Question

The uses of chi-square test are given below, choose the correct statements.
A. Used as test of Independence.
B. Used as a test of association between two events.
C. Used as a test of heterogeneity.
D. To measure degree of deviation.
Choose the correct answer from the options given below :

• A. A, B, C Only
• B. B, C, D Only
• C. A, B Only
• D. A, B, D Only

Hint:

Remember the three primary applications of Chi-square:
1. Goodness of Fit (1 variable, 1 population)
2. Test of Independence (2 variables, 1 population)
3. Test of Homogeneity (1 variable, 2+ populations).

Answer 1

The Correct Option is A

Step 1: Concept:
The question asks to identify the statistically valid applications of the Chi-square (\(\chi^2\)) test among the given options.

Step 2: Step-by-step Explanation:

• The Chi-square test is a non-parametric statistical tool heavily utilized to analyze categorical (qualitative) data.

• Statement A: The most common application of this test is the "Chi-square test for Independence". It evaluates whether two categorical variables from a single population are significantly associated or entirely independent of one another. Thus, Statement A is correct.

• Statement B: This is effectively synonymous with the test of independence. When the test determines that two variables are not independent, it implies there is a statistically significant association or correlation between those two events/variables. Thus, Statement B is correct.

• Statement C: The "Chi-square test of Homogeneity/Heterogeneity" is used to determine whether different subpopulations share the same distribution of a single categorical variable. If the distributions are significantly different, the populations are deemed heterogeneous. Thus, Statement C is correct.

• Statement D: The term "deviation" in strict statistical terms generally refers to measures of dispersion (like standard deviation or mean absolute deviation) for continuous numerical data. While the \(\chi^2\) formula calculates the difference between expected and observed frequencies (\(\sum \frac{(O - E)^2}{E}\)), its primary designated statistical purpose is not generically termed a "measure of degree of deviation" in standard statistical taxonomy compared to A, B, and C.

• The most universally accepted and rigidly defined primary uses in standard textbook curricula encompass A, B, and C.

Step 3: Final Answer:
Statements A, B, and C accurately reflect the standard primary applications of the test.