what is chi square test
TRANSCRIPT
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A Presentation
On
CHI-SQUARE TEST(Quantitative Techniques of Management)
Made by: AKASH SHARMA
MBA
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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
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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.
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Formula of Chi-square test
where, Observed frequency of the event
Expected frequency of the event
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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
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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.
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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.
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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
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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
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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)
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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
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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
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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
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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..
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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