Overview of Statistical Logic

In epidemiology, a goal of setting up the method by which we will take a sample from the population is to make the sample representative of the population. The best we can do is make samples representative of the population on the average. We do this by having chance be a determinant of the content of the sample. Then, we must take this role of chance into account whether we are making estimates or drawing inferences. One way to take chance into account is to calculate an interval estimate. An interval estimate is usually centered on the point estimatePoint estimate, our best guess at the corresponding value in the population. The width of the interval represents the precision of the estimate and the degree of confidence we want to have that we have the right answer. That degree of confidence is usually 95%. Another way to take chance into account is by testing statistical hypotheses. The hypotheses we test are statements that reflect no associations. These are called null hypotheses. If we find that our sample would be rare assuming a null hypothesis is true, we reject that null hypothesis. In that circumstance, we accept as true the alternative hypothesis. The alternative hypothesis subsumes all possibilities except the one in the null hypothesis. The bottom line in hypothesis testing is the P-value-value. This is the probability of getting the sample if the null hypothesis were true. If it is small enough, we reject the assumption that the null hypothesis is true. If it is not small enough, we remain inconclusive. This avoids the opportunity to accept a false null hypothesis, known as a type II errorType II error. The chance of making a type I errorType I error, rejecting a true null hypothesis is determined by our choice of alphaAlpha. Alpha is the probability of getting the sample assuming the null hypothesis is true that is small enough to lead to rejection of the null hypothesis.