Reliability, Separation and Strata: Percentage of Sample in Each Level

Test Reliability (Person Reliability) is routinely reported when analyzing responses to a test. It is the true variance of the sample of test respondents divided by their observed variance, where observed variance = true variance + error variance, and similarly Item Reliability can be reported for the sample of test items. Reliabilities are in the range 0 - 1, but when their values exceed 0.9, the practical implications of increases in Reliability become obscured by the range restriction toward 1.0. This motivated a transformation of Reliability into Separation, where Separation = square-root (true variance / error variance). Separation reports how many statistically distinguishable measurement levels exist in the sample when very high and very low measures are modeled to be accidental. A refinement of Separation is Strata, where Strata = (4 * Separation + 1) / 3. Strata models the very high and very low measures to be additional levels of performance.

For approximately normally-distributed samples, a rough estimate of the percentage of the sample in each Separation or Strata level can be computed. Levels are defined to be 3 errors apart. This distance slightly exceeds statistical significance at p = .05. The percentages in each level are shown in the Table.

John Michael Linacre

Wright BD. (1996). Reliability and separation. Rasch Measurement Transactions, 9(4), p. 472. Available at: www.rasch.org/rmt/rmt94n.htm

Wright BD, Masters GN. (2006). Number of Person or Item Strata: (4*Separation + 1)/3. Rasch Measurement Transactions, 16(3), p. 888. Available at: www.rasch.org/rmt/rmt163f.htm

Reliability, Separation and Strata: Percentage of Sample in Each Level. John M. Linacre … Rasch Measurement Transactions, 2013, 26:4 p. 1399

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