Fobserved

fobserved is a term used in statistics and data analysis to denote the value of a predefined function f evaluated on the observed data. It serves as a tangible summary statistic that can be contrasted with a reference or expected value derived from a model or from simulated data. If D_obs represents the observed dataset and f: D -> R is a chosen statistic or function, then fobserved = f(D_obs).

In practice, fobserved is often compared to a reference distribution to assess model fit or to test hypotheses. The reference distribution can be obtained through resampling methods such as bootstrap, permutation tests, or through simulation under a null or baseline model. The resulting comparison informs measures like p-values or confidence intervals and helps quantify how unusual the observed data are under the assumed model.

Examples of fobserved include common statistics such as the residual sum of squares in regression, the absolute difference in means between groups in a two-sample test, or the maximum deviation between observed and predicted values in a goodness-of-fit assessment. The choice of f defines the sensitivity and interpretation of the assessment.

Relation to fexpected and related concepts: In many frameworks, fexpected denotes the model-based expectation of f under the null or alternative model. Comparing fobserved to fexpected or to the simulated distribution of f under the model provides a basis for decision making.

Limitations should be noted: the meaning of fobserved depends on the specification of f and the underlying model, and results can be affected by sample size, outliers, and data collection design. See also observed value, statistic, permutation test.