What statistical analysis should I use?

The following table summarizes the parametric and non-parametric analyses.

 

omparison of Statistical Analysis Tools for Normally and Non-Normally Distributed Data
Tools for Normally Distributed Data Equivalent Tools for Non-Normally Distributed Data Distribution Required
T-test Mann-Whitney test; Mood’s median test; Kruskal-Wallis test Any
ANOVA Mood’s median test; Kruskal-Wallis test Any
Paired t-test One-sample sign test Any
F-test; Bartlett’s test Levene’s test Any
Individuals control chart Run Chart Any
Cp/Cpk analysis Cp/Cpk analysis Weibull; log-normal; largest extreme value; Poisson; exponential; binomial

The following links from UCLA explain these items briefly:

https://stats.idre.ucla.edu/spss/whatstat/what-statistical-analysis-should-i-usestatistical-analyses-using-spss/

https://stats.idre.ucla.edu/other/mult-pkg/whatstat/

 When two predictors do not interact, we say that each predictor has an "additive effect" on the response.

https://onlinecourses.science.psu.edu/stat501/node/310

 

In regression:

Low p-values don’t necessarily identify predictor variables that are practically important.