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paired: yes since you have within subject measurements two way: yes since the ANOVA didn't tell you which group it was that rejected the null hypothesis of three equal groups. You might look at group …

Especially when you have only one way (therefore no interaction effects) and few groups, the ANOVA is not the only valid tool. You could do t-tests as long as you correct for multiple testing. The com …

You might use one line in your data-set per shuffled element in B. In the multiple A column cells corresponding to a B element, you would always put the same value. You can then make a paired test on …

Your approach is about as sensible as doing the same with another statistical distribution. There are some problems that need to be addressed. Regarding p-values, if you allocate half of your $\alpha …

There are two possibilities as I see it. None of them have recourse to multiple testing. Your willingness to do corrections for multiple testing shows your honesty, your intent not to do p-hacking, bu …

Since you do only two tests, divide the $\alpha$ level per test in two. That's a Bonferroni correction. You don't need to correct for a third possible test that doesn't interest you. No need to divide …

You don't need your sample points to be normally distributed if your sample is big enough. 30 serves as a rule of thumb. You have 1% of 700M in each group, thus twice 7M. No worries there. As you don …

Do the latter with a Welch t test. I have never heard of a test comparing a subgroup of your data with the whole group that contains the subgroup. I'm not saying it's impossible, but at the very leas …

Yes, why shouldn't it? You can always compare confidence intervals to points (like 0) You shouldn't compare confidence intervals to other confidence intervals Only one out of 20 95% confidence inter …

There is the distinction between the population mean(s) that you want to make a pronouncement about by investigating the sample mean(s) and sample variance(s). You description isn't sufficiently expli …

ANOVA is quite robust to violations of normality if the variances are roughly equal and the sample sizes are similar as well. Both are not given here which is a problem. You could use Welch t-tests i …

This depends on how you compute the paired sample difference. before - after => greater after - before => less

As far as normality is concerned, this can be helped by increasing the sample size to 60. To your main question: If you see the 20 people as the population to draw the two samples from, then your re …

If your n is tiny, your test could be so under-powered that it will fail to reject all but the most ridiculous null hypotheses. edit: I see now that the standard deviations are 6 or 7 times as large …

There are a few possibilities. You could make it a two way ANOVA: A or notA B or notB That would also allow you to look at interaction effects. You would need to put some thought into how many an …