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z-test for independent rates

The z-test can also be used to compare differences between rates, such as those obtained from incidence density data.

The test statistic is obtained by dividing the difference between the rates by the standard error of the difference. The variance of the difference under the null hypothesis is estimated assuming a Poisson distribution of rates.<

Algebraically speaking -

z =    p1 - p2
[   1     +     1   ]
n1n2
Where:
  • z is the z-statistic which is compared to the standard normal deviate,
  • r1 and r2 are the two sample rates,
  • is the estimated true rate under the null hypothesis equal to [r1 + r2 /[n1 + n2]

Remember that if the two rates are expressed in integer rather than decimal form (say multiplied by 100) you will need to use the multiplier of 100 in the denominator.