# Vargha and delaney effect size

I have two samples A and B in excel and I want to use the vargha and delaney effect size in R. VD.A (A, B) gives me the result as. 0.170 (large)

My question is how it can be large with this value because the large value in vargha effect size begins with 0.7 and above.

If you had used VD.A(B, A), the result would be 0.83. With VDA, no effect is 0.50 and 0 or 1 is complete stochastic dominance of one group over the other. This can be a little disconcerting at first, but it makes a lot of sense for this statistic. VDA is the probability that an observation in one group will be larger than an observation in the other group. So the result of VD.A(A, B) is equal to 1 - VD.A(B, A).

It may be helpful to compare this to Cliff's delta, which is a linear transformation of VDA, where 0 is no effect, and -1 or 1 is complete stochastic dominance.

• thanks a lot. Can we use Cliff's d for data that is not normally distributed?
– Khan
Commented Oct 21, 2019 at 12:38
• You can use Cliff's delta any place you can use VDA. (Which I think is just needing two groups of observations of ordinal or numeric data). Cliff's delta is literally equivalent to VDA just translated from a scale of 0 to 1 to a scale of -1 to 1. Commented Oct 21, 2019 at 12:45
• thanks a lot once again
– Khan
Commented Oct 21, 2019 at 12:56
• Hi Sal, the Cliff's delta test gives the results as, what does it mean? -0.8337751 (large)
– Khan
Commented Oct 21, 2019 at 13:01
• The negative sign means that the second group has higher values than the first group. This is the common convention for Cohen's d and other comparisons of two groups. Just be careful that you know what order R is using for the groups. For example with levels(Group_var).... Both CD and VDA assess the same thing: the probability of an observation from one group being larger than an observation in the other group. VDA just reports this as an actual probability (0.50 is no effect), and CD translates this to a -1 to 1 scale (0 is no effect). Commented Oct 21, 2019 at 13:52