Enumerative Statistical Methods

This section discusses the basic concept of statistical inference. The reader should also consult the Glossary in the Appendix for additional information. Inferential statistics belong to the enumerative class of statistical methods.

The term inference is defined as 1) the act or process of deriving logical conclusions from premises known or assumed to be true, or 2) the act of reasoning from factual knowledge or evidence. Inferential statistics provide information that is used in the process of inference. As can be seen from the definitions, inference involves two domains: the premises and the evidence or factual knowledge. Additionally, there are two conceptual frameworks for addressing premises questions in inference: the design-based approach and the model-based approach.

As discussed by Koch and Gillings (1983), a statistical analysis whose only assumptions are random selection of units or random allocation of units to experimental conditions results in design-based inferences; or, equivalently, randomization-based inferences. The objective is to structure sampling such that the sampled population has the same characteristics as the target population. If this is accomplished then inferences from the sample are said to have internal validity. A limitation on design-based inferences for experimental studies is that formal conclusions are restricted to the finite population of subjects that actually received treatment, that is, they lack external validity. However, if sites and subjects are selected at random from larger eligible sets, then models with random effects provide one possible way of addressing both internal and external validity considerations. One important consideration for external validity is that the sample coverage includes all relevant subpopulations; another is that treatment differences be homogeneous across subpopulations.