Cramér's V is a measure of association between two nominal variables and it is based on the Chi-square statistic. It is calculated as the square root of the Chi-square statistic divided by the sample size and the minimum of rows and columns minus 1.

The confidence interval for a proportion is calculated using the formula: p ± (z*√(p(1-p)/n)), where p is the sample proportion, z is the z-score associated with the desired confidence level, and n is the sample size.

The primary purpose of an ANOVA test is to compare the means of different groups and determine whether any of those means are significantly different from each other.

In multiple linear regression, the F-statistic is used to test the overall significance of the model. This test checks the null hypothesis that all regression coefficients are zero against the alternative that at least one of them is not zero. If the F-statistic is significantly large and the corresponding p-value is small, we reject the null hypothesis, concluding that the regression model has some validity in predicting the outcome variable.

The least squares method is used to find the best-fitting line through the data points. This is done by minimizing the sum of the squares of the vertical distances of the points from the line.

A binomial distribution is appropriate when conducting an experiment where each trial has exactly two possible outcomes (often termed success and failure), the trials are independent, and the probability of success is constant across trials.

In simple linear regression, the dependent variable is the outcome we are trying to predict, and the independent variable is the predictor. The dependent variable is also known as the response or target variable, and the independent variable is also known as the explanatory or feature variable.

Discrete probability distributions are used when the outcomes are countable or discrete. Examples include the number of heads when flipping coins or the number of defective items in a batch. Continuous probability distributions are used when outcomes are uncountably infinite, typically involving measurements. Examples include the height of individuals or the time it takes to run a mile.

The Mann-Whitney U test is used for comparing independent distributions, particularly to determine whether two independent samples were drawn from a population with the same distribution.

A random variable in probability theory is a variable that can take on different values, each with an associated probability. It's not "random" in the everyday sense of the word, but its exact value is uncertain until it's observed.

A Paired t-test is used to compare two related samples or repeated measurements on a single sample. It's often used in before-and-after scenarios where the same individuals are measured twice.

The standard deviation, a measure of dispersion or spread, determines the width of a normal distribution. A larger standard deviation results in a wider, flatter distribution, while a smaller standard deviation results in a narrower, steeper distribution.