Relationship between two variables, cause and effect relationships

1. Correlation
Relationship between two variables
By Lekhan Lodhi
Ph.D Course Work
Department of Zoology
Dr. Harisingh Gour Vishwavidyalaya, Sagar (M.P.)

2. Correlation
• There must be cause and effect relationship
For example -
1) Rain and Raincoat
2) Rainfall and Yeild of Rice
3) Income and Savings
• There are simultaneously change in the value of two
variable

3. Definition
• Correlation is the statistical tool for measuring the
degree of relationship between two variables.
• A change in one variable results a positive or
negative change in other
• Denoted by “r”

4. Types of Correlation
• Positive, i.e., two variables X & Y are directly
proportional and fully correlated with each other
1) Income & Expenses
2) Price & Supply
• Negative, i.e., X & Y inversely proportional to each
other
1) Price & Demand
2) Expenses & Savings

5. • Partial positive , i.e., non zero value of correlation
coefficient lies b/w 0 & +1.
E.g., Age of husband & age of wife.
• Partial negative , i.e., non zero value of correlation
coefficient lies b/w -1 & 0.
E.g., Age and vital capacity in adults.
• Absolutely No Correlation, i.e., value of correlation
coefficient is zero, indication that No linear relationship
exists b/w the two variables.
E.g., Height and Pulse rate.

7. Scatter plots

9. Let us take a problem to examine the correlation
Calculate the coefficient of correlation b/w
X & Y.
X 10 9 8 7 6 5 4 3 2 1
Y 6 7 8 4 9 2 1 5 10 3

10. x x2 y y2 xy
10 100 6 36 60
9 81 7 49 63
8 64 8 64 64
7 49 4 16 28
6 36 9 81 54
5 25 2 4 10
4 16 1 1 4
3 9 5 25 15
2 4 10 100 20
1 1 3 9 3
Σx=55 Σx²=385 Σy=55 Σy²385 Σxy=321

15. Rank Correlation
Rank ? Relative standing or position

16. Rank Correlation
• Rank correlation is the study of relationships between
different rankings on the same set of items.
• It deals with measuring correspondence b/w two rankings ,
and assessing the significance of this correspondence.
• The correlation coefficient is calculated on the basis of value
of the variables but quite often situation arise in which data
can not be measured quantitatively, in this case rank
correlation method is applied.
• For e.g. Intelligence, beauty and honesty ,we may require to
rank the individual variables in order of merit by using 1,2,3,
etc for both variables

17. Coefficient of rank correlation

18. • The ICC rankings for one day international (ODI) and test matches for nine
teams are shown below
Team Test rank ODI rank
Australia 1 1
India 2 3
South Africa 3 2
Sri Lanka 4 7
England 5 6
Pakistan 6 4
New Zealand 7 5
West Indies 8 8
Bangladesh 9 9
Test whether there is correlation between the ranks

19. Team Test rank (r1) ODI rank (r2) d=(R1-R2) d²
Australia 1 1 0 0
India 2 3 1 1
South Africa 3 2 1 1
Sri Lanka 4 7 3 9
England 5 6 1 1
Pakistan 6 4 2 4
New Zealand 7 5 2 4
West Indies 8 8 0 0
Bangladesh 9 9 0 0
Total Σd²20

20. = 1-{6x20/9(81-1)}
= 1- (6x20/9x80)
= 1-(120/720)
=1- 0.166
= 0.833

21. What are the applications of correlation ?
• Correlation helps you understand the dependency between two variables.
• If they are highly correlated , it can help build linear model and predict one
variable using another
• Correlation is used to find the linear relationship between two numerically
expressed variables for example
• As the population increases, does the poverty rates increase? Relationship
between population and poverty rates is used effectively by government
through Census.

22. Thank you