This site offers an involved definition of the likelihood ratio test with examples and formulas.
This chapter of the "Concepts and Applications of Inferential Statistics" online textbook describes in detail the Kruskal-Wallis test, it's formulas, variables, and procedures using an example involving wine-tasters.
This page gives a description of correlation, Pearson's r, Spearman's rho. There are some scatterplots illustrating the different values of r.