PRESENTATION ON CORRELATION

RANK CORRELATIONBIVARITE ANANLSIS

& CHI SQURE TEST

PRESENTED BY-SUMIT BHARTI

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.

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

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.

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.

RANK CORRELATION

““Rank correlationRank 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.

TYPES OF RANK CORRELATIONIn 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

Steps To Find RC• Step 1:

– Draw the table like

.

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

.

• Step 3:• Give the Rank for the data

• Step 4– Find the difference d & d2

Step 5

• Step 5:– Apply the formula:

r =

Where d= difference, n=no.of data

• 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.

Bivariate analysis

ON TE OTHER HAND

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.

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

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.

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

.

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

• 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.

(v)Then check the degree of freedom = n-1

(vi) Compare the calculated value of X2

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.

.