Standard Error of Measurement (SEM)

Computes the standard error of measurement from the SD of scores and a reliability coefficient (ICC or test-retest correlation).

Usage

sem(x, icc_value = NULL, reliability = NULL)

Arguments

x

Numeric vector of observed scores. Used to compute SD.

icc_value

Numeric; ICC value to use as the reliability coefficient.

reliability

Numeric; alternative reliability coefficient (e.g., test-retest correlation). Exactly one of icc_value or reliability must be provided.

Value

Numeric SEM value.

Details

SEM is computed as: $$SEM = SD \times \sqrt{1 - r}$$ where \(r\) is the reliability coefficient (ICC or correlation).

References

Shrout PE, Fleiss JL (1979). "Intraclass Correlations: Uses in Assessing Rater Reliability." Psychological Bulletin, 86(2), 420-428.

See also

icc() for computing intraclass correlation coefficients, mdc() for minimal detectable change based on SEM.

Examples

scores <- c(10, 12, 15, 11, 13, 14, 9, 16, 12, 11)
sem(scores, icc_value = 0.90)
#> [1] 0.7