Difficulty with Rank-biserial correlation coefficient, N = 5

BOAZ

New Member
Hi there,

I am calculating Difficulty with Rank-biserial correlation coefficients in a spreadsheet using the following formula:

rb = (2/n)*(Y1 - Y0)

where Yo and Y1 are the means on Y of those scoring 0 and 1 on the dichotomy, respectively.

This was sourced from Glass (1966) - Note on Rank Biserial Correlation

For one calculation I have arrived at an rb value of -1.5! This is obviously difficult to interpret. I'm hoping that somebody may be able to point out where I have gone wrong. Here is the data set:

Dichotomous variable: 1,1,1,0,1
Ordinal variable: 3,3,3,2,4 (Scale ranged from 0 to 4)
(0 and 2 are paired)

Can you see an obvious problem with what I am doing here?

Many thanks!
B

Last edited:

Dragan

Super Moderator
Hi there,

I am calculating Difficulty with Rank-biserial correlation coefficients in a spreadsheet using the following formula:

rb = (2/n)*(Y1 - Y0)

where Yo and Y1 are the means on Y of those scoring 0 and 1 on the dichotomy, respectively.

This was sourced from Glass (1966) - Note on Rank Biserial Correlation

For one calculation I have arrived at an rb value of -1.5! This is obviously difficult to interpret. I'm hoping that somebody may be able to point out where I have gone wrong. Here is the data set:

Dichotomous variable: 1,1,1,0,1
Ordinal variable: 3,3,3,2,4 (Scale ranged from 0 to 4)
(0 and 2 are paired)

Can you see an obvious problem with what I am doing here?

Many thanks!
B
I think you mean: rb=(2/5)*(3.25 - 2) = 0.5

BOAZ

New Member
Hi Dragan, thanks again for your help. I actually posted the wrong data set! The correct data set is:

Dichotomous variable: 1,1,1,0,1
Ordinal variable: 2,1,1,5,1 (Scale ranged from 0 to 5)

Would you mind checking this. But yes, you are right, The formula I posted yields the same answer that you gave previously, 0.5.

Last edited:

Dragan

Super Moderator
Hi Dragan, thanks again for your help. I actually posted the wrong data set! The correct data set is:

Dichotomous variable: 1,1,1,0,1
Ordinal variable: 2,1,1,5,1 (Scale ranged from 0 to 5)

Would you mind checking this. But yes, you are right, The formula I posted yields the same answer that you gave previously, 0.5.

Okay, I see your problem. The formula you are using assumes that there are no tied scores on the Ordinal variable.

BOAZ

New Member
Great, thanks. I overlooked that assumption. Well, fo rthe data set above I've got quite a few ties and my sample size is extremely small. Are you aware of a correction that can be used? I've read Wilson (1976) - 'Critical Values of the Rank-Biserial Correlation Coefficient' but the correction offered only applies to 'bracket ties'. Most of the data sets (N=5 for each) I've been running the rb correlation on have had tied ranks, and none have bracket ties. Do you think this analysis is a lost cause, or can you see a workaround?

BOAZ

New Member
I had considered this but most advice I had read suggested that Somer's d was appropriate for two ordinal variables only. After reading your advice I searched a bit harder and found that Somer's d is indicated if you have one dependent ordinal variable and one two-point nominal variable, which is what I have in this instance. The next step is to find an appropriate test for the reverse - ordinal variable vs. two point nominal dependent variable. Again, I'm open to suggestions. Thanks again.