Poisson EXAMPLE 1: Occupational Health Let’s go back to the Example 1 dealing with health hazards faced by rubber workers. Recall that 4 deaths due to Hodgkin’s disease were observed compared with 3.3 deaths expected from U.S. mortality rates. Is there an excess of Hodgkin’s disease in this population? To answer this question, we will carry out a hypothesis test based on exact Poisson probabilities. Step 0: Check assumptions. For this test, you must check whether the Poisson distribution is appropriate for the problem. Step 1: Set up your null and alternative hypotheses. Ho: Ha: Step 2: Set α = .05. Step 3: Use the Poisson distribution to find the exact p-value. The following graphic shows the Poisson distribution for the number of deaths due to Hodgkin’s disease over the 10 years, assuming the null hypothesis is true (µ = 3.3): Recall that the p-value is the probability of observing a sample AT LEAST AS EXTREME as our data, assuming the null hypothesis is true. For this example, “at least as extreme” implies observing 4 or more deaths. We can use R to find the probability of 4 or more deaths due to Hodgkin’s disease: > 1 - ppois(3,lambda=3.3) [1] 0.4196618
Poisson EXAMPLE 1: Occupational Health Let’s go back to the Example 1 dealing with health hazards faced by rubber workers. Recall that 4 deaths due to Hodgkin’s disease were observed compared with 3.3 deaths expected from U.S. mortality rates. Is there an excess of Hodgkin’s disease in this population? To answer this question, we will carry out a hypothesis test based on exact Poisson probabilities. Step 0: Check assumptions. For this test, you must check whether the Poisson distribution is appropriate for the problem. Step 1: Set up your null and alternative hypotheses. Ho: Ha: Step 2: Set α = .05. Step 3: Use the Poisson distribution to find the exact p-value. The following graphic shows the Poisson distribution for the number of deaths due to Hodgkin’s disease over the 10 years, assuming the null hypothesis is true (µ = 3.3): Recall that the p-value is the probability of observing a sample AT LEAST AS EXTREME as our data, assuming the null hypothesis is true. For this example, “at least as extreme” implies observing 4 or more deaths. We can use R to find the probability of 4 or more deaths due to Hodgkin’s disease: > 1 - ppois(3,lambda=3.3) [1] 0.4196618
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