1. Correspondence Maps

2. Correspondence Map - Motivation
A picture is worth a thousand words.

3. Another example – a bit dated.

4. Correspondence Map - Business Needs
To understand consumers’ perceptions of different brands in the market
To understand the perception of a brand amongst different market segments
A correspondence map
Is an approach to portray categorical data in two dimensions (maps).
Visually displays relationships in a contingency table
Can show both brands and attributes in the same plot
Can demonstrate opportunities for brand re-positioning

5. Correspondence Map - Data Needs
Is appropriate for frequency data
Works with checklist (binary) or “top box” data from scaled questions
Can combine data gathered in different questionnaires
Needs at least three brands/segments as columns in the contingency table
Our research on research study finds that magnetic board question type gives far fewer associations than radio button and visual grid question types, but all yield similar correspondence maps.
From VCU:
Whitepaper: Better Engagement, Better Data – An Exploration of Multi Choice Visual Questions
Whitepaper: Better Engagement, Better Data – What Works Better, Scaled or Binary Brand Ratings?

6. Correspondence Map – Data Needs (Binary question types for Brand Association Questions)
Visual Grid
Radio Buttons
Magnetic Board

7. Correspondence Maps - Methodology
“Correspondence analysis uses one of the most basic statistical concepts, chi-square, to standardize the cell frequency values of the contingency table and form the basis for association or similarity. Chi-square is a standardized measure of actual cell frequencies compared to expected cell frequencies. In cross-tabulated data, each cell contains the values for a specific row/column combination. The chi-square procedure proceeds to calculate a chi-square value for each cell and then transform it into a measure of association.”
Adapted from Multivariate Data Analysis, Sixth Edition by Hair, Black, Babin, Anderson, Tathan, Pearson International

8. Correspondence Maps - Methodology
Consider the following cross-tabulation of attribute ratings by brand:
Brand A
Brand B
Brand C
Row Total
Innovative 63 73 83
219
Conservative 48 42
138
Brave 27 38 52
117
Creative 55 68 78
201
Stylish 56 65
176
Optimistic 40 47
139
Friendly 77
218
Boring 18 19
Environmentally responsible 51 62
161
Trustworthy 90 88 98
276
Intelligent 54 61 80
195
Professional 71
110
271
Efficient 75 86
106
267
Column Total
725
783
926
2434

9. Correspondence Maps - Methodology
Expected Values*
If there is no relationship between brands and attributes, the brand association ratings would be proportional to row/column totals
For example, the expected rating for Brand A on the “innovative” attribute=219*725/2434= The expected rating for Brand C on the “Efficient” attribute=267*926/2434=
Brand A
Brand B
Brand C
Row Total
Innovative
65.23
70.45
83.32
219
Conservative
41.11
44.39
52.50
138
Brave
34.85
37.64
44.51
117
Creative
59.87
64.66
76.47
201
Stylish
52.42
56.62
66.96
176
Optimistic
41.40
44.72
52.88
139
Friendly
64.93
70.13
82.94
218
Boring
16.68
18.01
21.30 56
Environmentally responsible
47.96
51.79
61.25
161
Trustworthy
82.21
88.79
105.00
276
Intelligent
58.08
62.73
74.19
195
Professional
80.72
87.18
103.10
271
Efficient
79.53
85.89
101.58
267
Column Total
725
783
926
2434
* The expected value is defined as the joint probability of the column and row combination. This joint probability is calculated as the marginal probability for the column (column total/overall total) times the marginal probability for the row (row total/overall total). This value is then multiplied by the overall total. For any cell, the expected value can be simplified to the following equation:
Expected cell count = (Column total of cell * Row total of cell)/Overall Total

10. Correspondence Maps - Methodology
Residual = Actual - Expected Value
Negative numbers indicate fewer actual rating than expected, positive numbers indicate higher actual rating than expected.
Brand A
Brand B
Brand C
Innovative
-2.23
2.55
-0.32
Conservative
6.89
-2.39
-4.50
Brave
-7.85
0.36
7.49
Creative
-4.87
3.34
1.53
Stylish
3.58
-1.62
-1.96
Optimistic
-1.40
2.28
-0.88
Friendly
12.07
-2.13
-9.94
Boring
1.32
0.99
-2.30
Environmentally responsible
3.04
-3.79
0.75
Trustworthy
7.79
-0.79
-7.00
Intelligent
-4.08
-1.73
5.81
Professional
-9.72
2.82
6.90
Efficient
-4.53
0.11
4.42

11. Correspondence Maps - Methodology
The next step is to standardize the differences across cells so that comparisons can be easily made. Standardization is required because it would be much easier for differences to occur if the cell rating is high compared to a cell with only a small rating. So we standardize the differences to form a chi-square value by
Residual2/Expected Value
The overall Chi-Square value is the sum of the Chi-Square values for each cell. It gives an indication of the overall strength of association between brands & attributes.
Brand A
Brand B
Brand C
Innovative
0.08
0.09
0.00
Conservative
1.16
0.13
0.39
Brave
1.77
1.26
Creative
0.40
0.17
0.03
Stylish
0.24
0.05
0.06
Optimistic
0.12
0.01
Friendly
2.24
1.19
Boring
0.10
0.25
Environmentally responsible
0.19
0.28
Trustworthy
0.74
0.47
Intelligent
0.29
0.46
Professional
1.17
Efficient
0.26
Overall Chi-Square Value = 14.56
* The residual for Brand A on “innovative” is The chi-square value is therefore equal to (-2.23)2/65.23=0.08.

12. Correspondence Maps - Methodology
The final step is to convert the chi-square value into a alignment measure. The chi-square value denotes how well the brands align with each attributes. To restore the directionality, we use the sign of the original difference.
Negative values indicate less association and positive values indicate greater association.
Brand A
Brand B
Brand C
Innovative
-0.08
0.09
0.00
Conservative
1.16
-0.13
-0.39
Brave
-1.77
1.26
Creative
-0.40
0.17
0.03
Stylish
0.24
-0.05
-0.06
Optimistic
0.12
-0.01
Friendly
2.24
-1.19
Boring
0.10
0.05
-0.25
Environmentally responsible
0.19
-0.28
0.01
Trustworthy
0.74
-0.47
Intelligent
-0.29
0.46
Professional
-1.17
Efficient
-0.26

13. Correspondence Maps - Methodology
A correspondence map is then created based on these similarity measures.

14. Correspondence Map - Interpretation
In general, the distance between two points describes the strength of the association
Brands are displayed as points in the space
Attributes are displayed as points in the space
Brands lying in the same direction away from the centre of the map will have similar image profiles, and the further away from the centre the more extreme & differentiated the brand.
By having a standardized measure of association, it takes away the halo effect of strong brands in consumers’ perception of attributes.
Should the axes be displayed?
It’s up to you! Can your client handle the axes?
Axes have no meaning by themselves. But having the axes there help with the interpretation. But clients sometimes get hung up on trying to interpret the meaning of the axes which bogs down the process.

15. Correspondence Maps - Data over Time
Since CA Maps present the degree of association between brands and attributes, tables of row or column variables collected over time (two or more consecutive years) can be used
If the row variables (attributes) are the same over time, the column variables (brands) can be analyzed over time, to present a map of the changing brand position over time
Such a map presents the changing association between the brands and its attributes over time
Caution! If brands are re-positioned over new attributes, CA maps may show huge shifts in brand positions
It’s possible to use Correspondence map to represent changes in brand perception over time, but it’s a tricky business.
In wave 1, we can use Corr map to map out the wave 1 brand perception
In wave 2, we can add the wave 2 brand perceptions to the map. Not only the brands would shift – so would the attributes.