Test for a difference in outcome variances between treatment arms

Computes the difference in sample variances between treated and control units and tests the null that the two variances are equal. Used in Chapter 9 as an indirect test of the null of constant treatment effects: under constant effects the two schedules of potential outcomes have equal variances, so a difference in variances is evidence of heterogeneity.

Usage

difference_in_variances(data)

Arguments

data

A data frame with columns Y (outcome) and Z (binary treatment indicator, 1 = treated).

Value

A one-row tibble::tibble() with columns estimate (Var(Y|Z=1) - Var(Y|Z=0)) and p.value.

Which test this is

stats::var.test(), the classical F test for the ratio of two variances. The F test assumes the outcome is normally distributed within each arm and is sensitive to departures from that assumption, so a small p-value can reflect kurtosis rather than a difference in dispersion. Levene- and Bonett-type tests trade power for robustness against exactly that.

This function previously called DescTools::VarTest(method = "bonett"), which documented a Bonett test that never ran: VarTest() takes no method argument in its two-sample branch, so the argument fell into ... and the F test was performed. Calling stats::var.test() directly gives the same numbers under a name that describes them.

The signature takes data first and returns one row, which is what DeclareDesign::label_estimator() expects of an estimator handler.

Examples

dat <- data.frame(Y = c(rnorm(50, sd = 1), rnorm(50, sd = 2)),
                  Z = rep(0:1, each = 50))
difference_in_variances(dat)
#> # A tibble: 1 × 2
#>   estimate   p.value
#>      <dbl>     <dbl>
#> 1     2.95 0.0000182