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STEPS INVOLVED IN THE CALCULATION OF CHI-SQUARE(χ2)



STEPS INVOLVED IN THE CALCULATION OF CHI-SQUARE (χ2):


Step 1: Formulation of Null and Alternative Hypothesis; one being independent and the other being dependent. For example:

H0: Null Hypothesis (Categories that are independent)
H1: Alternative Hypothesis (Categories that are dependent)


Step 2: Derive your Expected Values for all the cells in the Observed Table respectively. Using the following formula:
Expected Values= Row Total multiply by Column Total divided by Total Sample Size. (See picture below)


This formula will be applied on each cell in our Observed Values to arrive at our Expected Values.

Note: Total Sample Size or grand total is usually denoted using 'n'.

Step 3: Construct your Chi-Square Tables using the Chi-Square formula. (See pictures below)








Step 4: Obtain your Chi-Square value using the Chi-Square Critical Value Table.(picture below)
Compare your step 3 answer with the value you obtained from the Chi-Square Table (Critical Value). (See picture below)

Tips on how to read the table:
1- obtain your DEGREE OF FREEDOM=ROW MINUS ONE MULTIPLY BY COLUMN MINUS ONE(r-1*c-1).
2- Using the significance level given in the questions. i.e 5% (0.05).
Having known that information, you can easily match it with your table and obtain the Tabulated value(3.841).
Note: If the χ2 Calculated is greater than the χ2 Tabulated then you have to accept H1(reject H0). 

 If χ2 Calculated is lesser than χ2 Tabulated then you will have to accept H0 (reject H1). So simple.

Step 5: Conclusion.

(Note: this conclusion is subjected to the illustration given in class. Though, it still applies to any other illustration.)

If you accept H0 (reject H1), your conclusion will be that 'attending tutorials doesn't not necessarily indicate that you will pass or fail' which means that passing or failing is independent of tutorial attended after class. 

 If you accept H1 (reject H0), it signifies that 'attending class lectures depends on whether you want to pass or fail' meaning that passing or failing is dependent of class lectures only.

NB: H0 means H subscript 0
        H1 means H subscript 1.

It's as simple as that. Don't forget to leave a comment. It's really important to us. Thanks.

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