CORRECTION AT 8:51: in the chart, 'Wilcoxon' and 'Mann Whitney' should be switched. Wilcoxon is the non-parametric version of the PAIRED t-test (not unpaired as the video suggests). Mann Whitney is the non-parametric version of the UNPAIRED t-test (not paired as the video suggests).
One small caveat: in broader mathematics, "number of bacterial colonies" would be treated as a **discrete variable**, which means the variable is numeric but it's restricted to certain values (and between those allowable values are gaps that the variable can't take on). But if you're plugging that variable into a regression or t-test/ANOVA model, then you're treating it as continuous. To quote minitab, which has great articles on statistics:
"If you have a discrete variable and you want to include it in a Regression or ANOVA model, you can decide whether to treat it as a continuous predictor (covariate) or categorical predictor (factor). If the discrete variable has many levels, then it may be best to treat it as a continuous variable. Treating a predictor as a continuous variable implies that a simple linear or polynomial function can adequately describe the relationship between the response and the predictor. When you treat a predictor as a categorical variable, a distinct response value is fit to each level of the variable without regard to the order of the predictor levels. Use this information, in addition to the purpose of your analysis to decide what is best for your situation."
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One big caveat: some may take issue with the terms 'relationship' and 'comparison' and the way I'm using them. Consider a medical researcher who is testing a new drug by comparing a treatment group with a placebo group. She might say: "the video says I'm doing a *comparison* of two groups. But I disagree; I believe I'm seeking a relationship/correlation between the drug and the therapeutic effect." So who is right--the video or the medical researcher? The fact is that comparisons can allow us to deduce relationships, and this creates ambiguity. In the video, the term 'relationship' perhaps should be interpreted very narrowly to mean: 'you're seeking a mathematical equation that relates the variables.' And the term 'correlation' should be interpreted narrowly to mean: 'you're seeking a number showing how correlated your two variables are.' These terms (comparison & relationship) describe what you're doing with the data and variables themselves, not the larger goals of the experiment.
Nothing can replace practice; the more you use these tests, the more you'll understand how they apply and what their limitations are. I'm not an expert on statistical tests. If you find other good explanations or sources that go into subtleties that the video overlooks, please share them in the comments!
Lastly, here's one of the most rigorous descriptions of what p-values are, from a true expert, Daniel Lakens: [ Ссылка ]
He has a course on Coursera called "Improving Your Statistical Inferences" that I highly recommend: [ Ссылка ]
