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.

The degrees of freedom for a Chi-square test for a contingency table with r rows and c columns is calculated as (r-1)*(c-1). These are also known as independent degrees of freedom as they depend on the number of independent ways that the data can vary.

While you can technically compute a Pearson correlation coefficient for non-linear relationships, it may not provide meaningful results. The Pearson correlation measures the degree of a linear relationship between variables, and does not fully capture the dynamics of a non-linear relationship. In such cases, Spearman's rank correlation or other non-parametric correlations may be more appropriate.

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).

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.