Test values in cross calculations (AskiaAnalyse)

For a cell i, j

Case 1: Count when independent

CountWhenIndependent(i,j) = Total(i) * Total(j) / dBase

PrcInd (i,j) = CountWhenIndependent(i,j) / dBase

PrcObs (i,j) = Observe(i,j) / dBase

Sigma = (PrcObs (i,j) - PrcInd (i,j)) /sqrt(PrcInd (i,j) * (1. - PrcInd (i,j)) / dBase)

Case 2: Compared to columns

N1 = Total(j)
N2 = dBase - N1

If N1 and N2 >

P1 = Observe(i,j) / N1
P2 = (Total(i) - Observe(i,j) ) / N2

Denominator = Squared root ( P1 * (1.- P1) / N1 + P2 * (1.-P2) / N2)

Sigma = (P1-P2) / Denominator

Case 3: Compared to rows

N1 = Total(i)
N2 = dBase - N1

If N1 and N2 >

P1 = Observe(i,j) / N1
P2 = (Total(j) - Observe(i,j) ) / N2

Denominator = Squared root ( P1 * (1.- P1) / N1 + P2 * (1.-P2) / N2)

Sigma = (P1-P2) / Denominator

Case 4: Test Value (numeric) - Same formula for three options (options are not relevant for numeric test)

N1 = Total(i) in sample 1

X1 = Mean(i) in sample 1

SD1 = Standard Deviation(i) in sample 1

N2 = Total(i) in sample 2

X2 = Mean(i) in sample 2

SD2 = Standard Deviation(i) in sample 2

T = Test value

Denominator = Squared root (

(((SD1²(N1 – 1) + SD2²(N2 – 1)) / (N1 + N2 - 2)) * (1/N1 + 1/N2))

T = (X1-X2) / Denominator