siva correlation

Spearman’s Rank C.C.Spearman’s Rank C.C.Measuring CorrelationMeasuring Correlation

M.SIVASUBRAMANIANM.SIVASUBRAMANIAN

CORRELATION

Correlation can be easily understood as co relation. Correlation is the average relationship between two or more variables. When the change in one variable makes or causes a change in other variable then there is a correlation between these two variables.

Types Of Correlation

Positive correlation: r is close to +1. An r value of exactly +1

Negative correlation : r is close to -1. An r value of exactly -1

No correlation: r is close to 0.

A correlation greater than 0.8 is generally described as strong, whereas a correlationless than 0.5 is generally described as weak.

Uses of Correlation

correlations are used to construct indexesfrom data on several variables, such as:

Intelligence TestsPersonality TestsMarital happiness measuresMeasures of financial strengthStock Markets

Spearman’s Rank C.C. FormulaSpearman’s Rank C.C. Formula

This formula is on the formula sheet so you don’t need to learn it!

This formula is on the formula sheet so you don’t need to learn it!

Perfect Negative

Correlation

No Correlation

Perfect Positive

Correlation

Interpretation of S.R.C.C.Interpretation of S.R.C.C.

This applies to negative values tooThis applies to negative values tooThere are no hard and fast rules about There are no hard and fast rules about

when “weak” becomes “strong” when “weak” becomes “strong” If If rr > 1 then you went wrong !!!!!! > 1 then you went wrong !!!!!!

Outline of ProcedureOutline of Procedure

Let’s say you are exploring Let’s say you are exploring nn heights and heights and weights in an investigationweights in an investigation

Rank the heights i.e. put them in order Rank the heights i.e. put them in order (1 = biggest, (1 = biggest, nn = smallest) = smallest)

Rank the weights Rank the weights (1 = biggest, (1 = biggest, nn = smallest) = smallest)

dd = difference between the two ranks for = difference between the two ranks for each personeach person

Square and add these differencesSquare and add these differences

Problems With Equal RanksProblems With Equal Ranks

What if two things are 3rd= ?What if two things are 3rd= ?One has to be third, the other fourth.One has to be third, the other fourth.To be fair, each takes the average:To be fair, each takes the average:

(3 + 4) ÷ 2 = 3.5(3 + 4) ÷ 2 = 3.5What if three things are 5th= ?What if three things are 5th= ?Call them 5th, 6th and 7thCall them 5th, 6th and 7thGive each one the average rank:Give each one the average rank:

(5 + 6 + 7) ÷ 3 = 6(5 + 6 + 7) ÷ 3 = 6

Fertiliser v. Plant GrowthFertiliser v. Plant Growth

CropCrop AA BB CC DD EE

FertiliserFertiliser 12.812.8 17.117.1 8.38.3 6.76.7 10.210.2

YieldYield 103103 108108 8989 7575 105105

First, Rank The Data:First, Rank The Data:



FertiliserFertiliserRANKRANK 22 11 44 55 33

YieldYield 103103 108108 8989 7575 105105

YieldYieldRANKRANK 33 11 44 55 22

Second, Find The Rank Differences:Second, Find The Rank Differences:




YieldYield 103103 108108 8989 7575 105105


RankRankDifferenceDifference -1-1 00 00 00 11

Third, Square The Rank Differences:Third, Square The Rank Differences:




YieldYield 103103 108108 8989 7575 105105



d^2d^2 11 00 00 00 11

Now Find “Sigma D Squared”Now Find “Sigma D Squared”




YieldYield 103103 108108 8989 7575 105105



d^2d^2 11 00 00 00 11

Finally Use The Formula:Finally Use The Formula:

n = 5 (there were 5 crops)

ConclusionConclusion

There is very strong correlation between the amount of fertilizer and the crop yield

r= 0.9 r= 0.9

Reference

Business Statistics – S.Manoharanwww.statsoft.comwww.socialresearchmethods.net

siva correlation

Documents

fertiliser rank

yield rank

rank differences

average rank

smallest rank

spearmans rank

strong correlation

measuring correlation