If the expected frequency in any category is too small (common rule of thumb is less than 5), the Chi-square distribution approximation may be inaccurate, leading to incorrect conclusions.

If the calculated Chi-square statistic is greater than the critical Chi-square value (based on the chosen significance level and the degrees of freedom), we reject the null hypothesis. This means the observed distribution significantly differs from the expected distribution.

Factor analysis reduces the dimensions of data by combining similar variables into groups or factors.

The normal distribution, also known as the Gaussian distribution, is symmetric, and its mean, median, and mode are all equal. It is shaped like a bell curve, with the data evenly distributed about the mean.

The key assumption for applying the Sign Test is that the data must be at least ordinal. The Sign Test is a non-parametric test and does not require the assumption of normality.

The Mann-Whitney U test is a non-parametric test, meaning it does not assume that the underlying data follows a specific distribution.

Updating in Bayesian statistics refers to the process of using new evidence to update a prior probability to a posterior probability. Bayes' theorem provides the mathematical framework for this updating process.

The Variance Inflation Factor (VIF) is commonly used to detect multicollinearity in regression analysis.

The probability of an event that is certain to happen is 1. This is based on the definition of probability as a measure that takes values between 0 and 1, inclusive. An event with a probability of 1 is a sure event.

The optimal number of clusters in K-means clustering is often determined using the elbow method. This involves plotting the explained variation as a function of the number of clusters and picking the elbow of the curve as the number of clusters to use.