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

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