What is chi square test

BUSINESS RESEARCH

1. A Presentation On CHI-SQUARE TEST (Quantitative Techniques of Management) Made by: AKASH SHARMA MBA

2. 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

3. 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.

4. Formula of Chi-square test where, Observed frequency of the event Expected frequency of the event  

5. Steps to calculate   Step 1 : Calculate all the expected frequencies, i.e., for all values of i = 1,2,….,n Step 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  

6. 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.  

7. 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.

8. 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 – 1 where, n = number of variables in series in a row or column

9. 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

10. USES OF - TEST   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) 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)

11. 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  

12. WORKING RULE FOR -TEST   Step 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  

13. 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  

14. 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. .  

15. 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