Effectiveness means the capability of producing an effect.
In mathematics, effective is sometimes used as a synonym of algorithmically computable.
In physics, an effective theory is, similar to a phenomenological theory, a framework intended to explain certain (observed) effects without the claim that the theory correctly models the underlying (unobserved) processes. An example is an effective field theory that "pretends" that certain effects are caused by a field even if it is known that this is not actually the case. In a way, any theory of Physics is fundamentally an effective theory, since there is no meaningful distinction of observables and reality within the scope of Physics (see also FAPP, cogito ergo sum, Phenomenalism, Pragmatism).
efficiency is a term used in the comparison of various statistical procedures and, in particular, it refers to a measure of the desirability of an estimator or of an experimental design.[1] The relative efficiency of two procedures is the ratio their efficiencies, although often this term is used where the comparison is made between a given procedure and a notional "best possible" procedure. The efficiencies and the relative efficiency of two procedures theoretically depend on the sample size available for the given procedure, but it is often possible to use the asymptotic relative efficiency (defined as the limit of the relative efficiencies as the sample size grows) as the principal comparison measure.Efficiencies are often defined using the variance or mean square error as the measure of desirability.[2] However, for comparing significance tests, a meaningful measure can be defined based on the sample size required for the test to achieve a given.
Productivity is a measure of output from a production process, per unit of input. For example, labor productivity is typically measured as a ratio of output per labor-hour, an input. Productivity may be conceived of as a metric of the technical or engineering efficiency of production. As such, the emphasis is on quantitative metrics of input, and sometimes output. Productivity is distinct from metrics of allocative efficiency, which take into account both the monetary value (price) of what is produced and the cost of inputs used, and also distinct from metrics of profitability, which address the difference between the revenues obtained from output and the expense associated with consumption of inputs.
