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.


Differential Item Functioning DIF Sample Size Nomogram

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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