Statistical Tests Would Reject Existence of Rare Diseases? Why?

Question

I was wondering the other day. Given a rare disease that occurs 1 in every thousand. That would infect 7 million people in the world. Yet, most statistical tests, testing for the existence of this disease at even a 1% level would be rejected. How does statistical theory resolve this issue?

Answer 1

You wouldn't do a statistical test for whether or not the disease existed. Rather, you would do a statistical test to test a hypothesis about the prevalence of the disease. Using a large enough sample size, you could determine whether or not the hypothesis was likely to be accurate (the "% level" of the test refers to the probability that the observed prevalence of the disease closely matches the actual prevalence).

Statistical theory resolves this by dealing with intervals, and probabilities. You can never be 100% sure of something without looking at every member of the population. Testing a sample, you can say something like "we are 99% sure that less than .0001% of the population has this disease". This uses an assumption about the percentage of the population, using this you obtain a range of values that would be likely to occur from a random sample from the population, and you compare this to the data you obtain from an actual sample. But you are working with statistics, so you are not dealing with absolutes.