Spearman's rank correlation
Also called: Rank correlation coefficient · Topic: Economic Data: Census, NSS, Surveys and Statistical Tools · NCERT: Class 11, Ch 6 "Correlation"
Meaning
Spearman's rank correlation measures how closely two sets of ranks (positions such as 1st, 2nd, 3rd) move together. The formula is rs = 1 − 6ΣD²/(n³ − n), where D is the difference between the two ranks of each item and n is the number of items. Like r, it lies between −1 and +1. It is used for qualities that cannot be measured, such as beauty or honesty. It is also used when exact measurement is not possible and when the data have extreme values. If two items share a rank (tied ranks), each gets the average rank, and a correction of (m³ − m)/12 is added.
Example
Three judges rank the contestants in a beauty contest. The rank correlation between judges B and C is 0.9, so they largely agree. Between judges A and B it is only 0.3.
Don't confuse with
- Karl Pearson's coefficient (r): r uses the actual measured values. For precisely measured data, r is the better measure. Spearman's coefficient is for ranks and attributes, and it is generally no more than r for such data.
Related concepts
- Measures of central tendency
- Arithmetic mean
- Weighted arithmetic mean
- Median
- Quartiles
- Decile
- Percentiles
- Mode
- Bimodal and multimodal distribution
- Modal class