.79 – V-Test: -4.14 – Frequency in the population: 27.5 %
•
almond chocolate – Contribution: 1.07 – V-Test: -2.14 – Frequency in the population: 23.33 %
•
handle.lack.of.chocolate_pretty much – Contribution: 2.08 – V-Test: -2.87 – Frequency in the population: 17.5 %
•
milk chocolate – Contribution: 0.2 – V-Test: -1.01 – Frequency in the population: 36.67 %
•
juices – Contribution: 2.36 – V-Test: -2.86 – Frequency in the population: 5.83 %
•
savoured.alone_neither agree nor disagree – Contribution: 1.94 – V-Test: -3.42 – Frequency in the population: 45.83 %
•
cupboard – Contribution: 0.47 – V-Test: -3.62 – Frequency in the population: 88.33 %
•
savoured.with.people_neither agree nor disagree – Contribution: 1.74 – V-Test: -3.17 – Frequency in the population: 43.33 %
•
coffee – Contribution: 1.87 – V-Test: -2.66 – Frequency in the population: 13.33 %
•
frequency.eat.chocolate_once a week – Contribution: 1.48 – V-Test: -2.65 – Frequency in the population: 30.83 %
9
3
Typology on the individuals
3.1
Choice of the number of clusters
The ascendant hierarchical clustering (AHC) lead to a partition made of 3 clusters. Those clusters are displayed in the following representations: a graphical representation of the individuals according to the cluster they belong to, a representation of the center of gravity of each group enhanced by a confidence ellipse, a representation of the individuals according to the cluster they belong to by the use of density curbs.
MCA factor map 1.5
Choice of the number of clusters by cutting the dendrogram 1 2 3
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Figure 3: Number of clusters chosen by the analyst; representation of the individuals according to their cluster
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Figure 4: Centers of gravity with confidence ellipses; representation of the individuals according to their cluster with density curbs
number of individuals by groups
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Figure 5: Number of individuals per cluster
11
3.2 3.2.1
Simultaneous comparison of the clusters with respect with the most relevant variables Number of individuals by cluster for the variable savoured.alone
savoured.alone by cluster 80 1st bar: savoured.alone_disagree 2nd bar: savoured.alone_slightly disagree 3rd bar: savoured.alone_neither agree nor disagree 4 th bar: savoured.alone_slightly agree 5 th bar: savoured.alone_agree 60
40
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group 2
Figure 6: Variable savoured.alone
12
group 3
3.2.2
Number of individuals by cluster for the variable frequency.eat.chocolate
frequency.eat.chocolate by cluster
1st bar: many times a day 2nd bar: many times a week 3rd bar: once a month 4 th bar: once a week
60
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Figure 7: Variable frequency.eat.chocolate
13
3.2.3
Number of individuals by cluster for the variable When
When by cluster 60 1st bar: after meal 2nd bar: snack 3rd bar: working 50
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Figure 8: Variable When
14
group 3
3.2.4
Number of individuals by cluster for the variable frequency.buy.chocolate
frequency.buy.chocolate by cluster
1st bar: frequency.buy.chocolate_often 2nd bar: frequency.buy.chocolate_rarely 3rd bar: frequency.buy.chocolate_sometimes 4 th bar: frequency.buy.chocolate_very often
60
50
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Figure 9: Variable frequency.buy.chocolate
15
3.2.5
Number of individuals by cluster for the variable keep.chocolate
keep.chocolate by cluster
1st bar: cupboard 2nd bar: fridge
80
60
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group 2
Figure 10: Variable keep.chocolate
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group 3
3.2.6
Number of individuals by cluster for the variable Where
Where by cluster
70
1st bar: bed 2nd bar: dining room 3rd bar: others 4 th bar: TV 5 th bar: work
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Figure 11: Variable Where
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group 3
3.2.7
Number of individuals by cluster for the variable handle.lack.of.chocolate
handle.lack.of.chocolate by cluster 60 1st bar: handle.lack.of.chocolate_absolutely 2nd bar: handle.lack.of.chocolate_pretty much 3rd bar: handle.lack.of.chocolate_sometimes 4 th bar: handle.lack.of.chocolate_almost never 5 th bar: handle.lack.of.chocolate_never
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Figure 12: Variable handle.lack.of.chocolate
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3.2.8
Number of individuals by cluster for the variable savoured.with.people
savoured.with.people by cluster 70
60
1st bar: savoured.with.people_disagree 2nd bar: savoured.with.people_slightly disagree 3rd bar: savoured.with.people_neither agree nor disagree 4 th bar: savoured.with.people_slightly agree 5 th bar: savoured.with.people_agree
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Figure 13: Variable savoured.with.people
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3.2.9
Number of individuals by cluster for the variable sex
sex by cluster
1st bar: Man 2nd bar: Woman
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Figure 14: Variable sex
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group 3
3.2.10
Number of individuals by cluster for the variable inspires.relaxation
inspires.relaxation by cluster
1st bar: inspires.relaxation_no 2nd bar: inspires.relaxation_yes
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Figure 15: Variable inspires.relaxation
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group 3
3.3
Automatic description of each cluster
The cluster 1 (19 individuals) includes the individuals possessing the following categories: •
savoured.alone=savoured.alone_agree 9.17 % of the individuals possess this category in the global population versus 52.63 % in the cluster 1 . Moreover, 90.91 % of the individuals possessing this category belong to the cluster 1 .
•
When=working 15.83 % of the individuals possess this category in the global population versus 57.89 % in the cluster 1 . Moreover, 57.89 % of the individuals possessing this category belong to the cluster 1 .
•
frequency.eat.chocolate=once a month 20.83 % of the individuals possess this category in the global population versus 63.16 % in the cluster 1 . Moreover, 48 % of the individuals possessing this category belong to the cluster 1 .
•
keep.chocolate=fridge 11.67 % of the individuals possess this category in the global population versus 47.37 % in the cluster 1 . Moreover, 64.29 % of the individuals possessing this category belong to the cluster 1 .
•
frequency.buy.chocolate=frequency.buy.chocolate_rarely 20 % of the individuals possess this category in the global population versus 57.89 % in the cluster 1 . Moreover, 45.83 % of the individuals possessing this category belong to the cluster 1 .
•
sex=Man 21.67 % of the individuals possess this category in the global population versus 57.89 % in the cluster 1 . Moreover, 42.31 % of the individuals possessing this category belong to the cluster 1 .
•
handle.lack.of.chocolate=handle.lack.of.chocolate_absolutely 15 % of the individuals possess this category in the global population versus 47.37 % in the cluster 1 . Moreover, 50 % of the individuals possessing this category belong to the cluster 1 .
•
Where=bed 5.83 % of the individuals possess this category in the global population versus 26.32 % in the cluster 1 . Moreover, 71.43 % of the individuals possessing this category belong to the cluster 1 .
•
side.drink=nothing 52.5 % of the individuals possess this category in the global population versus 78.95 % in the cluster 1 . Moreover, 23.81 % of the individuals possessing this category belong to the cluster 1 .
•
Where=work 9.17 % of the individuals possess this category in the global population versus 26.32 % in the cluster 1 . Moreover, 45.45 % of the individuals possessing this category belong to the cluster 1 .
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The cluster 2 (75 individuals) includes the individuals possessing the following categories: •
savoured.alone=savoured.alone_neither agree nor disagree 45.83 % of the individuals possess this category in the global population versus 61.33 % in the cluster 2 . Moreover, 83.64 % of the individuals possessing this category belong to the cluster 2 .
•
Where=dining room 39.17 % of the individuals possess this category in the global population versus 52 % in the cluster 2 . Moreover, 82.98 % of the individuals possessing this category belong to the cluster 2 .
•
frequency.buy.chocolate=frequency.buy.chocolate_often 38.33 % of the individuals possess this category in the global population versus 50.67 % in the cluster 2 . Moreover, 82.61 % of the individuals possessing this category belong to the cluster 2 .
•
keep.chocolate=cupboard 88.33 % of the individuals possess this category in the global population versus 96 % in the cluster 2 . Moreover, 67.92 % of the individuals possessing this category belong to the cluster 2 .
•
inspires.relaxation=inspires.relaxation_yes 18.33 % of the individuals possess this category in the global population versus 26.67 % in the cluster 2 . Moreover, 90.91 % of the individuals possessing this category belong to the cluster 2 .
•
frequency.eat.chocolate=many times a week 41.67 % of the individuals possess this category in the global population versus 52 % in the cluster 2 . Moreover, 78 % of the individuals possessing this category belong to the cluster 2 .
•
When=snack 28.33 % of the individuals possess this category in the global population versus 37.33 % in the cluster 2 . Moreover, 82.35 % of the individuals possessing this category belong to the cluster 2 .
The cluster 3 (26 individuals) includes the individuals possessing the following categories: •
savoured.alone=savoured.alone_disagree 10.83 % of the individuals possess this category in the global population versus 50 % in the cluster 3 . Moreover, 100 % of the individuals possessing this category belong to the cluster 3 .
•
savoured.with.people=savoured.with.people_agree 10 % of the individuals possess this category in the global population versus 42.31 % in the cluster 3 . Moreover, 91.67 % of the individuals possessing this category belong to the cluster 3 .
•
frequency.eat.chocolate=many times a day 5.83 % of the individuals possess this category in the global population versus 26.92 % in the cluster 3 . Moreover, 100 % of the individuals possessing this category belong to the cluster 3 . 23
•
handle.lack.of.chocolate=handle.lack.of.chocolate_never 10 % of the individuals possess this category in the global population versus 34.62 % in the cluster 3 . Moreover, 75 % of the individuals possessing this category belong to the cluster 3 .
•
frequency.buy.chocolate=frequency.buy.chocolate_very often 11.67 % of the individuals possess this category in the global population versus 34.62 % in the cluster 3 . Moreover, 64.29 % of the individuals possessing this category belong to the cluster 3 .
•
When=after meal 55.83 % of the individuals possess this category in the global population versus 84.62 % in the cluster 3 . Moreover, 32.84 % of the individuals possessing this category belong to the cluster 3 .
•
inspires.relaxation=inspires.relaxation_no 81.67 % of the individuals possess this category in the global population versus 96.15 % in the cluster 3 . Moreover, 25.51 % of the individuals possessing this category belong to the cluster 3 .
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