The variance of a standardised effect when the two scores are paired

Treating a pre-post or crossover design as if the two arms were independent inflates the variance and, in a meta-analysis, silently down-weights exactly the designs that carry the most information. The correlation between the paired measurements enters the variance directly: at rho = 1 the sampling variance of the raw difference vanishes and only the term from estimating the standardiser survives.

Usage

Marba(g, n, rho)

Arguments

g

The corrected standardised mean difference.

n

Number of subjects; n >= 2.

rho

Correlation between the paired measurements, in [-1, 1].

Value

List with var_g, se, J, n, rho.

Details

Formula: V_g = J^2 (2(1 - rho)/n + g^2/(2(n-1))) with the small-sample correction J = 1 - 3/(4(n-1) - 1) – Morris (2008) eq. (7)-(8); Morris and DeShon (2002).

References

Morris, S. B. (2008). Organizational Research Methods 11(2):364-386. doi:10.1177/1094428106291059 .

Examples

Marba(g = c(1, 2, 3, 4, 5, 6, 7, 8), n = 5L, rho = 0.5)
#> $var_g
#> [1] 0.208 0.448 0.848 1.408 2.128 3.008 4.048 5.248
#> 
#> $se
#> [1] 0.4560702 0.6693280 0.9208692 1.1865918 1.4587666 1.7343587 2.0119642
#> [8] 2.2908514
#> 
#> $J
#> [1] 0.8
#> 
#> $n
#> [1] 5
#> 
#> $rho
#> [1] 0.5
#> 
#> $method
#> [1] "Variance of Hedges' g for a correlated design"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"