validation message
Information
Target: To check if the difference between the probability of succees (p) of two groups (populations) is significant, using sample dataHypotheses
H0: p1 ≥ = ≤ p2
H1: p1 < ≠ > p2
Test statistic
![Z statistic]()
Normal distribution
When using continuity correction
The correction adjust the statistic toward the zero.
p1 < p2: F = 1.
p1 > p2: F = -1.
p1 = p2: F = 0.
| Cont = | F | ( | 1 | + | 1 | ) |
| 2 | n1 | n2 |
The continuity correction cannot change the direction of the statistic i.e. correct positive statistic to negative, or vice versa.
Cont = Min(Cont,Abs(p1 - p2)).
| Z = | p̂1 - p̂2 + Cont |
| √( p̂(1-p̂)(1/n1 + 1/n2) ) |
Assumptions
 | Binomial distribution - the probability for event within each group is identical |
 | Expected difference d between the populations's average is known |
Required Sample Data
 | p̂1, p̂2 the sample probabilities or x1, x2 the number of successes |
 | n1,n2 - Sample size of group1 and group2 |
R Code
The following R code should produce the same results:
The prop.test uses the Chi-squared statistic with one degree of freedom, which is exactly as using the Z test: z2=χ2(1)