Arrange the following steps in sequence to get the required statistic for testing the association between Income and Gender using a chi-square test:
Options: (A) Calculate the expected cell frequencies. (B) Calculate the value of (Oi – Ei)²/Ei across all cell frequencies and add them. (C) Compare the calculated chi-square statistic with the critical value of chi-square at 1 degree of freedom with the statistical table. (D) Reject or accept the Null Hypothesis based on the analysis. (E) Tabulate the observed cell frequencies in a 2x2 contingency table.
Choose the correct answer:

Correct option is B

To conduct a chi-square test for association between two categorical variables, the correct sequence of steps is:
1. E. Tabulate the observed cell frequencies in a 2x2 contingency table: This is the first step to organize the raw data by putting observed frequencies into a table.
2. A. Calculate the expected cell frequencies: Calculate the expected frequency for each cell using the formula:

3. B. Calculate the value of (Oi – Ei)²/Ei across all cell frequencies and add them: This step involves calculating the chi-square statistic. The formula is:
where Oi is the observed frequency and Ei​ is the expected frequency.
4. C. Compare the calculated chi-square statistic with the critical value: Compare the obtained chi-square statistic with the critical value from a chi-square distribution table at 1 degree of freedom (for a 2x2 table).
5. D. Reject or accept the Null Hypothesis based on the analysis: If the calculated chi-square statistic exceeds the critical value, reject the Null Hypothesis; otherwise, fail to reject it.
Information Booster:
1. Chi-Square Test:
· Used to test for independence between two categorical variables.
· Null Hypothesis (H₀): The variables are independent.
· Alternative Hypothesis (H₁): The variables are associated.
2. Contingency Table:
· A matrix used to display the frequency distribution of categorical variables.
3. Expected Frequency:
· Derived using the formula:

· The critical value depends on the significance level (commonly 0.05) and degrees of freedom (df).
· For a 2x2 table, df = 1.
4. Degrees of Freedom:
· Formula for df in contingency tables: (r−1)(c−1), where rrr = number of rows, ccc = number of columns.
Additional Knowledge:
· Types of Chi-Square Tests:
· Goodness of Fit Test: Determines if a sample fits a population distribution.
· Test of Independence: Checks the association between two categorical variables.
· Conditions for Validity:
· All expected frequencies should be ≥5 for the chi-square test to be valid.
· Interpretation:
· A higher chi-square value indicates a stronger deviation from independence, suggesting a significant association.