I've been working on a little project. Last year I delivered pizzas. I recorded data for 300 of my deliveries like tip amounts, order totals, and delivery times. I have a few hypotheses I would like to test. For example, after examining the data I've noticed that the average tip from orders over the phone is pretty substantially less than the average tip from orders over a device. But as you all know, I can't take the difference in the average at face value. I have to perform a significance test to see if it's statistically significant. The problems I have are as follows:

1. The sets of data are pretty skewed and don't pass normality tests so I don't feel comfortable using a parametric test like Welch's two-sample t test. Also, I can't transform my data because it contains data values of 0 (when customers didn't tip).

2. The shapes of the distributions of the data sets I'm comparing aren't real similar (let alone identical) so I don't feel comfortable using the Mann Whitney U test, Kruskal-Wallis test, or Mood's Median test (because they assume identically shaped distributions).

I just found out about a non-parametric test called the randomization test (known by others as the permutation test or exact test) as mentioned here:

https://www.youtube.com/watch?v=BvdNZNl09eE

Unfortunately, this test doesn't seem to be incorporated into Minitab. (I may be mistaken on that. I hope I am.) And there isn't a lot of guidance on the internet about how to perform this test (which makes me worry that some have a concern about it's validity).

I would appreciate any and all solutions to these problems. I've been working on this project for quite a while and am a bit frustrated. Thank you for your help in advance!