Essentials of the Theory of Data

A wrong analytical result begins in one of five places: binding (a business name points at the wrong measure), declaration (a constitutive choice was never made), premise (the records are not what was assumed), realization (the code computes something other than the definition) or composition (the result was assembled against the rules). Many of these failures are silent: the systems run, the tests pass, and the number is plausible but wrong, such as a mean of means, an order counted once per order line, or a missing value read as zero. This paper is a short synthesis of the Theory of Data focused on what goes wrong. Using one running retail example, it presents the Data World between business meaning and material storage: populations, units, anchors and anchor points; datums and the value states Value, NA and None; measure families, expressions and derivation paths; and passages between populations. It states the anchors principle (business names carry no anchor, measures two, stored fields one), seven rules a correct result must obey, and how each of the five failure sources is told apart and who can fix it. It ends with what may be stored and a glossary. It takes the three worlds of analytical data from The Three Worlds of Analytical Data v2.0 and the laws from The Theory of Data: Minimum Core v9.0, whose Proposition 10.1 establishes that a construction obeying the rules determines a measure.