Where does inference collide?

Drawing a conclusion about an unobserved population from an observed sample, together with a stated measure of how uncertain that conclusion is. In On the Problem of the Most Efficient Tests of Statistical Hypotheses, Neyman and Pearson framed the task in 1933 as choosing between hypotheses so as to control the long-run rate of two kinds of error, and Fisher built a parallel account around significance and estimation. The referent is a population parameter, the input is a random sample, and the output is an interval or a test decision with a known error rate. What makes this meaning distinct is that the conclusion reaches past the data in hand to a population that was never fully seen, and its warrant is frequency behaviour over repeated samples, not the validity of any single logical step.[1][2]

Unit

A population parameter estimated from a sample

Recovery means

Not applicable

Measured by

Confidence intervals, p-values, and error rates computed from sample data

A rule-governed step in which a thinker moves from premises already accepted to a conclusion, taking the conclusion to be supported by them. Boghossian, examining the question in 2014 in What Is Inference?, argued that inference in this meaning is a personal-level mental act governed by a rule the reasoner follows, not merely a logical relation that happens to hold between sentences. The referent is a transition in someone's reasoning: deductive when the premises guarantee the conclusion, inductive when they only raise its probability. What sets it apart from the statistical meaning is that the warrant lives in the form of the step itself, and a valid inference can be drawn with no sample, no data, and no population in view.[3]

Unit

A step from premises to a conclusion

Recovery means

Not applicable

Measured by

Judged by the validity or strength of the argument form, not by data

The reader or listener supplying a connection or fact that the text left unstated, so that the discourse hangs together. Graesser, Singer, and Trabasso set out in 1994, in Constructing Inferences During Narrative Text Comprehension, which inferences comprehenders actually generate as they read, such as the bridging inference that links a new sentence to an earlier one; the idea traces to Grice's account of conversational implicature, where a hearer works out what a speaker meant beyond what was literally said. The referent is a mental filling-in during comprehension, and the unit is a single inferred proposition. Unlike the logical meaning, the step need not be valid and the reader is rarely aware of taking it; unlike the statistical meaning, nothing is estimated about a population.[4][5]

Unit

An unstated proposition supplied during comprehension

Recovery means

Not applicable

Measured by

Reading-time, recall, and question-answering measures of what readers infer