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Submitt ed By : Divyanshu Singh
Yalin Wang
Submitt ed To : Prof. Dr. Dr. Franz Peren
WS- 2011 MBA-NGO : Business Stati sti cs
Correlation Analysis using SPSS software.
Hochschule Bonn Rhein Sieg
Suppose you have now your own NGO, and you find yourself asking a question like one of the following: A) Your NGO is still at the starting phase, you have different budget each year, and you want to expand the NGO size, have more staff, then you have a list of the recent years staff numbers and budget numbers, you wonder if there is any connection between. B) You ask two of your project officers to independently evaluate all the 5 projects in your NGO according to how good they perceive each project to be (by giving from low to high points) . Are the evaluations consistent between the two officers, or do they have different perceptions about which the better performing project is? If you have faced such questions and don't know exactly how to approach them, this presentation will provide you some help. The appropriate approach for these examples is correlation analysis, and we would like to introduce you the ABC of correlation analysis and how to use SPSS to perform all the necessary calculations.
1) What is Correlation Analysis?
2) How is it calculated?
3) What is the purpose of Correlation Analysis?
4) How are the results of Correlation Analysis interpreted?
5) How to perform Correlation Analysis using SPSS software?
6) How to interpret the results from SPSS?
Contents
1.1 Definition:o Statistical technique to determine the dependence between 2 or more variables.
In another word, Correlation is a statistical technique that can show whether and how strongly pairs of variables are related.
o a) Linear dependence
b) Non-linear correlation
c) No correlation
o Correlation coefficients:
a) Pearson’s coefficient (r)
b) Spearman's coefficient (rho or ‘ρ’)
c) Kendall’s coefficient (tau-b )
d) Point biserial coefficient etc…
1. What is Correlation Analysis?
o The ratio of the covariance of 2 variables to the product of their standard deviations.
where,N = Number of values or elements X = First ScoreY = Second ScoreΣXY = Sum of the product of first and Second ScoresΣX = Sum of First ScoresΣY = Sum of Second ScoresΣX2 = Sum of square First ScoresΣY2 = Sum of square Second Scores
2. How is it calculated?
Your NGO
YearNumber of staff
(X Values) Project Budget, 10K
(Y Values)
200818
2.1
2009 17 2.0
2010 22 1.5
2011 21 2.2
Correlation Co-efficient Example: To find the Correlation of
Step 1:
Count the number of values or elements, suppose we want to evaluate the relationship between X and Y N = 4
X Value Y Value X*Y X*X Y*Y
18 2.1 18 * 2.1 = 37.8 18 *18 = 324 2.1 * 2.1 = 4.41
17 2.0 17 * 2.0 = 34 17 * 17 = 289 2.0 * 2.0= 4
22 1.5 22 * 1.5 = 33 22* 22 = 484 1.5 * 1.5 = 2.25
21 2.2 21 * 2.2 = 46.2 21* 21 = 441 2.2 * 2.2 = 4.84
Step 2:
Find out the value of XY, X2, Y2 See the below table
Step 3: Find ΣX, ΣY, ΣXY, ΣX2, ΣY2.
ΣX = 78 ΣY = 7.8 ΣXY = 151 ΣX2 = 1538 ΣY2 = 15.5
Step 4: Now, Substitute in the above formula given.
Correlation(r) =[ NΣXY - (ΣX)(ΣY) / ([NΣX2 - (ΣX)2][NΣY2 -
(ΣY)2])]
= ((4)*(151)-(78)*(7.8))/sqrt([(4)*(1538)-(78 )2]*[(4)*(15.5)-
(7.8)2])
= (604 – 608.4)/ ([6152 - 6084]*[62 – 60.84])
= -4.4/ (68*1.16)
= -4.4/ (78.88)
= -4.4/8.88
= -0.495
3. How are the results of Correlation Analysis interpreted?
o Correlation coefficient value ranges between +1 and -1
o Correlation Coefficient Values symbolized by ‘r’ :
+1 and -1 Linear dependence r = 1 Perfect positive linear correlation r = -1 Perfect negative linear correlation 0 No correlation 0 < r < 1 positive linear correlation -1 < r < 0 negative linear correlation
3. Interpretation of results of Correlation Analysis
o To determine the extent to which 2 variables vary together.
o To determine the strength and direction of relationship.
o Does not indicate: One variable could be used to predict the other variable One variable causes the other variable
o Applied in the fields of: Scientific Data Analysis Marketing research Business Analysis etc.
4. What is the purpose of Correlation Analysis?
5.1 Introduction
o SPSS (Statistical Package for the Social Sciences) from IBM
o Not an open source software
o Purpose : Data mining , text analytics, statistical analysis
5.2 Steps for correlation analysis using SPSS
CONTD….
5. How to perform Correlation Analysis using SPSS software?
1) Create data for analysis or upload an existing data file.
2) Select the data for analysis.
5. How to perform Correlation Analysis using SPSS software?
3) To visualize data and variables.
Using SPSS…
4) Correlate the data using Bivariate function.
Using SPSS…
Using SPSS…5) Parameters for statistical analysis.
Selection of Variables to correlate. Selection of type of Correlation Coefficient. Selection of type of Significance test.
6.How to interpret the results from SPSS?
In this case the results look good but when they are not scatter plot can be used to reveal the outliers which could be avoided for further analysis. This is how we get the scatter plot of the data.
6.How to interpret the results from SPSS?
6.How to interpret the results from SPSS? Split the data file using the Data->Split File->Compare groups->No.of working hours-> Ok More accurate view of association
Increase in the use of Technology and Efficient service by the
bank increase simultaneously.
Computerized techniques and ATMs made banking easier
and faster.
Automated procedures reduced errors caused manually.
The same applies to other variables as well.
But there is no causation between these variables.
Interpretation of Case Study
http://idlastro.gsfc.nasa.gov/idl_html_help/Correlation_Analysis.html
http://www.statsoft.com/textbook/basic-statistics/
SPSS- Tutorial
http://www.csulb.edu/~msaintg/ppa696/696stsig.htm
http://academic.uofs.edu/department/psych/methods/cannon99/level2a.html
http://mathworld.wolfram.com/CorrelationCoefficient.html
http://www.cs.uu.nl/docs/vakken/wo2/SPSS/spss3.pdf
http://easycalculation.com/statistics/learn-correlation.php
References
Thank You For Your Attention
