Spearman's Rank Correlation: Case of Tied Ranks | Correlation Coefficient
Quantitative Techniques in Management:
How to find the Coefficient of Correlation also called the Correlation Coefficient when the Ranks are given and there is a case of tie between two or more ranks?
Correlation is an Important topic of Statistics.
Spearman's Rank Correlation is a method finding the correlation between two variables when their ranks are mentioned instead of their score.
The other popular method of finding the correlation between two variables is the Karl Pearson's Coefficient of Correlation.
Case of Tied Ranks arise when two or more variables have the same rank.
Here we learn how to resolve this case and find the correlation between two variables.
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Mijanur Rahman (3 months ago)

thanks a lot. best tutorial.

Edupedia World (3 months ago)

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Kieran Miles (5 months ago)

Most helpful video i could find!

Edupedia World (5 months ago)

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kritika kumari (5 months ago)

This explanation helped me ... Really thankfull to you..

Edupedia World (5 months ago)

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Afzal Ahmed (6 months ago)

Veryyyyyyyy thanks

Edupedia World (6 months ago)

Welcome!

Michael Mary (6 months ago)

Tnq so much sir

Edupedia World (6 months ago)

Stay tuned for more such videos!

Boro (7 months ago)

Your explanation is so lucid that even a math illiterate like me understood. Thank you very much.

Boro (7 months ago)

Welcome

Mobasshir Quamar (7 months ago)

Thanks for such a nice complement, Go ahead and share the video with those who, you think would benefit from it.

Edupedia World (7 months ago)

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Gab Reyes (8 months ago)

Thankyou. It helped me a lot. Got a sub. You deserved it. :)

Gab Reyes (8 months ago)

Thanks man... I'm looking forward for more informative vid of yours. :D

Edupedia World (8 months ago)

Thanks, It's really motivating to see it helped you and you liked it. Best Wishes.

dhiraj GUPTA (10 months ago)

Sir what happens when there are no tied ranks in one series and the other series have tied ranks? Pls help

Mobasshir Quamar (10 months ago)

It is the same. depending on how many ties you have you have to use a correction factor irrespective of whether it is in one series or the other.

abdur rahim (1 year ago)

what will be the spearman co-relation if the value of x is 5, 8, 12, 10, 15, 16,16,10,12,8 and the value of y 15, 17, 18,20,23,28,22,20,20,15 consecutively? how will I put them rank?

Mobasshir Quamar (1 year ago)

Well! Just take the numbers as they are and rank them from the highest to the lowest. In case of X there is a tie at the highest number i.e. at 16 so they will be ranked as per the average of their ranks if the ranks were going to be 1 and 2. so both will have rank 1.5. Then 15 will be assigned rank 3. Like wise there are ties at 12 for rank 4 & 5, so they both will have ranks 4.5. Similarly at 10, both the 10 will have ranks average of 6 & 7. Again a tie at 8 will have the ranks of both the 8s as 8.5. Last one remaining is no. 5 which will be ranked as 10. In the same manner the series Y will have the rank 1 for 28, 2 for 23, 3 for 22, now there is a tie at 20 and there are 3 numbers. So taking the average of 4,5 & 6 there prospective ranks had they been different, we get rank 5 for all the three. Then rank 7 for 18, 8 for 17 and again another tie at number 15 will have rank 9.5 for both. You can see the arrangement and working below.
The correction factor for a tie with 2 numbers will be 0.5 and for a tie with 3 numbers will be 2.We have 4 tie with 2 numbers in X and 1 tie with 2 numbers in Y. Also there is a tie of 3 numbers in Y. so total correction factor would be (0.5+0.5+0.5+0.5+0.5+2) = 4.5
The whole working is illustrated here.
Hope that makes it clear.
X : 5, 8, 12, 10, 15, 16,16,10,12,8
Y: 15, 17, 18,20,23,28,22,20,20,15
Rank X: 10, 8.5, 4.5, 6.5, 3, 1.5, 1.5, 6.5, 4.5, 8.5
Rank Y: 9.5, 8, 7, 5, 2, 1, 3, 5, 5, 9.5
d = Rank X - Rank Y = 0.5, 0.5, -2.5, 1.5, 1, 0.5, -1.5, 1.5, -0.5, -1
d^2 = 0.25, 0.25, 6.25, 2.25, 1, 0.25, 2.25, 2.25, 0.25, 1
Sum of (d^2) = 16
d^2 + cfs = 16+4.5 = 20.5
n = 10
n((n^2)-1) = 990
6(Sum(d^2)) = 123
Rho = 0.875757576

abdur rahim (1 year ago)

and the serial is also given for x and y values, i.e. for 1 x is given 5 and y is 15, for serial 2, x is 8 and y is 17. so how would I rank? I saw in another lecture that the rank, in case of tied, has given by average number of serial. so if I search for the rank 1 to highest number what are 16 and 16. then how to rank? if i rank both the 16 are 6.5 by average their serial number what will be the next rank? of course 3, is not it? as the first 2 numbers has been ranked. what will be third rank? 15? and the fourth? there is again tie of 12 whose serial number are 3 and 9. if I average the serial number the rank will be 6 for both the fourth and fifth rank? is not it?
help me to assign ranks?

abdur rahim (1 year ago)

I know know how to rank of these series?

Mobasshir Quamar (1 year ago)

Do you want me to solve it or just assign ranks ?
If I have to teach this, I'll have to do a new video.
Anyways, let me know....
The solution to this is 0.875757...
Try out with the help from the video, very similar steps. In case you need any more steps, let me know.

pankaj saini (1 year ago)

very help full tutorial. thanks

xyza faye cervantes (1 year ago)

Thank you very much.

Prativa Subedi (1 year ago)

thank you soo much..it helped me a lot..

julmore pesito (1 year ago)

I just wanna ask if anybody knows the formula using the excel....Please please

laxmi fozdar (1 year ago)

loved it.... u r awesome sir😊

Harsh Rai (1 year ago)

Thanks a lot for this video. I have my exam tomorrow and I was really confused with the case of more than two variables having same rank. Thank you soo much for clearing the doubt. Keep up the good work..!! :-)

Mobasshir Quamar (1 year ago)

Great to know it helped you. Your comment is a motivator for us to keep going. Thanks a lot and keep watching our videos. Best wishes for your exams.
Happy Learning.

Michael Durrant (1 year ago)

Just one question, i did the calculation on the graphics calculators and used the x and y values you got, yet managed to get a slightly varied answer of 0.974789916 instead of the 0.967... you calculated. Is it possible my calculation is wrong, or have you calculated an error? Many thanks.

Edupedia World (1 year ago)

The value of r = 0.9844... and the value of rho = 0.966666666666667. I do not know how you got 0.9747899. In the video, it has been done twice by two methods, first manually and then on excel and you the answer is the same. Again here it is explained, so there is no chance of error.

Michael Durrant (1 year ago)

Mobasshir Quamar I used the x and y values, calculated to the same as yours, but also put these values in the calculator( stats mode, mode 2) in the table it gives, and used the table to find an r value of 0.9844... . Using your method exactly, got another result which is the same as yours. I was just wondering if either result could be used in an exam.

Mobasshir Quamar (1 year ago)

Yeah Dear, sure. Well...!
You have 1-((6*4)/(9*80)) you can cancel (6/9) to get (2/3) and cancel out (4/80) to get (1/20). Again you can cancel (2/20) to get (1/10). Now the equation would look like 1-(1/30), which can be written as (30-1)/30 =29/30 =0.966666666666667. This can be round off to 0.967 and that is what we have got.
So, the calculation for this method is correct. But if you change the method the answer would be different. Like if you calculate the Karl Pearson Coefficient of Correlation you will get 0.984425072.
I do not know what method you have used to get the value 0.9747899, please check or let me know elaborately as to how you managed to get that value.

Purple Carrot (1 year ago)

YOU EXPLAINED THIS REALLY WELL THANK YOU!!!!!!!!!!!!!!
IT HELPED ME OUT A LOTTT

Mobasshir Quamar (10 months ago)

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Prasanna Aditya (1 year ago)

Thanks a lot.....Great video....please keep teaching..the teacher is awesome

Mobasshir Quamar (1 year ago)

You are Welcome Prasanna, It's a pleasure you liked the video. It's a real complement from you.

Sayan Ghatak (1 year ago)

In case of tied ranks, I believe as per mu intuitive understanding, coefficient of correlation decreases.for example, in a particular sample of observations, 3 observations of x variable are the same while the corresponding 3 observations of the y variable increases steadily. So, for these 3 observations coefficient of correlation, I suppose, is 0 and therefore it is bringing down the coefficient of correlation of the entire sample in turn. In this connection, I am not understanding the the concept of the correction factor. What is it actually correcting? what is the derivation of the formula of the correction factor?

Sayan Ghatak (1 year ago)

Is it that Spearman's rank formula of correlation does not consider ties and that is why it is adding back the difference that is there as correction factor?

aliya khan (1 year ago)

omg tysm 😊😊😊😊😊😊😊😊😊😊

Mobasshir Quamar (1 year ago)

You are welcome.

Tim Sok (1 year ago)

achaaa h

Edupedia World (1 year ago)

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vivek narayanan (1 year ago)

monday is my exam. thank you very much. I understood this thoroughly. you earned a like and a sub.

Edupedia World (1 year ago)

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Thank you very much. It was really very helpful.:)

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shirli v (2 years ago)

thank you but there's something I really don't get - why aren't you first sorting the values from the lowest to the highest? It seems like the ranking is meaningless if it's not really sorted.. Am I wrong?

Mobasshir Quamar (2 years ago)

Well, you first sort the values and then assign ranks and see what answer you get.

shirli v (2 years ago)

thank you very much! "In the example the ranks are allotted in the order from the highest data to to the lowest data" - but according to what values? values that are not displayed but were used to sort it according to them beforehand?

Mobasshir Quamar (2 years ago)

Well dear, it can be either sorted from "the lowest to the highest" or from "the highest to the lowest". Since the data given here is already in the order from highest to lowest, we are not sorting it further.
In the example the ranks are allotted in the order from the highest data to to the lowest data. Since the order is taken care of while allotting the ranks, it already got sorted. You can even first sort the data and then allot the ranks. You will get the same ranks and the same answer.
Hope that makes things clear.

Edupedia World (2 years ago)

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MesterReenge (2 years ago)

Hey, thanks for the great video.
I have a question (im not really strong in math).
If i have more than one number tied at "series a", and more than one number tied at "series b", do i then calculate cf for each tie and then add them to find di2 like this: di2 = di2 + cf1 + cf2 + cf3 + cf4 etc..?
Hope you understand?

MesterReenge (2 years ago)

+Mobasshir Quamar thanks for the quick reply! It was really helpful!

Mobasshir Quamar (2 years ago)

+MesterReenge
Yes, in case if you have more than 1 number tied in both the series A and B then you need to calculate the cf for each of those ties and find the "Sum of di square (new)" = "Sum of di square (old) + cf1 + cf2 + cf3 + cf4 ... and so on till you add all the cf's for all the ties separately.
Hope your doubt is clear.
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Edupedia World (2 years ago)

+MesterReenge
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Shivya Vasishth (2 years ago)

Thank u so so much today is my exam and I know that this qs will be surely there and I didn't know how to solve it but now m relaxed.

Edupedia World (2 years ago)

+Shivya Vasishth
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DHAVAL THAKKAR (2 years ago)

Thanks a lot .... The excel example made everything clear

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+DHAVAL THAKKAR
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thanks Great help...

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Masha Allah ... very good explanation, i was searching this from past many days

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