SMD: Within-case standardized mean difference

In SingleCaseES: A Calculator for Single-Case Effect Sizes

Within-case standardized mean difference

Description

Calculates the within-case standardized mean difference effect size index

Usage

SMD(
  A_data,
  B_data,
  condition,
  outcome,
  baseline_phase = NULL,
  intervention_phase = NULL,
  improvement = "increase",
  std_dev = "baseline",
  bias_correct = TRUE,
  confidence = 0.95
)

Arguments

A_data	vector of numeric data for A phase. Missing values are dropped.
B_data	vector of numeric data for B phase. Missing values are dropped.
condition	vector identifying the treatment condition for each observation in the series.
outcome	vector of outcome data for the entire series.
baseline_phase	character string specifying which value of condition corresponds to the baseline phase. Defaults to first observed value of condition.
intervention_phase	character string specifying which value of condition corresponds to the intervention phase. Defaults to second unique value of condition.
improvement	character string indicating direction of improvement. Default is "increase".
std_dev	character string controlling how to calculate the standard deviation in the denominator of the effect size. Set to "baseline" (the default) to use the baseline standard deviation. Set to "pool" to use the pooled standard deviation.
bias_correct	logical value indicating whether to use bias-correction (i.e., Hedges' g). Default is TRUE
confidence	confidence level for the reported interval estimate. Set to NULL to omit confidence interval calculations.

Details

The standardized mean difference parameter is defined as the difference between the mean level of the outcome in phase B and the mean level of the outcome in phase A, scaled by the within-case standard deviation of the outcome in phase A. The parameter is estimated using sample means and sample standard deviations and (optionally) making a small-sample correction.

By default, the scaling factor is estimated using the sample standard deviation in phase A (the baseline phase) only. Set std_dev = "pool" to use the sample standard deviation pooled across both phases. Hedges' (1981) small-sample bias correction is applied by default.

Value

A list containing the estimate, standard error, and confidence interval.

Examples

A <- c(20, 20, 26, 25, 22, 23)
B <- c(28, 25, 24, 27, 30, 30, 29)
SMD(A_data = A, B_data = B, bias_correct = FALSE)
SMD(A_data = A, B_data = B)
SMD(A_data = A, B_data = B, std_dev = "pool")

SingleCaseES documentation built on Sept. 11, 2024, 7:04 p.m.