The only response I can think of here is I'm not sure either. Best wishes, David Booth

Thank you sir! I know it is a vague question but I just want to know what I can do with my data that makes some kind of sense

But why did you collect the data? You had a reason right? This tells you what you do with your data. For example what properties do you want to compare? Best wishes, David Booth

Mike, here are a couple of things to try:

1. Mann-Whitney rank-based test between population 1 and population 2 on feature1 and feature2.

2. Spearman rank-based correlation test on feature1 and feature2 within each population. These correlations can then be compared between populations.

Since I don't know what your data represent I have no idea how meaningful these comparisons might be, but at an algorithmic level, they are tests that are suited to your data.

PS on the variability comparison, try plotting the cumulative frequencies together. A more uniformly distributed data set will have a more linear S-curve. A data set with more coinciding values will have bigger steps in it. This is a qualitative comparison only. Or you could draw a non-cumulative frequency histogram.

I don't know any formal quantitative non-parametric tests of variability. Maybe just compare the ranges?

Ian Dash Apologies but how do you know what to do without knowing the research question(s)?. You know like in experimental design. You know what you wish to do before you try to do it. In my experience that makes life a lot easier.

Best wishes, David Booth

David Eugene Booth, that would take all the fun out of it! 🙂

Seriously though, see the end of my first answer.

@ian thanks for the additional reply. I understand your other reply but I'm somewhat concerned about leaving the impression that it's ok to grab a few numbers from somewhere hit them with a test or two and believe that this is of some value. I meant no disrespect and I certainly understand that if we had some idea of where the numbers came from you have made some valuable suggestions. Thanks for the additional reply and may Efron be with you.. David

David Eugene Booth, I agree that this question gave very little contextual information and I agree that in the best of all possible worlds it would be greatly preferable to have enough details on the study to be able to advise on the appropriateness of comparisons if necessary.

Unfortunately, when one asks for more information on this forum, the reply more often than not is silence. I think when people ask for advice online, they are often nervous about looking foolish, and they may believe that the more information they give, the more exposed they are. Or perhaps they have a research idea that they don't want to publicise prematurely.

Whatever the reason for silence, if no further information is given, one is left with the choice of whether to offer tentative advice in an information vacuum or to abstain. Since I have had a few silent replies on other questions now, and since you had already hinted that you wanted more details on this question and received none, I opted to offer some tentative advice but added a caveat emptor rider. I guess I will have to trust Mike to use the supplied information wisely. 🙂

David Eugene Booth PS when I was drafting my initial reply, your second reply was not visible on my feed, even though it reached the server before mine did. There was no intention on my part to short-circuit your dialogue with Mike, and if I inadvertently did this then I offer my apologies.

@Ian thanks very much. No problem here. Best wishes, David

Ian Dash David Eugene Booth Thank you both for your replies! I hope I didn't cause any annoyances for any of you and if I did, I apologize. Also apologies for the radio-silence on my part, I caught some vaccin-related illness and was out for a couple of days.

I am not a statistician nor a professional scientist in any form, just a student, therefore my use of your given information will only affect my own study results ;)

I can attempt to give some background. However because of the reasons stated above I can't be sure of the value of this, but I will try!

Biological background (long story):

The features described in my orginal questions are a small subset of Tandem Repeats, repeated sequences of DNA which are found all over the genomes of many organisms. This subset is a Tandem Repeat with the bases C-G-G (in any combination e.g. CGG, GCG, GGC etc.) repeated a couple of times.

Repeats are highly variable in length due to their repetitive nature, which causes errors in DNA repair, so they can rapidly expand or contract in copy number over generations.

In humans there is a specific example of a disease caused by a CGG repeat in the promoter of the gene FMR1, which causes a neurodegenerative disorder. The length of this repeat exists in a 'healthy' range in the population but when it reaches a certain length, the FMR1 gene gets silenced and disease occurs. Many other diseases related to repeats are known (called repeat expansion disorders), the majority of which with neurodegenerative symptoms. It is also known that length-variation of some repeats, especially ones located in promoters of genes, can influence the expression of that gene.

It is hypothesized that these repeats have a basal function in tuning gene expression of genes. When comparing humans with primate species, one can observe subtle differences in gene expression and it is hypothesized that these differences are an important factor determining the phenotypic differences between humans and their relatives. This difference in gene expression in turn is sometimes correlated with variation in Tandem repeats length. Thus ultimately, repeat length could have contributed to the speciation of humans and could be maybe responsible for some human specific traits such as having a larger brain (for example).

Now for the data and research question:

The data is generated by a tool that can estimate copy number of repeats from aligned whole genome sequencing data. (this specific tool: Article Profiling the genome-wide landscape of tandem repeat expansions

I have used this tool on a population of humans from the Human Genome Diversity Project and Rhesus Macaque (Rhesus Macaque because this was the only organism with suitable data). Both populations are 25 individuals (with more on the way). The final resulting data is the matrix as described in the original question: Copy number (positive integer) of all CGG tandem repeats found in both human and Rhesus macaque. It is important to note that some repeats for some individuals could not be genotyped, so the matrix has NA for some individuals. (the matrix is not completely 'filled').

My supervisor divided the research in two parts: comparison between the two species and inter-individual comparison for both populations. Her hypothesis is: "Tandem Repeats are important targets for natural selection over evolutionary time, especially in the primate brain".

So I have now the data as I have described and want to get something interesting from it. What I think would be the best strategy is find a small set of tandem repeats that are 'different' between the two populations: Either the length is more 'variable' in one species compared to the other or the length is different, longer (higher copy number) or shorter (lower copy number) in one species compared to the other one. This would give me repeat groups to compare.

For example: 'Tandem repeats in neurodevelopmental genes are more variable in humans' or something like that. The H0 then would be something like: No difference in repeat length/ repeat length variation between the two species.

Now as I said, I am not a statistician (and neither is my supervisor) but I know enough that i have to know the distribution of my data before I can throw any statistical comparisons. The data however is a bit unsual (for me), most repeats have the same copy number across all individuals, except one or two (so what kind of distribution is that)? I would just like to find the repeats that are 'different' between the two populations in copy number or degree of variation in copy number between the two populations. (Then I can at least philosophize about the implications for evolution, considering which genes these repeats belong to). I don't expect that I can answer my supervisor's hypothesis of important targets over evolutionary time but at least I want to make some kind of assessment of this.

I also want to note there are no generalized models/statistics/packages or something of the kind that people use tackling this kind of questions related to repeats (as far as I am aware). There is no general model for repeat mutation. So I would have to make do with some of my own statistics to find interesting repeats. (Therefore I turned to researchgate to get some advice from people who actually know what they are doing).

I hope I made things slightly more clear

Also Ian Dash is absolutely spot on. It is kind of scary to show the scientific community how ignorant one is still :) (but I will get there)

Mike, thanks for your reply and for your kind comment. I'm sorry to hear of your illness and trust that you are now recovering. We live in dangerous times and even the few protections we have from danger carry their own risks. I had a small reaction to my first vaccination too, although from the sound of it, not as bad as yours. I am glad we have the vaccines though - the alternative is far worse. It seems to be a real challenge though for researchers to convey this message to the general public.

Thanks also for all the background information on your project. Since your variables are quantitative data, the Mann Whitney rank-based test is applicable. I had assumed because the example data were numerical that they were quantitative, but it did occur to me that people sometimes use numbers to represent categories (not a good practice - it leads to much confusion). I probably should have added that rider to my answer.

Similarly, if your feature 1 and feature 2 are genetic traits in the same individual, the Spearman correlation test is also applicable.

On looking foolish, a colleague of mine was fond of saying that there are no foolish questions, only foolish answers. All researchers are still learners - some have just been at it longer than others.

Good luck with your project.

Mike de Groot , rather than hypotheses, I think you have some guiding questions for an exploratory analysis of differences between populations. It seems to me that you can define several indicators, including the ones you and Ian Dash have already mentioned. It seems that the concept of randomness and run-based indicators (number of runs and length of the longest run) can be helpful. To compare each indicator in the two populations you could bootstrap, as I thought David Eugene Booth subtly suggested. Being an exploratory analysis, the results would not necessarily have the character of hypothesis tests.

Ian Dash I am good thanks! Just had a mild fever as a side effect but I count myself lucky as one of the people with access to the vaccines.

I often find that genuine well-meant comments from more experienced scientists like yourself help a lot with confidence and motivation so I hope you are pleased to know you did that for me ;)

Glad to help, Mike, and thanks for your feedback.

I agree also with Jorge Ortiz Pinilla : when you are looking for clues to solve a mystery, an exploratory analysis may be more valuable than hypothesis testing. The latter gives you yes/no answers for differences (always a good starting point, but that's as far as it takes you). The former can help you create a model for the form of those differences that you can investigate further.