Correlation and partial correlation-using SPSS and M.S. Excel with example

1. Speaker:
M.Udaybhaskar
AGRICULTURAL COLLEGE: BAPATLA – 522 101
ACHARYA N G RANGA AGRICULTURAL UNIVERSITY
UsingM.SExcelandSPSS
Seminar
On

2. MEANING OF CORRELATION
ANALYSIS
• Correlation is the degree of inter-relatedness among the two or
more variables.
• Correlation analysis is a process to find out the degree of
relationship between two or more variables by applying various
statistical tools and techniques.
• Term correlation coined by Karl Pearson in 1902
• Denoted by r
• Value lies between -1 and +1

3. Types of correlation
On the basis of
degree of correlation
On the basis of
number of variables
On the basis of
linearity
•Positive
correlation
•Negative
correlation
•Simple
correlation
•Partial
correlation
•Multiple
correlation
•Linear
correlation
•Non – linear
correlation

4. CORRELATION : ON THE BASIS OF DEGREE
Positive Correlation
If one variable is increasing and with its impact on average other variable is also increasing
that will be positive correlation.
For example :
Income ( Rs.) : 350 360 370 380
Weight ( Kg.) : 30 40 50 60
For example :
Income ( Rs.) : 350 360 370 380
Weight ( Kg.) : 80 70 60 50
If one variable is increasing and with its impact on average other variable is also decreasing
that will be negative correlation.
Negative Correlation

5. CORRELATION : ON THE BASIS OF NUMBER OF
VARIABLES
Simple correlation Partial correlation : Multiple correlation :
Correlation is said to be simple
when only two variables are
analyzed.
When three or more variables are
considered for analysis but only two
influencing variables are studied and
rest influencing variables are kept
constant.
In case of multiple correlation three
or more variables are studied
simultaneously.
For example :
Correlation is said to be simple
when it is done between
demand and supply or we can
say income and expenditure
etc.
For example :
Correlation analysis is done
with demand, supply and
income. Where income is
kept constant.
For example :
Rainfall, production of rice and
price of rice are studied
simultaneously will be known
are multiple correlation.

6. CORRELATION : ON THE BASIS OF LINEARITY
Linear correlation :
If the change in amount of one variable tends to make changes in amount of other variable bearing
constant changing ratio it is said to be linear correlation.
For example :
Income ( Rs.) : 350 360 370 380
Weight ( Kg.) : 30 40 50 60
Non - Linear correlation :
For example :
Income ( Rs.) : 320 360 410 490
Weight ( Kg.) : 21 33 49 56
If the change in amount of one variable tends to make changes in amount of other variable
but not bearing constant changing ratio it is said to be non - linear correlation.

7. USES OF CORRELATION ANALYSIS
• It is used in deriving the degree and direction of relationship within the variables.
• It is used in reducing the range of uncertainty in matter of prediction.
• It is used in presenting the average relationship between any two variables through
a single value of coefficient of correlation.

8. EXAMPLE
• Compute the correlation coefficient between panicle length (cm) and grain yield in
paddy to the following data and test for the significance of
Panicle
length
cm(X)
30 28 26 24 25 23 27 28 26
Grain
yield (Y)
16 19 17 19 24 21 23 23 25

9. CALCULATION OF CORRELATION COEFFICIENT
USING M.S-EXCEL :
• After copying or entering data in excel sheet, click data menu-choose data analysis tool-then
select correlation option. Then required dialog box appears
• Select the entire range of data in the input range box to which you wish to compute correlation
coefficient.
• Afterwards ,select row/column option of data grouping based on arrangement of selected data

10. • Now decide to choose tick mark button for lables in the first row based on selected input data having
label (or) not.
• After this ,check output options. Select output range option and choose any cell reference for
displaying the result
• Click OK and a table will be displayed showing the correlation coefficient (r) for the data
• = CORREL (array1, array2) also returns the correlation coefficient between two data sets.

11. CALCULATION OF CORRELATION COEFFICIENT
USING SPSS :
• After selecting spss programme,variable view has to be clicked to give variable names,
afterwards enter the data of that particular variables in the data view
• Then click – analyze menu-choose correlation-choose bivariate.Then required dialog box
will be opened

12. • Now select all variables and send to variables box only
• Click Pearson correlation coefficient
• After that choose two tailed/one tailed option
• Finally click ok this dialogue box to get output window

13. COMPUTATION OF PARTIAL CORRELATION
COEFFICIENT USING SPSS :
• Calculate partial correlation coefficient between plant height and ear length when no of
panicles controlled
Yield Plant height Ear length Panicle no Test effect
3.5 101 15 24 51
4.15 106 17 30 63
4.8 104 14 26 56
4.2 108 18 32 65
3.95 107 17 29 48
4.17 104 19 31 59

14. • After selecting SPSS Programme ,variable view has to be clicked to give variable names,
afterwards enter the data of that particular variables in the data view
• Then click – analyze menu-choose correlation-choose partial .Then required dialog box will be
opened

15. • Then keep the selected variables in the variables box and select other variables
which you like to control is placed in the box “ controlling for”
• After that choose two tailed/one tailed option
• Finally click ok in this dialogue box to get the output window

16.  Sabine Landau and Brian S. Everett(2004).A Handbook of
Statistical Analyses using SPSS,Chapman press,U.S.A
 Microsoft MS-Excel & SPSS13.0. Online help