# About correlation of ordinal variables having different number of categories and about correlation of mixed type of variables

I have three questions:

1. For data with different response categories (likert type or ordinal) what type of correlation should be calculated? I know for ordinal variables Spearman's rank correlation can be used. Am I right?

2. Do I need to order the categories and recode the responses according to their importance to calculate these correlations? I think I should clarify my question.

Suppose that I have two variables that I believe responsible behind profitability of a company. I have the following variables:

For variable 'regular staff meetings', responses are collected as:

1='yes' and 2='no'

For variable 'proportion of staffs given formal performance appraisals', responses are collected as:

1=10%, 2=20%,..., 10=100%

Now as intuitively I believe that the more regular staff meetings are held or performance appraisals are given the better will be the profit of that company, so should we recode for variable 'regular staff meetings' 'yes'=2 and 'no'=1 that responses with 'yes' receives the first rank while spearman's rank correlation is calculated?

Similarly for variable 'proportion of staffs given formal performance appraisals' responses with 10 (100% staffs receiving performance appraisal) will receive the first rank while spearman's rank correlation is calculated. Otherwise if I don't recode the responses from the variable 'regular staff meetings' then the ranks the responses receive becomes of opposite direction as responses with 'yes'=1 receives the second rank but it was supposed to increase profitability!

3. What if I want correlation between mixed type of variables (both interval and ordinal)? Is it possible to calculate?

Thanks for your patience and upcoming kind clarification. :)

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If you have access to the R statistical software, it would be worth taking a look at the polycor package. – chl Jul 9 '12 at 21:48
– Peter Ellis Aug 15 '12 at 11:11

@Blain. Your scoring method for regular or no meetings is not correct. Probaly, you do not have a reason for 2,1 or 1,2. The profitablity is continuous variable. May be you can look for possibility of applying point-biserial correlation. Also, the objeicve you have in mind may be realised through a linear multinomial type regression or a mixed model (nominal preferably, simple regression with some control variable.The factor analysis is a data-reduction technique and it should be used with care.

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 In my case profitability is a categorical variable. Because there were predefined answer options in the questionnaire. The answer options for profitability were like, "increasing", "decreasing", "stable" etc. Actually you are right that there is no reason for 1,2 or 2,1. – Blain Waan Jul 16 '12 at 7:11

1.) I think nonparametric correlation methods Spearman's or Kendall's can be used. 2.) Reversing the order in the code only changes the sign of the correlation not the magnitude. So changing order is not necessary. 3.) The nonparametric methods require that the data be ordered. So they can be applied when one variable is ordinal and the other is interval scale.

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 That means I can also use Spearman's rank correlation for correlating an ordinal or likert type variable and a continuous variable, right? – Blain Waan Jul 9 '12 at 17:55 @BlainWaan yes it should be okay. – Michael Chernick Jul 9 '12 at 18:00 @Blain Polyserial correlation is a good option in this case. – chl♦ Jul 9 '12 at 21:53
1. (and 3.) Spearman can deal with mixed data.
2. As I read it, it sounds like you want multiple regression, with profitability ~ reviews + meetings (where meetings is coded to a dummy variable where 0 = no, 1 = yes). That said, you may want to reconsider the 0-10 scale and just make it nominal with the actual percentage of staff given formal performance reviews.
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 I actually want to use the correlation matrix found from about 40 variables like the ones I mentioned above, in the factanal() function in R to make a factor analysis. I want to make comments about how much each factor affects profitability. So I wanted correlation matrix from ordinal variables and mixed type variables. Thanks all for your kind suggestions. – Blain Waan Jul 10 '12 at 6:52