Variind

Variind, short for Variability Indicator, is a dispersion statistic designed to measure how much a group of indicators varies after normalizing their scales. It is used for multivariate data where indicators have different units and ranges, making direct comparison difficult.

Definition and calculation: To compute Variind for a given observation, first normalize each indicator to the [0,1] interval using min–max scaling across all observations. Then compute the standard deviation of the normalized indicator values. Finally, multiply the standard deviation by two to bound the index between 0 and 1.

Interpretation: A Variind near 0 indicates that the indicators agree closely for that observation, while a value near 1 signals substantial dispersion among the indicators after normalization. The measure is intended to provide a single, scale-free summary of dispersion across heterogeneous indicators.

Applications: Variind is used in multi-criteria decision analysis, dashboard reporting, and feature selection to summarize heterogeneity across indicators in a compact form. It helps identify observations or cases where indicators diverge markedly.

Limitations: The result depends on the chosen normalization method and can be sensitive to outliers. It is not a universal standard and should be interpreted alongside other dispersion statistics. It is most informative when the indicators are expected to measure related constructs.

See also: Coefficient of variation, normalization, dispersion measures, multi-criteria decision analysis.