Statistical Calculator

Difference Between Two Proportions

Formula

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Large (Infinite) Populations

test statistic:  z = |p₁-p₂ |/s

where:

p₁ = proportion 1
p₂ = proportion 2

s = sqrt(p(1-p)/n₁ + p(1-p)/n₂)    p = (p₁n₁+p₂n₂)/(n₁+n₂)  n₁ = sample size 1  n₂ = sample size 2

significance test:
z > 
2.576 for 99% level of confidence
1.96 for 95% level of confidence
1.645 for 90% level of confidence

Finite Populations

test statistic:  z = |p₁-p₂ |/s

where:

p₁ = proportion 1
p₂ = proportion 2

s = sqrt(p(1-p)/n_1adj + p(1-p)/n_2adj)   
p = (p_1adjn_1adj+p_2adjn_2adj)/(n_1adj+n_2adj) 
n_1adj = (N-1)n₁/(N-n₁)
n_2adj = (N-1)n₂/(N-n₂)
n₁ = sample size 1 
n₂ = sample size 2

significance test:
z > 
2.576 for 99% level of confidence
1.96 for 95% level of confidence
1.645 for 90% level of confidence