How to calculate the correlation between two ordinal variables?

[Yannu Zheng]

Hi,
I want to calculate the correlation between two ordinal variables, one is skill level for occupations (4 levels in order) and the other is education level (6 levels in order, 1 <primary, 2=primary, 3=secondary high school, 4=post-secondary <3 years, 5=post-secondary >=3 years, 6=PhD). These two variables are ordinal but cannot say that they are interval variables as the education year difference between each education level is different. Is it right to use "polychoric" in stata?
Thanks a lot!
Best
Yannu

[Oded Mcdossi]

Try help ktau for Kendall's rank correlation coefficients

[wbuchanan]

polychoric correlations are typically used for the estimation of correlations between ordinal scaled variables. Stas Kolenikov wrote a Stata program to estimate these correlation coefficients a while ago, but you can find more information in his slides from this year's Stata conference.

[Clyde Schechter]

There is also the Spearman correlation, -help spearman-. And there is Goodman-Kruskal gamma, too. -help tabulate twoway-

[Marcos Almeida]

Hello Yannu,


You may type something like this:

 . webuse dose

. tab dose function

           |             Function
    Dosage |    < 1 hr     1 to 4         4+ |     Total
-----------+---------------------------------+----------
     1/day |        20         10          2 |        32
     2/day |        16         12          4 |        32
     3/day |        10         16          6 |        32
-----------+---------------------------------+----------
     Total |        46         38         12 |        96


. ktau dose function, stats(p taub)

  Number of obs =      96
Kendall's tau-a =       0.1518
Kendall's tau-b =       0.2378
Kendall's score =     692
    SE of score =     270.100   (corrected for ties)

Test of Ho: dose and function are independent
     Prob > |z| =       0.0105  (continuity corrected)

. */ check it with the taub option of tabulate

. tabulate dose function, taub

           |             Function
    Dosage |    < 1 hr     1 to 4         4+ |     Total
-----------+---------------------------------+----------
     1/day |        20         10          2 |        32
     2/day |        16         12          4 |        32
     3/day |        10         16          6 |        32
-----------+---------------------------------+----------
     Total |        46         38         12 |        96

          Kendall's tau-b =   0.2378  ASE = 0.086

Best,

Marcos

[Yannu Zheng]

• Hi all,
  
  Thanks so much for all of your kind help! I decide to use Goodman and Kruskal Gamma now as there are many ties in the data
  
  Best
  
  Yannu