The plan must identify important variables related to the conjecture and specify how they are to be measured. From the data collection plan, a model can be formulated from which inferences can be drawn. . Probability is the tool used for anticipating what the distribution of data should look like under a given model. The mathematical description of variation is central to statistics. The probability required for statistical inference is not primarily axiomatic or combinatorial, but is oriented toward describing data distributions. .
Statistical inference guides the selection of appropriate models.
Inference from data can be thought of as the process of selecting a reasonable model, including a statement in probability language of how confident one can be about the selection.