Where does estimation collide?

The procedure of using a sample of data to infer the unknown numerical values, called parameters, that describe the population the sample was drawn from: an estimator is a rule that turns the observed sample into a best guess of such a value, and estimation theory studies which rules are most accurate. Fisher's 1922 On the mathematical foundations of theoretical statistics named estimation as a distinct problem and set out maximum likelihood, the method of choosing the parameter value that makes the observed data most probable. Here the referent is a mathematical inference from data to a population number, judged by bias and spread, not a person's number for how strong something feels or a forecast of what a project will cost.[1]

Unit

One estimate of a population parameter, produced by an estimator applied to a sample

Recovery means

Not applicable

Measured by

Judged by the estimator's bias, variance, and efficiency, and reported as a point value with a standard error

A laboratory method in which an observer assigns numbers to match how strong a stimulus feels, so that a doubled number is meant to report a sensation twice as intense: it turns a private impression of brightness, loudness, or weight into a reported quantity. Stevens's 1957 On the psychophysical law used this method to argue that sensation grows as a power of physical intensity, a relation later called Stevens's power law. Here the referent is a human observer's numerical report of a felt magnitude, gathered under controlled stimuli, not a statistical inference about a population or a forecast of a project's resources.[2]

Unit

One observer's number reporting the felt strength of a single stimulus

Recovery means

Not applicable

Measured by

Elicited by presenting stimuli of varied intensity and fitting the assigned numbers to a power function of the physical measure

The practice of predicting how much effort, time, and money a software project will require before it is built, usually by relating the expected size of the program to past productivity data. Boehm's COCOMO model, introduced in his 1981 book and published in his 1984 Software engineering economics, predicted project effort as a function of estimated lines of code adjusted by cost drivers such as team skill and product complexity. Here the referent is a forward forecast of the resources a piece of work will consume, checked later against what the finished project actually cost, not a report of a felt magnitude or an inference from a sample to a population.[3]

Unit

One forecast of a project's effort, schedule, or cost, made before the work is done

Recovery means

Not applicable

Measured by

Derived from estimated program size and cost-driver multipliers, then compared with the effort and cost actually recorded on delivery