My knowledge of math is very basic, my statistics knowledge is even less. It was suggested to me that I try asking this question here, so here we go:
I am developing a software application that will measure and analyze properties of an object's surface. We want to determine how uniform the surface is and compare it to another object to determine which is "more uniform". Due to confidentiality issues as well as simplicity, I'll use an analogy of a dirt field:
- Field "A" is level, however it has many small pits and little mounds. All of the bumps and pits are pretty close to the same size, but they are everywhere on the field.
- Field "B" is also level and has much less pits and bumps than field A, however the pits and bumps it DOES have are quite large (and deep).
Let's say we have this great machine that can measure the the depth and height of the field in a 6" grid pattern - so we have this large set of data presenting an evenly spaced grid of points for each field.
The first part of my problem was to determine uniformity and after asking around and doing some research it seems that "variance" is what I was after. I am now determining variance by dividing the sum of the squared distances from the mean for each point, something like: 1. determine the mean 2. for each point, calculate the square of the distance from the mean 3. Divide the sum of squared distances by number of points.
So { 1, 3, 3, 2, 1 } = 0.8
Honestly I'm not sure I'm doing it correctly, but let's assume I am (for now). My next question is "what is 0.8?" It's my variance... OK, but how would I explain that to a layperson? Our application is not intended for the scientifically minded person, we basically want to convey the message that "Field A is smoother than field B" or "Field A, while it has more imperfections they are evenly spread out and not as intense as field B"
This is difficult to describe... I basically need to know what 0.8 "means"? Percentages are easy, you can say that "XYZ is 98% efficient" (at something) and most people can process that information and understand it. However I don't know how I can say "XYZ's surface is 0.8 uniform." The person would say "Well what does that mean? Is that good?"
That's my first problem: How to express uniformity in simple terms or relative to some other value that makes it easily understandable. If I plug some more severe numbers into my test program, say { 1,1,1,1,60 } I get a variance of 652.6875 - what!?
Please keep in mind, I really don't know what I'm talking about Math wise. What it boils down to is how to express uniformity of a set of values in a meaningful way to a layperson.
I also wasn't sure what tags to use, so if I missed some relevant ones please let me know.
Thanks for reading.