siva correlation
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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:
CropCrop AA BB CC DD EE
FertiliserFertiliser 12.812.8 17.117.1 8.38.3 6.76.7 10.210.2
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:
CropCrop AA BB CC DD EE
FertiliserFertiliser 12.812.8 17.117.1 8.38.3 6.76.7 10.210.2
FertiliserFertiliserRANKRANK 22 11 44 55 33
YieldYield 103103 108108 8989 7575 105105
YieldYieldRANKRANK 33 11 44 55 22
RankRankDifferenceDifference -1-1 00 00 00 11
Third, Square The Rank Differences:Third, Square The Rank Differences:
CropCrop AA BB CC DD EE
FertiliserFertiliser 12.812.8 17.117.1 8.38.3 6.76.7 10.210.2
FertiliserFertiliserRANKRANK 22 11 44 55 33
YieldYield 103103 108108 8989 7575 105105
YieldYieldRANKRANK 33 11 44 55 22
RankRankDifferenceDifference -1-1 00 00 00 11
d^2d^2 11 00 00 00 11
Now Find “Sigma D Squared”Now Find “Sigma D Squared”
CropCrop AA BB CC DD EE
FertiliserFertiliser 12.812.8 17.117.1 8.38.3 6.76.7 10.210.2
FertiliserFertiliserRANKRANK 22 11 44 55 33
YieldYield 103103 108108 8989 7575 105105
YieldYieldRANKRANK 33 11 44 55 22
RankRankDifferenceDifference -1-1 00 00 00 11
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
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