Association between the ranks, In many situations the volunteers are ranked by two judges, or the measurements had been taken for 2 variables are assigned ranks inside the samples independently.

Now it’s miles preferred to understand the quantity of affiliation among the ranks.

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Spearman’s rank correlation association between the ranks

The method of calculating the association between ranks was given by Charles Edward Spearman in 1906 and is known as Spearman’s rank correlation.

In a common scenario, the term rank correlation alone stands for Spearman’s rank correlation.

If for n volunteers, d_i is the difference between ranks of the i^th volunteer for i=1, 2, 3,….n; the formula for Spearman’s rank correlation is,

The formula for r_s is based on the usual Pearsonian formula for the correlation coefficient.

Here it’s far assumed that no ties arise withinside the ranks inside a sample.

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The value of correlation lies between -1 and 1.

What will happen if ties occur in the sample?

Often the measurements are taken on volunteers and then ranked. In such a situation, sometimes ties to occur.

If so, then a correction has to be made in a rank correlation.

If the number of tied observations in X for a particular rank is t_X. There can be more than one t_X in X sample units.

Then the rank correlation become

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