# Analysing correlation between two (or more) categorical variables?

Context: I ran a survey where I asked one person to qualitatively assess multiple wines. They was asked to choose one or more adjective to describe the taste, the smell (non-dichotomous categorical) of each wine. They was also asked to select one (out of four) evaluation of the strength (dichotomous categorical) for each wine.

Below is an example of results I obtained. The number in each cell represents the number of different wines that matches both metrics.

|Taste                                        |Smell                                       |Strength
|fruity     fleshy     full-bodied none of the|red fruits nuts       earth      none of the|very strong strong    mild      very mild
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Taste     fruity     |          9                                  |                                            |
fleshy     |          4          9                       |                                            |
full-bodied|          2          4          5            |                                            |
none of the|          0          0          0           5|                                            |
-------------------------------------------------------------------------------------------------------------------------------------------------------------
Smell     red fruits |          3          3          0           2|          6                                 |
nuts       |          2          2          1           3|          1          7                      |
earth      |          4          4          2           2|          2          3          8           |
none of the|          2          2          3           1|          0          0          0          5|
-------------------------------------------------------------------------------------------------------------------------------------------------------------
Strength  very strong|          3          1          2           0|          0          2          1          2|          4
strong     |          2          2          0           1|          4          0          1          0|          0          4
mild       |          3          3          1           2|          1          2          3          2|          0          0          6
very mild  |          1          2          1           2|          1          3          3          0|          0          0          0          5

Examples:

• 2 wines were considered having a full-bodied (left) and fruity (top) taste.
• 9 wines were considered having a fruity (left and top) taste. Note that, because the expert could choose more than one taste (and more than one smell, but only one strength) per wine, the 2 wines mentioned above are include in the 9 here mentioned.

(There are 19 wines in total)

Issue: I want to know wether some of the values/variables are correlated or not.

• Either between two values of a single variable, e.g.:

Fleshy and full bodied tastes are significantly correlated.

• Or between values of different variables; e.g.:

The fruity taste is significantly correlated with the red fruit smell.

Question: Which test should I use in such context? Is there a difference between dichotomous and non-dichotomous variables?

• Please explain what the numbers in this table represent. – whuber Feb 2 '18 at 19:16
• @whuber done. Thank you for the advice, it's indeed important. – ebosi Feb 3 '18 at 22:13
• It looks like you have a burt table. Look into correspondence analysis: stats.stackexchange.com/questions/200905/… or search this site for visualization of contingency tables. Very few posts here about Burt tables. – kjetil b halvorsen Sep 19 '18 at 19:51