A New Kind of Science: The NKS Forum (http://forum.wolframscience.com/index.php)
- Applied NKS (http://forum.wolframscience.com/forumdisplay.php?forumid=4)
-- Statistical Designs - Randomized Blocks (http://forum.wolframscience.com/showthread.php?threadid=1619)

Statistical Designs - Randomized Blocks

I've long admired Wolfram, though I'm an old fashioned sort of scientist and my primary interest very narrow, particularly the common randomized block statistical design. There doesn't seem to be much interest in statistical designs on the forum or by Wolfram in general beyond a good explanation of essentials. So, I thought I'd start a thread and see if I can generate more.

My motives are partly selfish, of course. I have never been satisfied with the vague and incomplete assumptions used in randomized block designs since I used one for my thesis in 1979 on yield and nutritional quality of sainfoin/alfalfa. While struggling with that, I discovered a nifty theorem that expresses the covariance among treatment pairs across blocks and noted that this expression can be used to measure the degree to which a set of randomized blocks can be oriented with respect to the gradient that causes them to differ, and that this should be the appropriate method used to minimize distortion in both block effects and treatment effects within blocks. It can also be used to fully justify including extraneous variables related to such effects in standard multiple regression analysis for treatment effects, something that is usually avoided, but unnecessary given this particular method of optimizing and measuring gradients.

At the time I was not encouraged in these interests and found myself out of the academic loop, but finally found time in the last few years to complete the Randomized Block Theorem and demonstrate how it can be used to good advantage in research, and actually ought to be used often. I would certainly not risk sounding this pretentious if I was not certain in my own mind that these claims are correct and worthwhile. The mathematics is a bit complicated, but quite natural logically for a good statistician and consisting of completely straightforward, basic algebra.

I've been saddened that my lifelong ambition to contribute to good science has been met with such a cold response, and am still hoping for a show, so anyone who might be able to help both causes, PLEASE examine my Randomized Block Theorem and give me good feedback. Please IGNORE the Unified Field and other sections since I am not a physicist by nature and wish to keep one set of issues from interferring with the work particularly unique to my own ambitions. Here's the site, click on the Randomized Block button or MS Thesis for studying this subject, ignore the other buttons. Thank you for your interest. Alan
http://foossolvesunified.com