What statistics model to use when the data is heteroskedastic, not normally distributed and has unequal sample sizes (n<25)? A little bit about myself: I don't have absolutely any background in statistics. (I only learnt it till grade 11th and after that my job is in such a field where I do not have to encounter statistics. However, since I have taken on added responsibilites, I have to perform data analysis for a project which requires great amounts of statistics skills which I lack. I'm working on bridging the knowledge gap, however, when there is a deadline, I have to show atleast a draft).
Here is the type of data I'm dealing with (all the variables are fictitious for anonymity). So, here we go:
If I have two farms: Farm A and farm B, I have three types of fruits growing on these farms: fruit X, Y and Z. I grow 6 of each kind of fruits (so, 6 samples of X, 6 of Y and 6 of Z) by watering them for two hours at both farm A and B; and I grow 6 of each types of fruits by watering them for 4 hours at both farm A and B. I finally harvest these 6 of each kinds of fruits (so 6 of X, 6 of Y and 6 of Z from farm A that were watered for 2 hours, another 6 of X, 6 of Y and 6 samples of Z which were watered for 4 hours from farm A; and I do the same from farm B), so that I can make juice out of them.
I have to determine, 1) For farm A, when the fruits were watered for 2 hours, which type of fruit gave more juice (juice measured in milliliters)?


*For a given time to water (so, say for 2 hours) and a given type of fruit (so, say fruit X), is more juice obtained when harvested from farm A or when harvested from farm B?

Now, the problem is: my data is not normally distributed and also, heteroskedastic at times. Also, sometimes, say a rat comes by and eats a piece of fruit, so we cant use it, in those cases I would have 5 of X, 6 of Y and 6 of Z (or if the rat eats two fruits then 5 of X, 5 of Y and 6 of Z)
Given this problem, could you please suggest me what to go for?
Please let me know if you need any more clarifications.
Thanks.
 A: The first thing to do is to produce a good data visualisation that helps you to see everything you need. For what I understand you want, I'd use six dot plots in the following layout:
2hX 2hY 2hZ
4hX 4hY 4hZ
where each dot plot shows all the observations belonging to the given time in farm A and farm B side by side, using two different colors for these. A single one of these may look like this (this one has three groups per plot but my proposal has just two for the farms, although you may put all three plots from a row into a single one as long as different fruits can clearly be distinguished):
https://cdn.scribbr.com/wp-content/uploads/2020/03/oneway-final-plot.png
Note that here some random "jittering" has taken place in left-right direction. This makes sense if there are (almost) equal observations to avoid overplotting. Otherwise you could plot just all observations for a group on the same x-coordinate. The plot also shows the means and an interval of the mean plus/minus (probably) one or two standard errors to assess uncertainty (I'd personally prefer two standard errors but one is in use as well - as long as you know and communicate well what it is, both are valid - also you don't have to do these if you don't understand what they are). The a-a-b letters in the plot are a distraction and I would avoid doing such a thing unless there is a very strong reason to do it.
Make sure all your plots have the same value range on the y-axis to enable easy comparison. If you plot the 2h results on top and the 4h results on bottom, these two are most difficult to compare visually, and I have proposed to do it like this because in the question you don't mention you want to compare these. If you actually do want that, a different layout will be better. You could try to plot all twelve groups in one row, grouping them so that what you are most interested in becomes easiest to see (also using suitable colors and maybe plot symbols, separating by some space different levels of time).
People often use boxplots for this kind of thing, but I think with 6 observations in each group they're not very sensible and plotting all observations is better. Also I'd think that this way of plotting the data is easiest to understand without stats background.
For everything else I'd start from there. For assessing your cited model assumptions, you need to look at data group-wise (you may know this, not sure whether you have looked at the data in this way already). The plots will also show if any of the violations you mentioned are problematic or not (models are idealisations and always violated in one way or another, but sometimes - not always - this is harmless). Obviously the plot in itself, without any model assumptions and without running hypothesis tests (which chances are you have in mind discussing heteroscedasticity and stuff), may already convey a strong message.
