This post is a collection of hypothesis test methodologies. The full collection is listed here: http://www.biostathandbook.com/testchoice.html. My post just goes over several hypothesis tests that are relevant to my research.
One-way ANOVA: http://www.biostathandbook.com/onewayanova.html
If you have one measurement variable and one nominal variable, and the nominal variable separates subjects into multiple groups, you want to test whether the means of the measurement variable are the same for the different groups. Sometimes, the measurement variable is called dependent variable; the nominal variable is called independent variable.
Two-way ANOVA: http://www.biostathandbook.com/twowayanova.html
When you have one measurement variable but two nominal variable, then you would need to use two-way ANOVA. It tests whether the means of the measurement variable are equal for different values of the first nominal variable and whether the means are equal for different values of the second nominal variable. Additionally, it also tests whether there is interaction among the two nominal variables, i.e., whether the means of the measurement variable are the same when fixing one nominal variable and changing the other nominal variable.
MANOVA: https://www.researchgate.net/post/What_is_the_difference_between_ANOVA_MANOVA
When you have multiple measurement variables, you can use MANOVA to test whether measurement variables are influenced by one or more nominal variables simultaneously.
Paired t-test (dependent t-test): http://www.biostathandbook.com/pairedttest.html
It is a test on whether the means of two paired populations are different significantly. What are paired populations and unpaired populations? See example here. It assumes the differences of pairs are normally distributed.
Wilcoxon signed-rank test: https://en.wikipedia.org/wiki/Wilcoxon_signed-rank_test
It is a non-parametric test which achieves the same goal as paired t-tests:
compare two related samples, matched samples, or repeated measurements on a single sample to assess whether their population mean ranks differ, in other words, whether the rankings of the means of two populations differ significantly. (It doesn’t need to assume the differences of pairs are normally distributed like paired t-test. It takes into account the absolute values of the differences.)
Signed test: https://en.wikipedia.org/wiki/Sign_test
If you want to calculate whether the differences of ranks are significant and the absolute values of the differences don’t matter.
Kendall rank correlation coefficient (Kendall $latex \tau$): https://en.wikipedia.org/wiki/Kendall_rank_correlation_coefficient
It is a test on rank correlation (association) between two measured quantities. See one usage in “Deep Neural Networks for Optimal Team Composition”
Spearman’s rank correlation coefficient: https://en.wikipedia.org/wiki/Spearman%27s_rank_correlation_coefficient
Similar to Kendall rank correlation coefficient.
One way Chi Square Test: http://www.okstate.edu/ag/agedcm4h/academic/aged5980a/5980/newpage28.htm
Test if observed data falling in categories meets expectation.
More non-parametric statistical method: https://en.wikipedia.org/wiki/Nonparametric_statistics#Methods