Which of the following is a pre-requisite for the Chi square test to compare –
The core concept here is understanding statistical tests, specifically the Chi-square test. The Chi-square test is used to determine if there's a significant association between two categorical variables. But there are certain assumptions that must be met for the test to be valid.
Now, the correct answer is likely related to expected frequencies in the contingency table. I remember that one of the key assumptions is that no more than 20% of the expected counts should be less than 5. If that's violated, the Chi-square test might not be appropriate, and a Fisher's exact test should be used instead. So the correct answer should be about the expected frequencies.
Looking at the options (even though they're not provided), the correct answer would be an option stating that all expected frequencies should be at least 5 or that no more than 20% are below 5. The other options might include things like normality, sample size requirements, or independence of observations, which are for other tests.
For the incorrect options: Option A could be about normal distribution, which is for parametric tests like t-test or ANOVA. Option B might mention sample size being large enough, which is a general requirement but not a strict prerequisite for Chi-square. Option C could be about the data being continuous, but Chi-square is for categorical data. Option D might refer to the test being parametric, but Chi-square is non-parametric.
The clinical pearl here is to remember that the Chi-square test's validity hinges on expected cell counts. If the sample size is small, the test can be misleading. Students should remember this cutoff for expected frequencies to avoid common mistakes on exams.
**Core Concept** The Chi-square test requires that expected frequencies in each cell of the contingency table meet specific criteria to ensure valid results. A key prerequisite is that **no more than 20% of cells have expected counts <5**, and **all expected counts ≥1**. This ensures the approximation to the Chi-square distribution holds. **Why the Correct Answer is Right** The Chi-square test assesses associations between categorical variables by comparing observed vs. expected frequencies. Its validity depends on the **central limit theorem**, which assumes sufficient sample size. If expected frequencies are too low (20% of cells), the test overestimates significance, increasing Type I error risk. For 2×2 tables, Fisher’s exact test is preferred when any expected cell count <5. **Why Each Wrong Option is Incorrect** **Option A:** *"Normal distribution of data"* is incorrect. The Chi-square test is **non-parametric** and does not require normality. **Option B:** *"Paired observations"* is incorrect. The Chi-square test assumes **independent** observations; paired data require McNemar’s test. **Option C:** *"Continuous variables"* is incorrect. The Chi-square test is designed for **categorical** (discrete) variables. **Clinical Pearl / High-Yield Fact** Always check expected frequencies before using the Chi-square test. If 20% of cells