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.