Recently I've been reading a lot about DNA tests and ethnicity estimates. I am a statistician and try to explain things by using simple analogies. Hopefully the following explanation will help, but if anyone has any enhancements to suggest I would be most grateful.
I have a jar holding 100 blue marbles representing a father. I have another jar holding 100 red marbles representing a mother. The father is 100% blue and the mother is 100% red. When they have a child they each give 50% of their DNA marbles to the child, so the child will have 50% blue DNA and 50% red DNA. Any further siblings will also have the same 50-50 blue and red DNA.
Let's look at another example. I have a jar holding 100 blue marbles representing a father. I have another jar holding 50 green marbles and 50 red marbles representing a mother. Any children they have will have DNA consisting of 50 blue marbles inherited from the father and a random selection of green and red marbles from the mother. That random selection could be 50 green marbles or 50 red marbles but is statistically more likely to be a random combination of both. The children would all have 50 blue marbles and a varying proportion of green and red marbles.
Now let's look at a more complex scenario. I have a jar containing 50 blue marbles and 50 yellow marbles representing a father. I have another jar containing 50 green marbles and 50 red marbles representing the mother. Any children they have will have a random selection of 50 blue or yellow marbles and 50 red or green marbles in varying proportions. Statistically it is likely that the children will have roughly 25 of each colour, but extremes in either direction could and would occasionally happen.
Now let's take it back a few generations to either 64 or 128 ancestors. For simplicity we'll go for 100 ancestors! Let's say that each of those 100 has 99 marbles of one colour and one black marble. Statistically there is a 50% chance that anyone person will pass the Black Marble on to their child. Then, statistically it is likely that many of the black marbles will not be passed on over several generations. However if we have 1 million sets of 100 ancestors then there is a chance that very occasionally the Black Marble will be successively passed down so that occasionally out of the 1 million sets somebody could end up with 50 or even 100 black marbles. Although it is statistically unlikely that if your parent has 50 black marbles and 50 black marbles, it is possible occasionally that you would inherit 50 black marbles, possibly even from both parents.
I hope this long but hopefully clear analogy explains how there can be such diversity in ethnicity estimates. It is therefore important to not just look at your current ethnicity but at the ethnicity of your ancestors, for many generations. As only a very small percentage of our DNA differs from person to person the extreme examples I have given are not quite so unlikely.
I would recommend the following 8-minute video on YouTube, which explains how we really only inherit our DNA from about 120 ancestors. Try and avoid the numerous other videos from people failing to correctly interpret their ethnicity ESTIMATES!!
https://www.youtube.com/watch?v=9g-VwtRd8ksMartin