
O.K. about 5th try here. I tried uploading a picture to show what I meant, but got the spinning wheel of death and lost my text each time so no fancy pic.
What you are describing sounds a lot like statistical testing "differ substantially." This is both a really important idea in science (that we do a horrible job with) and something that is very hard for me to teach to my college students (in part because K12 does such a crap job).
The first thing is to realize that it takes multiple measurements. At its core, statistical testing is measuring whether the between group difference is bigger than the within group difference. But that means groups of data. At least 3 points in in group. (it is amazing how many of my students "know" they should take 3 measurements, but have no idea why... "3 is a holy number in science?" Facepalm).
But this is an elementary science thread. So how to do this without using a lot of math.
I would put 2 numberlines, 1 right above the other. If the data comes out like this, then they are "substantially" (to use your word) different.
But if the data looks like this, we should conclude that there is no substantial difference.
This is where how we teach K12 is absolutely counterproductive. Because these are numbers, and instead of plotting them like this the first thing my students want to do is average them. And since the biggest number in group 2 is slightly bigger than the biggest number in group 1 ... and the 2nd, and the 3rd and the 4th, then the average of the second group is slightly bigger than the average of group 1. So they will look at those 2 averages (which completely hides any spread) and say 2>1, even if they are 10.04 and 10.03 (and the standard deviation in each is 1).
So. Rule 1 graph them on a number line.
Rule 2. No averages allowed.
Rule 3. If there is minimal or no overlap, they are different.
Rule 4. If there is overlap, we say there is not a significant/substantial/meaningful difference. One of the tennets of the Nature of Science is that science is tentative. We don't jump to conclusions. The purpose of an experiment is not to PROVE our hypothesis was right (10.04 is bigger than 10.03, so we were right, group 2 is bigger/faster/better than group 1). It is to discover what is out there.
Now all the rest.
1. Thank you for posting a real question. My inbox gets so flooded with elementary methods students from a couple of garbage schools who post idiotic questions that they don't even bother to spell check. It is obvious they are being required to do so for a class and even more obvious that the teacher of the class is not reading the garbage that they are posting.
2. I see this problem a lot when I judge science fairs. Out of 10 projects with numerical data, I am lucky if 1 of them actually considers the spread of the data before jumping to the conclusion that A>B, invariably in the direction that confirms their hypothesis.
