This presentation discusses correlation, rank correlation, bivariate analysis, and the chi-square test. Correlation measures the strength and direction of association between two variables. Rank correlation analyzes relationships between different rankings using Spearman's correlation coefficient. Bivariate analysis examines the empirical relationship between two variables. The chi-square test statistically tests if an observed distribution differs from an expected distribution using a chi-square distributed test statistic.

1. PRESENTATION ON
CORRELATION
RANK CORRELATION
BIVARITE ANANLSIS
&
CHI SQURE TEST
PRESENTED BY-SUMIT BHARTI

2. CORRELATION
Definition:
while studying two variables at the same time,if it
is found that the change in one variable is
reciprocated by a corresponding change in the
other variable either directly or inversely ,then the
two variables are known to be associated or
correlated.
In correlation analysis ,we must be careful about a
cause and effect relation between the two
variables.

3. example
If the quantities(X,Y) vary in such a way that
change in one variable corresponds to
change in the other variable then the variables
X and Y are correlated.
Types of Correlation:
The important ways of classifying the
correlation are:
1. Positive correlation
2. negative correlation

4. POSITIVE CORRELATION
If two variables move in the same direction i.e.an increase (or
decrease) on the part of one variable introduces an
increase(or decrease)on the part of the other variable, then
the two variablea are known to be positively correlated.
As for example,
profit and investment, Height and weight,yield and rainfall
etc are positively correlated.

5. NEgATIVE CORRELATION
on the other hand. If two variables move in the
opposite directions i.e.an increase (or a decrease ) on the part
of one variable result a decrease (or a
increase)
on the part of the other variable, then the two variables are
known to have a negative correlation .
EXP-
The price and demand of an item,the profit of insurance
company and the number of claims it has to meet etc. are
exp. of variables having a negative correlation.

6. RANK CORRELATION
“Rank correlation” is the study of relationships
between different rankings on the same set of items. It
deals with measuring correspondence between two
rankings, and assessing the significance of this
correspondence. Spearman’s correlation coefficient is
defined as:
r = 1-((6∑D2)/(N(N-1)2))
Where r , denotes rank coefficient of correlation and D
refers to the difference of rank relation between paired I
tems in two series.

7. TYPES OF RANK CORRELATION
In the rank correlation we may have two types of
problems:
• Where ranks are given
• Where ranks are not given
• Where repeated ranks occur
Note:
If r = 1 then there is a perfect Positive correlation
If r = 0 then the variables are uncorrelated
If r=-1 then there is a perfect Negative Correlation

8. Steps To Find RC
• Step 1:
– Draw the table like

9. .
• Step 2:
– Fill the data field with the given data

10. .
• Step 3:
• Give the Rank for the data

11. • Step 4
– Find the difference d & d2

12. • Step 5:
– Apply the formula:
r=
Where d= difference, n=no.of data

13. BIVARIATE ANALYSIS
• Bivariate analysis is one of the simplest forms
of the quantitative (statistical) analysis . It involves the
analysis of two variables (often denoted as X, Y), for
the purpose of determining the empirical
relationship between them.
• In order to see if the variables are related to one
another, it is common to measure how those two
variables simultaneously change together.

14. Bivariate analysis can be contrasted with
univariate analysis in which only one
variable is analysed. Furthermore, the
purpose of a univariate analysis is
descriptive. The major differentiating
point between univariate and bivariate
analysis, in univariate there is only one
variable is analysed. Where as bivariate
is the analysis of the relationship
between the two variables.

15. EXAMPLE
A businessman may be keen to know what
amount of investment Would yield a desired level
of pofite.
Student may want know whether performing
better in the selection test would enhance his
or her chance of doing well in final examination

16. CHI-SQUARE TEST
a chi square test is an statistical hypothesis test in
which the test statistic has a chi square distribution
when the null hypthepothesis is true, or any in which
the probability distribution of the test
statistic(assuming null hypothesis is true) can be
made to approximate a chi square
Distribution as closely as desired by making the sample
size large enough.

17. STEP OF CHI SQUARE TEST
(i)Calculate the expected frequency (E)
(ii)Compute the deviation (0-E)and then square
these deviation to obtain (O-E)2.
(iii)
divide the square deviation i.e. (O-E)2
by the corresponding expected frequency .
(O-E)2
E

18. .
(iv) Obtain the sum of all value
computed in the step (iii) to
compute

19. • This gives the value of X2 , if it is zero
multiplies that there is no
discrepancy between the observed
and the expected frequencies.
• The greater the value of X2 the
greater will be discrepancy between
the observed and expected
frequencies.

20. .
(v)Then check the degree of freedom =
n-1
(vi) Compare the calculated value of X 2
with table value if it is less than the
table value then it will be accepted if it
is more than table value then it will be
rejected.