Not true about chi- square test is-
**Core Concept**
The chi-square test is a statistical method used to determine if there is an association between two categorical variables. It calculates the probability of observing the observed frequencies in a sample, assuming no association between the variables.
**Why the Correct Answer is Right**
The chi-square test is not a test of significance, but rather a test of independence. It is used to determine whether there is a significant association between two categorical variables. The test statistic is calculated as the sum of the squared differences between the observed and expected frequencies, divided by the expected frequency. The chi-square distribution is then used to determine the probability of observing this test statistic, assuming no association between the variables.
**Why Each Wrong Option is Incorrect**
**Option A:** The chi-square test is a test of significance, which is incorrect. While the chi-square test does produce a p-value, it is not a test of significance in the classical sense.
**Option B:** The chi-square test assumes a normal distribution of the data, which is incorrect. The chi-square test is actually used for categorical data, and it assumes that the observed frequencies follow a multinomial distribution.
**Option C:** The chi-square test is used to compare means between groups, which is incorrect. The chi-square test is used to determine the association between two categorical variables.
**Option D:** The chi-square test is sensitive to sample size, which is correct. The power of the chi-square test increases with increasing sample size, making it easier to detect associations between variables.
**Clinical Pearl / High-Yield Fact**
It's essential to remember that the chi-square test is not a substitute for a more robust analysis, such as logistic regression or generalized linear mixed models, when dealing with complex data sets.
**Correct Answer: B. The chi-square test assumes a normal distribution of the data.**