If the occurrence of A does not affect the occurrence of B, we say A and B are independent. This is a key concept in probability theory where the occurrence of one event does not change the probability of another.

The assumptions of an ANOVA test can be checked by: 1. Checking the normality of residuals using a normal probability plot or a statistical test like the Shapiro-Wilk test; 2. Checking the homogeneity of variance using a Levene's test or Bartlett's test; 3. Checking the independence of observations which usually pertains to the study design (random sampling, random assignment).

A Principal Component is a linear combination of the original features in a dataset. Each principal component is orthogonal to each other, meaning they are uncorrelated and each represents a different direction in which the data varies.

No, the Mann-Whitney U test is not used for paired samples. It is designed for two independent samples. For paired samples, a different test, such as the Wilcoxon signed-rank test, would be more appropriate.

The Mann-Whitney U test is more appropriate to use than a t-test when the data is not normally distributed. This test is a non-parametric alternative to the independent t-test and does not assume normality.

If the p-value is less than the chosen significance level in the Kruskal-Wallis Test, we reject the null hypothesis. It means there is enough evidence to suggest that at least one of the groups is different from the others.

The main difference between a population and a sample is that a sample is a subset of a population. A population refers to the entire group of individuals or observations that we're interested in, while a sample is a smaller group that's been selected from that population.

Increasing the sample size makes the test more sensitive, reducing both Type I and Type II errors. Similarly, a more stringent significance level (lower α) reduces the chance of a Type I error. However, it's important to note that decreasing Type I error probability often leads to an increase in Type II error probability, and vice versa. This is known as the Type I/Type II tradeoff.

The interquartile range (IQR) in a box plot represents the middle 50% of the data. It is the range within which the central half of the values fall and is calculated as the difference between the third quartile (Q3) and the first quartile (Q1).

Non-parametric statistical methods are used to analyze data without making assumptions about the population distribution. These tests are based on differences in medians or ranks rather than differences in means.