A Z-test is used to compare the mean of a sample to the mean of a population when the population standard deviation is known. It's not used to calculate correlations or assess relationships between categorical variables.

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).

The Spearman’s Rank Correlation test handles ties in data ranks by averaging the ranks. For example, if two values tie for a place in the ranking, they are assigned a rank equal to the average of those places.

R-squared is a statistical measure in regression models that represents the proportion of the variance for a dependent variable that's explained by an independent variable or variables.

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.

A value of 0 in Pearson's Correlation Coefficient means there's no linear correlation between the two variables. However, it's important to note that this doesn't necessarily mean there is no relationship at all, it could be that the relationship is nonlinear.

A probability distribution is a mathematical function that provides the probabilities of occurrence of different possible outcomes in an experiment. For a random variable, the probability distribution is the probability that the variable takes a particular value.