1. Calculate N_same (or the number of concordant pairs)
2. Calculate N_different (or the number of discordant pairs)
3. Calculate gamma.

   

4. Interpret using interpretation guidelines.

Somer’s d: similar to gamma, except it adjusts for tied ranks on the DV. Ties occur when two pairs of scores are both either concordant or discordant for the IV and tied on the DV.

1. Calculate N_same (or the number of concordant pairs)
2. Calculate N_different (or the number of discordant pairs)
3. Calculate Tiesy, or the number of ties: Ties_y=a(b+c)+b(c)+d(e+f)+e(f)+g(h+i)+h(i)
4. Calculate Somer’s d using the following equation:

   

Kendall’s Tau-b: Conceptually similar to gamma and Somers’ d, but it goes one step further and corrects for tied pairs on both the DV and the IV.

1. Calculate N_same (or the number of concordant pairs)
2. Calculate N_different (or the number of discordant pairs)
3. Calculate Ties_y, or the number of ties in the dependent variable.
4. Calculate Ties_x, or the number of ties in the dependent variable:Ties_x=a(d+g)+d(g)+b(e+h)+e(h)+c(f+i)+f(i)
5. Calculate Kendall’s tau-b using the following equation:

   

1. Organize the observations into a chart, with columns for score on each variable of interest, their respective ranks, the differences between the two (D), and differences between the two squared (D²). D² will the most useful for calculating rho.

   

2. Calculate rho as

   

• The equation to calculate z_obtained for Gamma (which can also be used for Tau-b and Somer’s d) is:

  

• If you have less than 120 observations, the t-statistic the degrees of freedom are defined as df = n–1.
• For Spearman’s rho, use the following equation: