IANAGeneticist, but I think the answer is that the number is in fact precise, and has a precise meaning, but the interpretation of the number in terms of “how alike you are to genetic group X” is much trickier.
If I understand correctly, what these analyses generally do is look for a collection of SNPs in your genome (Wikidefinition of SNP here: Single-nucleotide polymorphism - Wikipedia). So they are NOT, actually, comparing your entire genome – all your DNA – to some stored database of genomes, and they’re also not comparing functional genes, for the most part, meaning we see here that you have/don’t have this gene for a particularly big honking nose that we find in Arabs of this-and-such historical tribe, or you have/don’t have this gene for Nordic blue-eyed blondness.
What they are doing is finding places in the genome, often enough noncoding places (meaning parts of the DNA that do NOT code for an actual protein, but are involved in regulation, or have no purpose at all), where there happens to be a recognized single-nucleotide flip. They look at the pattern of such flips you have, and compare this to a database of flips, that says, for example, people we’ve tested from Eastern Poland have flips a, b and c with probability 99%, 2% and 88%, while for people from Brazil it’s more like 1%, 100% and 70%, and since you’ve got a and c we conclude you’re probably more Polish than Brazilian. That’s a gross oversimplification without question and involves a bunch of guesswork, but the point is that I think it’s possible to construct a pretty precise number, something like saying you have a 12.5% chance of being a member of this particular cohort.
But what that number means is much trickier. Keep in mind almost all of our DNA is not only identical, it is identical to that of apes, dogs, and dandelions. It’s only a small amount that distinguishes humans from baboons, and an even smaller amount that distinguishes races and families. We know very little about what differences are “critical,” in the sense that they make the macroscopic observable differences about which we care. There’s no labeling on the DNA that tells us this – all we know is that this DNA is similar in this ethnic group, and different in this other. Does it matter? Unless we know what that stretch of DNA does, we don’t know. Maybe it codes for some difference we consider extremely important. Or maybe it codes for nothing at all and this variation in the DNA produces no variation between the groups at all.
I think the assumption is that similarity in the collection of SNPs is probably *generally *correlated with similarity in the characteristics we consider important in discriminating between tribal groups. So if your SNP distribution has only a 12.5% chance of being drawn from the distributions of distributions we’ve measured in actual Ugandans, we conclude you have a low probability of an Ugandan ancestors – but we *can’t * say you have a 12.5%, or indeed put any really precise number on the conclusion. Or we can say you have a low probability of having Ugandan genetic characteristics, but we can’t specify whether you do or do not have any particular macroscopic characteristic we identify as important in deciding who’s an Ugandan.
Hopefully a more modern-educated bioinformatics guy will come along and clean that up, or set me straight if I’ve wandered into error.