Equations
The following is a list of the equations used by the Arc-WofE extension:
db = deposits in class | |
ds = total deposits (less points that occur in areas of missing data) | |
b = unit cell area class | |
s = total unit area of theme (less areas of missing data) | |
unit = unit area | |
b = b / unit | |
s = s / unit | |
pbd = db / ds | |
see note below1 | pbdb = (b - db) / (s - ds) |
ls = pbd / pbdb | |
W+: | wp = ls.Ln |
variance of W+: | vp = (1 / db) + (1 / (b - db)) |
s(W+): | swp = vp.Sqrt |
b1 = (ds - db) / ds | |
see note below1 | b2 = (s - b - ds + db) / (s - ds) |
lm = b1 / b2 | |
W-: | wm = lm.Ln |
variance of W-: | vm = (1 / (ds - db)) + (1 / (s - b - ds + db)) |
s(W-): | swm = vm.Sqrt |
contrast2: | c = wp - wm |
s(contrast)2: | sc = (vp + vm).Sqrt |
studentized contrast: | stud = c / sc |
priorp (prior probability)1: | ds / s |
lprioro (prior logit): | (priorp / (1 - priorp)).Ln |
total (sum of weights): | sum of each wp for each class occurring in a unique condition |
totalv (sum of variances of weights): | sum of each vp for each class occurring in a unique condition |
lposto (posterior logits): | lprioro + total |
posto (posterior odds): | exp(lposto) |
postp (posterior probability): | posto / ( 1 + posto) |
prp1: | (priorp * (1 - priorp)) |
vprip (variance of prior probability): | prp1 / totArea |
sprip (standard deviation of prior probability): | vprip.Sqrt |
sprilo: | 1 / ((prp1 * totArea).Sqrt) |
vprilo: | sprilo * sprilo |
spostp (standard deviation of posterior probability / uncertainty due to weights): | ((vprilo + totalv).Sqrt * postp * (1.0 - postp) |
ucD2M (uncertainty due to missing data)3: | |
totalUnc (total uncertainty): | (spostp^2 + ucD2M^2).Sqrt |
1 When the limiting value of the unit area is used, the following equations are substituted for those listed:
unit = 0.00001 |
pbdb = b / s |
b2 = (s - b) / s |
2 When the evidential theme has more than two classes, contrast* is calculated as a substitute for contrast in the summary weights table (Caclulate Response Theme stage).
contrast* = wpMax - wpMin |
standard deviation of contrast* = (variance of wpMax + variance of wpMin).Sqrt |