This is about the correlation analysis in statistics. It covers types, importance,Scatter diagram method Karl pearson correlation coefficient Spearman rank correlation coefficient

1. Correlation analysis
GROUP A ‘EVEREST’
Anil Pokhrel
Amit Budachhetri
Ajit Pudasaini
Rikriti Koirala
Roji shrestha
Puja Neupane 1

2. CONTENTS
• Introduction to correlation
• History of correlation
• Importance of correlation
• Types of correlation
• Methods of studying correlation
• Scatter diagram method
• Karl pearson correlation coefficient
• Spearman rank correlation coefficient
• Advantages and disadvantages of correlation
• Conclusion
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3. History of correlation
• Francis Galton created stastical concept of
correlation
• It firstly used to relate the relationship
between two things.
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4. Introduction of correlation
4
• If two variable are so related that change in one
variable affects the other variables are said to be
correlated
• A mutual relationship or connection between two
or more things
• The process of establishing a relationship or
connection between two or more things
• Correlation analysis shows us how to determine
both the nature and strength of relationship
between two variables

5. Importance of correlation analysis
It is used in deriving the degree and direction
of relationship within the variable
It is use to reduce the range of uncertainty in
matter of prediction
Useful in presenting the average relationship
between two variables
In science, technology and philosophy these
are used to make progressive conclusion
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7. Positive and negative correlation
• In positive correlation both variable moves in
same direction
• Increament in one variable also increase in
another variable and vice versa
• Example
Age
(year
)
5 8 10 14 16
Weig
ht(kg
)
20 28 34 40 49
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8. Negative correlation
• In negative correlation both variable moves in
opposite direction
• If one variable increase then another decrease
and vice versa
• Example
X 15 20 25 30
Y 25 20 10 8
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9. Linear and non-linear correlation
• A correlation between two variable is linear if
corresponding to a unit change in unit variable
over a entire range of value
• Example
• ple
X 6 7 8 9
Y 5 7 9 11
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10. Non linear correlation
• In this correlation there is unit change in
one variable and no constant change in other
variable
• Example
X 1 2 3 4
Y 7 8 10 15
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11. Partial correlation
• Partial correlation is a relationship between
two variables keeping the other variabes
constant or fixed.
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12. Multiple correlation
• The relationship among three or more at the
same time
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14. Scatter diagram methods
• It is one of the simplest ways of diagrammatic
representation of the bi variate
• Here points are represented by dots by
keeping the independent variable on the x-
axis and dependent variables on the y-axis
• It is the simplest methods of measuring
correlation
• It is least affected by size of extra value
• However it cannot give the exact idea (it gives
rough idea only about correlation) 14

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22. Karl Pearson’s correlation coefficient
Introduction:
 The Karl Pearson’s correlation coefficient
measure the degree of association between
the two variables.
It is also known Pearsonian correlation
coefficient
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23. Formula of Karl Pearson’s correlation
coefficient
Let X and Y be two variables then Karl Pearson’s
correlation coefficient is denoted by rᵪᵧ or rᵧᵪ or
simply r is define as
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25. Deviation method(change in origin):
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26. Step deviation method:
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27. Properties of correlation coefficient
• Correlation coefficient lies between -1 to 1
• Correlation coefficient is symmetrical i.e.
rᵪᵧ=rᵧᵪ
• It is independent of change in origin
• It is the geometric mean of two regression
coefficient r²=bᵧᵪx bᵪᵧ
• It has no unit because of relative measure
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28. Interpretation of calculated value of r
• If r=+1, there is Perfect Positive Correlation
between two variables
• If r=-1, there is Perfect Negative Correlation
between two variables
• If r=o, there is no correlation
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29. Goodness of fit measure
• Probable error- use to test the calculated
correlation coefficient whether it is significant
or not then We have
• S.E.(r)=1-squr(r)/√n
Where “r” is the calculated correlation
coefficient in “n” pair of observation
• P.E.(r)=0.6745x1-squr(r)/√n
• If r<P.E.(r), then value of r is not significant
• If r>6P.E.(r), then the value of r is significant
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30. Spearman rank coefficient
• A method to determine correlation when the data
is not available in numerical form then, as an
alternative method the method of rank correlation
is used
• When the value of two variables are converted into
their ranks
• Then the correlation is obtained called as rank
correlation
• Rank correlation coefficient is also known as
spearemans’s rank correlation
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31. • Where ∑d=0 is always zero
• D=R1-R2 or
R2-R1
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32. It can be computed in three condition
a. When ranks are given
b. When ranks are not given and not repeated
c. When rank are not given and repeated
Properties:
a. This is the only methods for finding the correlation while
dealing with qualitative features like beauty , GK ,
honesty
b. How ever it is not suitable in case of large observation
c. There is always some loss of information due to the
ranking is used
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33. EXAMPLE of Rank correlation
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34. Advantages and disadvantages of
correlation
Advantages:
• Can show strength of relationship between two variables
• Study behaviour that you cannot study
• It can collect much information from many subjects at a
time
• Gain quantitative data which can be easily analysed
Disadvantages:
• cannot show cause and effect (what variables control
what)
• No control of third variable that might affect the
correlation
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35. conclusion
• Correlation is the relationship between variables
• Correlation coefficient is symmetric
i.e.r(xy)=r(yx)
• Correlation coefficient is a pure number
independent of unit of measurement
• It is measured of direction and degree of linear
relationship between variables
• It cannot be used in estimating values
• It studies only relationship between variables
• It’s values lies between +1 to -1
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36. Reference
• Google.com
• Vikash Raj Satyal--Probability and
statistics
• Teacher’s notes –Mahesh lal sir
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