Calculate correlation of nominal and ordinal variables and hypothesis test in r

Question

I would like to statistically analyze three variables. One variable is "consortium mostly academic" (nominal, dichotomous), the second variable is "evaluation method" (nominal, non- dichotomous), and the third variable is "technology category" (ordinal, non- dichotomous).

A contingency table looks like this:

+─────────────────────────+─────────────────────────────────+─────────────────────────────+
| evaluation method used  | consortium not mostly academic  | consortium mostly academic  |
+─────────────────────────+─────────────────────────────────+─────────────────────────────+
| No                      | 28                              | 23                          |
| Yes                     | 6                               | 3                           |
+─────────────────────────+─────────────────────────────────+─────────────────────────────+

The other contingency table looks like this:

+──────────────────────+──────────────────────+──────────────────────+──────────────────────+──────────────────────+──────────────────────+
| technology category  | evaluation method A  | evaluation method B  | evaluation method C  | evaluation method D  | evaluation method E  |
+──────────────────────+──────────────────────+──────────────────────+──────────────────────+──────────────────────+──────────────────────+
| Category 1           | 0                    | 0                    | 0                    | 0                    | 0                    |
| Category 2           | 2                    | 2                    | 3                    | 3                    | 0                    |
| Category 3           | 0                    | 0                    | 0                    | 0                    | 0                    |
| Category 4           | 1                    | 0                    | 0                    | 0                    | 0                    |
| Category 5           | 1                    | 1                    | 3                    | 0                    | 0                    |
| Category 6           | 6                    | 4                    | 3                    | 1                    | 0                    |
| Category 7           | 8                    | 5                    | 2                    | 0                    | 1                    |
| Category 8           | 0                    | 0                    | 0                    | 0                    | 0                    |
| Category 9           | 1                    | 1                    | 1                    | 0                    | 3                    |
+──────────────────────+──────────────────────+──────────────────────+──────────────────────+──────────────────────+──────────────────────+

What is the best way to calculate the correlation for this? With Cramer's V, which is based on chi-square test?

What is the best way to test the two hypotheses?

• The evaluation method used depends on the consortium composition?
• The use of an evaluation method depends on the technology category?

Do I use the chi-square test for this?

Answer 1

This is actually pretty simple and can easily be done in Excel. Forget the one-hot encoding and just use the first table you show. Test one pair of variables at a time, i.e. don't use all three variables in one contingency table. Read any website explaining the very simple arithmetic used to calculate the Chi Squared statistic: sum up for each cell (observed - expected)^2/expected, determine the degrees of freedom in your table (nbr rows - 1) x (nbr cols- 1) and then use those two numbers to look up the cutoff chi - squared value for, say, 95%. If your chi squared stat is above that cutoff, then there's an interaction, either attracting two variable values or repelling two variable values. That's all there is to it.