A Presentation

On

CHI-SQUARE TEST(Quantitative Techniques of Management)

Made by: AKASH SHARMA

MBA

CONTENTS INTRODUCTION OF CHI-SQUARE TEST FORMULA OF CH-SQUARE TEST STEPS TO CALCULATE CHI-SQUARE TEST DEGREES OF FREEDOM CASES IN DEGREES OF FREEDOM USES OF CHI-SQUARE TEST

What is Chi-square test?

Chi-square is a statistical test commonly used to compare observed data with data we would expect to obtain according to a specific purpose.

Formula of Chi-square test

where, Observed frequency of the event

Expected frequency of the event

Steps to calculate Step 1 : Calculate all the expected frequencies, i.e., for all values of i = 1,2,….,nStep 2 : Take the difference between each observed frequency and the corresponding expected frequency for each value of i , i.e., find (-).Step 3 : Square the difference for each value of i , i.e., calculate for all values of i = 1, 2, 3…….,n

Step 4 : Divide each square difference by the corresponding expected frequency , i.e., calculate for all values of i = 1 , 2 , 3……,n.Step 5 : Add all these quotients obtained in STEP 4, then

is the required value of Chi-square.

DEGREES OF FREEDOM

The number of data that are given in the form of series of variables in a row or column or the number of frequencies that are put in cells in a contingency table, which can be calculated independently is called the DEGREES OF FREEDOM.

CASES IN DEGREES OF FREEDOM

CASE 1 : If the data is given in the form of a series of variables in a row or column, then the Degrees of Freedom will be calculated as

v = n – 1where, n = number of variables in series

in a row or column

CASE 2 : When number of frequencies are put in cells in a contingency table, the Degrees of Freedom will be

v = (R-1)(C-1) where, R = number of rows

C = number of columns

USES OF - TEST1. Test of goodness fit : The term goodness of fit is used

to test the concordance of the fitness of observed frequency curve and expected frequency curve.

v = (n-1)2. Test of Independence of Attributes : The Chi-square

test is used to see that the principles of classification of attributes are independent.

v = (R-1)(C-1)

3. Test of homogeneity : The Chi-square test may be used to test the homogeneity of the attributes in respect of a particular characteristic or it may also be used to test the population variance.

=(n-1)/where, = sample

variance = hypothesized

value of proportion

WORKING RULE FOR -TESTStep 1 : Set up the

Null Hypothesis : No association exists between the attributes.

Alternative Hypothesis : An association exists between the attributes.Step 2 : Calculate the expected frequency E corresponding to each cell by the formula

where, Sum total of the row in which is lying Sum total of the column in which lying n = Total sample size

Step 3 : Calculate - statistics by the formula

Step 4 : Find from the table the value of for a given value of the level of significance and for the degrees of freedom v, calculated in STEP 2.

If no value for is mentioned, then take = 0.05..

Step 5 : Compare the computed value of ,with the tabled value of found in STEP 4.

a) If calculated value of <tabulated value of , then accept the null hypothesis

b) If calculated value of >tabulated value of , then reject the null hypothesis and accept the alternative hypothesis