Statistical Comparision between Conditional Probability

[johngoogle]

Suppose

X1 Y1 Z1
0 0 0 (5 times Z1 is 0 for X1=0 and Y1=0)
0 0 0
0 0 0
0 0 0
0 0 0
0 1 0
0 1 0
0 1 0
0 1 0
0 1 0
0 1 0
0 1 0
0 1 1
0 1 1
0 1 1
0 1 1
0 1 1
0 1 1
0 1 1
0 1 1
.
.
.

Which is..
(Same table which is above..)

X1 Y1 Z1 (Count of Zeros) (Count of Ones)
0 0 5 2
0 1 7 8
1 0 0 10
1 1 5 1



X2 Y2 Z2(Count of Zeros) (Count of Ones)
0 0 10 4
0 1 14 16
1 0 0 20
1 1 10 2

Finding P(Z1|X1Y1) AND P(Z2|X2Y2)
HERE it is the same..

example
X1 Y1 Z1 (Probability of Zeros)
0 0 5|7


X2 Y2 Z2 (Probability of Zeros)
0 0 10|14

But what if this is not the case and we have

X2 Y2 Z2(Count of Zeros) (Count of Ones)
0 0 7 5
0 1 12 2
1 0 2 0
1 1 1 5

Than how to know how close is P(Z1|X1Y1) AND P(Z2|X2Y2) using some method..

 

[Valkarie]

?In this situation, one way to compare the probabilities is to calculate the likelihood ratio for each value of X2, Y2 and Z2. The likelihood ratio is defined as the ratio of P(Z2|X2Y2) to P(Z1|X1Y1). For example, for the first row (X2 = 0, Y2 = 0), the likelihood ratio would be: P(Z2 = 0 | X2 = 0, Y2 = 0) / P(Z1 = 0 | X1 = 0, Y1 = 0) = 7/5. This ratio can then be compared to other values of X2, Y2 and Z2 to determine how close the probabilities are.