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 |