Tests of Differences between Proportions (3 of 5)

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4. (continued) Therefore, z = 0.344/0.0713 = 4.69. A z table can be used to find that the two-tailed probability value for a z of 4.69 is less than 0.0001.
   
   If n₁ = n₂ then p is simply the average of p₁ and p₂:
   
   
   
   The two p values are averaged since the computations are based on the assumption that the null hypothesis is true. When the null hypothesis is true, both p₁ and p₂ are estimates of the same value of π. The best estimate of �π is then the average of the two p's.
   
   Naturally, if one p is based on more observations than the other, it should be counted more heavily. The formula for p when n₁ ≠ n₂ is:
   
   
   
   The computations for the example on early childhood intervention are:
   
   
   
   =