Trailhorserider, you know I have never thought to try the string test on any of my adult horses. That would be an interesting test. I'll do that.
I have been keeping record of Finn and Fiona's heights as they have grown. I string tested Finn at 6 months initially, and Fiona at about 3 months initially (and have several times since with both - the numbers have remained constant.) Fiona has been consistently 3 inches taller than Finn was at the same age, throughout all the measurements since her birth - but Freyja was also malnourished when I got her, and was likely malnourished throughout her pregnancy with Finn (he was also subsequently weaned at 4 months) - an obstacle she didn't face while carrying and raising Fiona (and Fiona wasn't weaned completely until nearly 8 months).
I do have a measuring stick - complete with the little level built in - I picked up pretty cheaply. If you go to tack auctions, you can usually find them for about 25 bucks.
It's not so uncommon for a foal to be taller than either of his parents. The best example I can think of is a pair of Appaloosa's that my Dad showed back in the '70s. The mare and stud were both just barely over 14 hands and of 5 foals that they had, 4 were about the same height. Then Devilweed was born and he matured to about 16 hands. So, yep, 16.2 is dang sure possible.
I can't attest to the accuracy of the string test yet. Rafe is supposed to mature to 17 flat and he is standing just short of 16 now at 18 months so......
You have to remember that height is a trait that isn't one or the other, it's a spectrum of possibilities. Since height is determined by multiple genes it really is a toss up. Obviously a smaller horse will have more "short genes" (just like people) and a taller horse has more "tall genes" but that's not to say that a smaller horse has some "tall genes" in there somewhere, and if paired with a taller horse that's why you'd end up with something usually in between the parents' heights, but it's not unlikely to have a horse with two parents of the same size and still outgrow them both if it happened to get all the "tall genes" from both parents.
I don't really know how to describe it other than that, lol.
Lots of foals get taller than there parents. There are generations of horses that a foal can take after. Crickets sire was only 15.1h and her dam was 15.3h and she ended up being 16.2 hands and 1350lbs. I have no idea how acurate a string test it. I tried it on duchess once (she was 6 or 7yrs old, fully grown) and it said she should have been 16.1h.... she is only 15.3h.