Two Sample/Population Proportion Test

Comparing two Proportions from Samples/Populations/Groups/

Similar to the single sample proportion tests, when the population proportions, rates, percentages, ppm, etc. are better representative statistics as compared to the mean or variance, the proportion tests are applied. Some specific examples, include comparison between two populations or samples for mortality rate, employment rate, survival rate, etc.

Limitations on Population Proportion Testing

  1. The sample size, n must be large enough and taken from a large population
  2. Both n and p are the parameters from a binomial distribution.
  3. Both np and n(1-p) must be larger than 5.
    • Therefore, the binomial distribution could be approximated as the normal (Gaussian) distribution.

Shocking Drug Abuse Fatality/ Death Rate in the United States

Drug abuse related fatality/death rate in the United States is observed to be one of the highest in the world. In fact, it is sitting at the top with Russia and Ukraine averaging over 100 per million population. More interestingly, the drug abuse related fatality rate in the US female is statistically highest in the world, averaging over 70 per million population (second is Russia with 35/million). Typically, female has a history of less drug abuse. However, with the highest in the world, you are interested to see whether female fatality rate related to drug abuse is still less than the male population in the United States. Drug abuse related fatality data is provided in Table 10.

Table 10. Drug Abuse Statistics for Male and Female in the United States (average between 1999 and 2018)

[Data Source:] average between 1999 and 2018. The current rate is even higher, averaging about 70,000 per year in the United States:

Step 1


Step 2


The experimental situation fulfills all the criteria for a two sample/population proportion tests. Therefore, the test statistics is calculated by Equation 7.

Equation 7

Either MS Excel or Minitab or any other statistical software can be used to analyze the data.

Step 3


Figure 12. Two Sample/Population Proportion Test Results Output using MS Excel

Figure 13. Two Sample/Population Proportion Test Results Output using Minitab

Statistical Interpretation of the Results

We reject the null hypothesis because the p-value (0) is less than the level of significance (0.05).

Step 4

Contextual Conclusion

Statistically, the drug abuse related fatality rate in female population is still significantly less than the male population in the United States.