This session covers hand calculation of chi-square and interpretation of hypothesis

1. Understanding and
calculation of
Chi Square (χ2)
DR. RAJEEV KUMAR,
M.S.W. (TISS, MUMBAI), M.PHIL (CIP, RANCHI), UGC -JRF, PH.D. (IIT KHARAGPUR )
VISITING FACULTY, RKMVERI, RANCHI
Lecture-7: Research Methodology (Chi-square calculation)

2. A survey result
During lockdown, wine shops were opened. A small survey was conducted among 180 people in
Ranchi. These 180 people were selected randomly. Of those 180 people, 105 were males and 75
were females.
In the survey the opinion on sale of alcohol was sought.
The result is following
Response Male Female Total
There should be sale of alcohol
(Yes)
65 15 80
There should be no sale of alcohol
(No)
40 60 100
Total 105 75 180

3. Hypothesis bases on the survey results
Alternative hypothesis
Ha: There will be insignificant association of gender and opinion on the sale of alcohol.
Null hypothesis
H0: There will be no significant association of gender and opinion on the sale of alcohol.
Response Male Female Total
There should be sale of alcohol
(Yes)
65 15 80
There should be no sale of alcohol
(No)
40 60 100
Total 105 75 180

4. Why we call association in (χ2)?

5. Another way of writing hypotheses
Alternative hypothesis
Ha: There will be a significant gender difference of opinions on the of alcohol.
Null Hypothesis
H0: There will be no significant gender difference of opinion on the sale of alcohol.

6. How to prove this hypothesis
We need to apply Chi Square test (χ2 ).
Chi square is applied between two categorical variables ( nominal or ordinal variables).
Chi square assess the statistical difference and association between two categorical variables.
If in the contingency table, in any cell, value is less than 5, then Chi square will not be applicable.
Fisher Exact test will be applicable

7. Chi square calculation (χ2): Step-1
calculation of expected frequencies

8. Chi square calculation (χ2).
Step-2: Arrangement in a table

9. Chi square calculation (χ2).
Step-3: subtract (O-E)

10. Chi Square calculation (χ2)
Step-4: square the value of (O-E)

11. Chi square calculation (χ2)
Step-5: Divide ‘E’ from square of (O-E)
Step-6: Summation of all values of

12. What we should have to interpret the
(χ2) result?
1. The alpha values
2. Degree of freedom (df)
3. Significant critical values
4. Our test value
5. Then compare the test value with the respective critical values and obtain the conclusion.

13. What is our alpha value (χ2)?
Step-7: find out your critical value

14. Step 8: compare the test value (χ2) with
critical value and see the significance

15. How it is associated?

16. The final result
The value of chi square (χ2 = 23.10, df=1), is the higher than the critical value at (P ≤0.001)
(10.82) is highly significant at (p≤0.001).
Alternative hypothesis
Ha: There will be insignificant association of gender and opinion on the sale of alcohol.
Null hypothesis
H0: There will be no significant association of gender and opinion on the sale of alcohol.
There is a highly significant association of gender and opinion on sale of alcohol. Mostly women
don’t support the use and sale of alcohol, however, most of the men expressed their opinion in
the favour of sale of alcohol.
Therefore, the alternative hypothesis is accepted and null hypothesis is rejected

17. How to write the result
Amidst lockdown and unlock-1, a small survey was conducted among 180 people in Ranchi.
These 180 people were selected randomly. Of those 180 people, 105 were males and 75 were
females. In the survey the opinion on sale of alcohol was sought.
The results reveals that there is a highly significant association of gender and opinion on sale of
alcohol. Mostly women don’t support the use and sale of alcohol, however, most of the men
expressed their opinion in the favour of sale of alcohol.
Therefore, the alternative hypothesis is accepted and null hypothesis is rejected at the
confidence interval of (CI=99.99%). We can say that 99.99% males support the sale of alcohol.
However, this generalization is depend on the sample we choose and the sampling method. The
result and generalization may vary from region to region.

18. Thank you and keep learning