How accurate is the step counter in the health app on the iPhone

I noticed a peculiar thing. The number of steps and the distance depend on the pants I am wearing. I walk a carefully measured distance of .33 miles verified by my car odometer average of 5 circuits and by my hand held GPS. When I wear jeans the iPhone is accurate within .01 miles in 2 miles. When I wear shorts the iPhone is over by varying amounts sometimes almost double. I have tried this several times and the results are consistent (in the sense that the shorts are always significantly more). The jeans distances are very consistent from trip to trip. The shorts are not consistent with either the jeans or themselves. I think the reason is that when I wear jeans they are tight enough to keep the iPhone on the front of my upper thigh. The shorts have a pocket more like dress pants and the iPhone sort of swings back and forth in the pocket beside my thigh. I think it “rebounds” at the back of the swing and counts more steps then there are. I would be very interested if anyone else has experienced this.