Question

The significance of difference between proportions can also be tested by :

• A. ‘t’ test
• B. Chi square test
• C. ANOVA
• D. Correlation and regression

Answer 1

The Correct Option is B

The significance of difference between proportions can be tested by the Chi square test. The Chi square test is a statistical method used to determine if there is a significant difference between the expected frequencies and the observed frequencies in one or more categories.

Explanation: In the context of proportions, the Chi square test assesses whether the observed proportion in a sample differs significantly from the expected proportion, assuming the null hypothesis of no difference is true.

The steps for conducting a Chi square test for proportions are:

1. Define the null hypothesis (H0) and alternative hypothesis (H1).
2. Calculate the expected frequencies for each category based on the null hypothesis.
3. Compute the Chi square statistic using the formula: Χ² = Σ[(O-E)²/E], where O is the observed frequency and E is the expected frequency.
4. Determine the degrees of freedom, which is usually (number of categories - 1).
5. Compare the calculated Χ² value with the critical value from the Chi square distribution table at a chosen significance level (e.g., 0.05).
6. Conclude whether to reject or fail to reject the null hypothesis based on the comparison.

This method is particularly useful in fields like social and preventive medicine where it's necessary to test hypotheses about distributions that involve categorical data.