CHAPTER 5

Hypothesis Tests and Confidence Intervals

TWO TYPES OF STATISTICAL INFERENCE

Statistical inference encompasses two procedures: hypothesis testing and parameter estimation. Both are concerned with the unknown value of a population parameter. A hypothesis test determines if a sample of data is consistent with or contradicts a hypothesis about the value of a population parameter, for example, the hypothesis that its value is less than or equal to zero. The other inference procedure, parameter estimation, uses the information in a sample to determine the approximate value of a population parameter.1 Thus, a hypothesis test tells us if an effect is present or not, whereas an estimate tells us about the size of an effect.

In some ways both forms of inference are similar. Both attempt to draw a conclusion about an entire population based only on what has been observed in a sample drawn from the population. In going beyond what is known, both hypothesis testing and parameter estimation take the inductive leap from the certain value of a sample statistic to the uncertain value of a population parameter. As such, both are subject to error.

However, important differences distinguish parameter estimation from hypothesis testing. Their goals are different. The hypothesis test evaluates the veracity of a conjecture about a population parameter leading to an acceptance or rejection of that conjecture. In contrast, estimation is aimed at providing a plausible value or range of values ...