### Spearman's Rank

We are not strangers to the concept of correlation, as it implies the relationship between two variables. The number of fans sold by a superstore with the rise of humidity on a summer period is a case in point.

In the above example, we can quantify the variables involved - they take numbers. So, we plot a graph of the two variables to see a relationship between the two and they go a step further to justify it in a mathematical manner to make it statistically appealing

Variables cannot be represented by numbers, though. yet, they can arrange them in a certain order so that the pattern makes sense to people who are interested in them.

**E.g. **

Some bottles of wine can be arranged by the response to their taste. The arrangement makes sense to people who are fond of wine, despite the absence of an index to measure it.

In these circumstances, Spearman's rank comes to our rescue. It can easily be used to determine the relationship of two variables that escape numbers. Since it is universally accepted as a trusted method, we can easily cash in on this encouragingly simple method.

Since we do not have numbers for the variable, we assign numbers to them, in a sensible way. They are called

**E.g. **

There are five wine bottles A, B, C, D and E in the order of taste. We can assign ranks to them in the order of 5,4,3,2,1 or 10, 8.6, 4,2 . These are arbitrary values assigned to variables in a sensible way; there are not hard and fast rules about it. However, the simpler the better.

The ranking system must be extended to both sets of variables. Then a formula must be used to find the Spearman's rank, value of which determines the correlation.

Ranks of variable X | Ranks of variable Y | Ranks of variable X - Ranks of variable Y |
---|---|---|

x_{1} |
y_{1} |
d_{1} |

x_{2} |
y_{2} |
d_{2} |

x_{3} |
y_{3} |
d_{3} |

**Spearman's rank (r _{s}) = 1 -
6∑d^{2} / [n(n^{2}-1)]**

The value of lies between o and 1 (inclusive)

**Spearman's Rank Calculator**

Item | A | B | C | D | E |
---|---|---|---|---|---|

Rank By Judge-1 | |||||

Rank By Judge-2 |

**Practice is the key to mastering maths; please visit this page, for more worksheets.**

Please work out the following questions to complement what you have just learnt.

1)The height of some baby girls are as follows:

87, 88.8, 90.9, 87.4, 88.7, 90.8, 91.5, 92.2, 88.4 and 94

The corresponding weight in (kg) are 12.7, 11.8, 12, 12.2, 12.4, 12.5, 12.6, 12.7, 12.8 and 13. Find Spearman's Rank.

2)The height of some baby boys are as follows:

92.1, 90.5, 89.8, 93.1, 89.2, 92.4, 95.1, 90.7, 93.9 and 93.8

The corresponding weight in (kg) are 14.1, 13.2, 13.3, 13.4, 12.5, 13.6, 13.7, 13.8, 14 and 14.4. Find Spearman's Rank.