I don't know how to measure spline and i don't know what spline refers to. the part that the handle fits on is about 1/4 inch in diameter and approximately 5/8 inch long.
Yes, that would be the piece that it goes on. Are you sure it's 1/4"? That's pretty small. Are you making sure to account for the ridges in your measurement as well?
We just bought a house with the same issue... the spline is too small for 11/32, or even 5/16. I'd guess (and the measurement matches) that I need 1/4 inch Inner Diameter crank.
A 1/4" spline is very unusual, it is normally used on Mobile home window operators. Please send us some photos of your existing operator spline and, if you have one, a handle from another window for us to look at. That could help us identify the parts you need.