The reason with example 2 was such low percent correlation is you did not use the Tau-b formula to account for ties, which is a different denominator that accounts for total number of possible pairs minus the Taus. For other viewers look up the Tau-b formula for ties
The formula you are using for Kendall's Tau is not correct - you are using gamma. This is similar, but not the same. The difference is, that using gamma you are ignoring possible ties, giving you the possibility to still reach the extreme values of +-1. In other terms: C+D is only 1/2*N(N-1) if you have no ties. Anyway, thanks for the video :)
"(C-D)/(C+D)" is known as Goodman and Kruskal's Gamma. In the case there are no ties, that's the same as Kendall's Tau-a. So -- yes, you're right, the formula in the video was Gamma's.
It was in a book called "Statistics in a Nutshell" by Sarah Boslaugh. Perhaps I misread the heading, but I'm almost positive that the formula you gave for KT alpha here was notated as gamma in that book. Do you by any chance have an example of calculating Kendall's tau beta correcting for ties in the rankings? Thanks again...I'll see if I can't find out what the n(n+1)/2 represents...it looks like it just represents the number of all possible pairings, rather than just concordant or discordant pairs.
They are used for ordering the student ranks. If you are given the student ranks sorted according to the master's, then the master's ranks don't matter anymore. But it is important to sort the student's ranks according to master, in order to get the number of concordant and discordant counts.
Perhaps I'm confused, but I thought the formula (C-D)/(C+D) was the formula for a measure of correlation called gamma (or Goodman and Kruskals gamma). I was under the impression that Kendalls tau alpha was actually (C-D)/((n)(n+1)/2), where n is the total number of observations. So in the first example, the Kendalls tau alpha would be .818 divided by [12(11)]/2, or .818 divided by 66. Am I mistaken? Thanks for the video!
You must be mistaken somewhere, as dividing .818 by 66 gives .012, which would suggest virtually no consistency between the ratings. I've confirmed the value of .818 with statistical software (SPSS), so it is likely correct. Where did you see the formula with the divisor of [12(11)]/2?
Wikipedia seems to define the ratio of C-D to C+D as gamma as well, and KT as (C-D) divided by 1/2n(n+1), which is equivalent to my denominator from earlier. Perhaps SPSS just mislabeled the name of the statistic, calling it KT alpha instead of gamma?
Social scientists would view the formula presented in the video as Kendall's tau. Technically, what SPSS does is Kendall's tau - beta, but that is simply an extension of alpha to account for tied ranks. You may be interested in the how2stats video that explains in detail what this Kendall's tau formula represents, as distinct from Spearman's rank correlation. I have no idea what a formula would represent, in this case, that yields a value of .012.
Well, I think I figured out the apparent discrepancy. The denominator of gamma (C+D) will represent the total number of pairs in the sample, assuming no ties in the data. This is exactly what the n(n-1)/2 in the denominator of KT alpha (which does not correct for ties) represents...the TOTAL number of pairs possible in the data, each of which will be either concordat or discordant if ties are not present. So, (C+D) and n(n-1)/2 will be equal by definition. Thus, with no ties, gamma and KT alpha are equal!
Yes, you're correct. I specifically used an example without ties for simplification. In the social sciences, people tend to use the terms Kendall's tau - alpha (can not accommodate ties in the data) and Kendall's tau - beta (can accommodate ties in the data). The formula I used was Kendall's tau - alpha (but some people seem to call it gamma).
(C-D)/(C+D) is actually Goodman and Kruskal's Gamma, isn't it .. not Tau! Kendall Tau is slight different, though it relies on number of concordant and discordant pairs. Please see wiki pages.
Thank you very much for answering the question of calculating concordant vs. discordant pairs! That was the piece I was missing!
You did a great job. Thank you.
Very clear and easy explanation, thanks a lot.
Great explanation. Thank you!
You are the boss! Thank you very much!
Great video! Thanks a lot.
So helpful. Thank you!
helped a lot, thank you.
Very, very helpful!
Wonderful! Thank You!
i missed one class , so I was stuck , thank you so much ! greetings from Belgium !
Thanks a million!
Nicely explained.
thank u... it really helps... :)
Vous m'avez rassuré.
Merci
That was very helpful
The reason with example 2 was such low percent correlation is you did not use the Tau-b formula to account for ties, which is a different denominator that accounts for total number of possible pairs minus the Taus. For other viewers look up the Tau-b formula for ties
The formula you are using for Kendall's Tau is not correct - you are using gamma. This is similar, but not the same. The difference is, that using gamma you are ignoring possible ties, giving you the possibility to still reach the extreme values of +-1.
In other terms: C+D is only 1/2*N(N-1) if you have no ties. Anyway, thanks for the video :)
thanks!
what is gamma...
@@Samuftie Gamma is another metric that can be used, for example instead of Kendall's Tau.
Thank you so much ❤️❤️
"(C-D)/(C+D)" is known as Goodman and Kruskal's Gamma. In the case there are no ties, that's the same as Kendall's Tau-a.
So -- yes, you're right, the formula in the video was Gamma's.
It was in a book called "Statistics in a Nutshell" by Sarah Boslaugh. Perhaps I misread the heading, but I'm almost positive that the formula you gave for KT alpha here was notated as gamma in that book. Do you by any chance have an example of calculating Kendall's tau beta correcting for ties in the rankings? Thanks again...I'll see if I can't find out what the n(n+1)/2 represents...it looks like it just represents the number of all possible pairings, rather than just concordant or discordant pairs.
This was very helpful
excellent thanks
can you help me understand the Somers' D in the most simplest form. Thank you
Does kendal tau has anything to do with sample size? For a sample size >100 does low value of tau (-0.2 to 0.2) makes any sense if p-value is low (
What independent and dependent variable did you use on your example?
brilliant
nice video.
Thanks for the explanation, but if this is Kendall's tau, then what is the gamma statistic?
thanks!
thank you
I have a question: what's the point of having the scores of the master there at all, when they are not used at all in kendalls tau calculation?
They are used for ordering the student ranks. If you are given the student ranks sorted according to the master's, then the master's ranks don't matter anymore. But it is important to sort the student's ranks according to master, in order to get the number of concordant and discordant counts.
Smart thinking to divide the video in two
Perhaps I'm confused, but I thought the formula (C-D)/(C+D) was the formula for a measure of correlation called gamma (or Goodman and Kruskals gamma). I was under the impression that Kendalls tau alpha was actually (C-D)/((n)(n+1)/2), where n is the total number of observations. So in the first example, the Kendalls tau alpha would be .818 divided by [12(11)]/2, or .818 divided by 66. Am I mistaken? Thanks for the video!
You must be mistaken somewhere, as dividing .818 by 66 gives .012, which would suggest virtually no consistency between the ratings. I've confirmed the value of .818 with statistical software (SPSS), so it is likely correct. Where did you see the formula with the divisor of [12(11)]/2?
how2stats n(n+1)/2 is equal to C+D. The former is the number of pairing possible and the latter is also the number of pairings possible! :-)
Please and if 1 number appears 2 time on the student1 what can i do
Wikipedia seems to define the ratio of C-D to C+D as gamma as well, and KT as (C-D) divided by 1/2n(n+1), which is equivalent to my denominator from earlier. Perhaps SPSS just mislabeled the name of the statistic, calling it KT alpha instead of gamma?
Social scientists would view the formula presented in the video as Kendall's tau. Technically, what SPSS does is Kendall's tau - beta, but that is simply an extension of alpha to account for tied ranks. You may be interested in the how2stats video that explains in detail what this Kendall's tau formula represents, as distinct from Spearman's rank correlation. I have no idea what a formula would represent, in this case, that yields a value of .012.
What happens in case of same rank? Is it counted as a concordant or a discordant pair? Or is it just not counted in any?
plz explain cases of tied ranks also
Well, I think I figured out the apparent discrepancy. The denominator of gamma (C+D) will represent the total number of pairs in the sample, assuming no ties in the data. This is exactly what the n(n-1)/2 in the denominator of KT alpha (which does not correct for ties) represents...the TOTAL number of pairs possible in the data, each of which will be either concordat or discordant if ties are not present. So, (C+D) and n(n-1)/2 will be equal by definition. Thus, with no ties, gamma and KT alpha are equal!
Yes, you're correct. I specifically used an example without ties for simplification. In the social sciences, people tend to use the terms Kendall's tau - alpha (can not accommodate ties in the data) and Kendall's tau - beta (can accommodate ties in the data). The formula I used was Kendall's tau - alpha (but some people seem to call it gamma).
what if there is a tie in masters rank?
(C-D)/(C+D) is actually Goodman and Kruskal's Gamma, isn't it .. not Tau! Kendall Tau is slight different, though it relies on number of concordant and discordant pairs. Please see wiki pages.
I didnot understand one thing that ..why we are finnding statistical significane??????? and in what case we find that?????
can you do it with 3 pairs of data?
No, but Fleiss' Kappa might give you what you are looking for.
@@how2stats Ok thank you.
This is the calculation for Gamma, not Tau.
That breathing tho..
not well explained