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Standardized Mean Difference Using the Control Group as the Basis of Standardization

Source: R/smd_c.R
smd_c.Rd

Estimates the standardized mean difference using the control group standard deviation as the basis of standardization (Glass's g), from either raw data or summary statistics, in ordinary or unbiased form. Standardizing by the control group alone keeps the scale of the effect free of any treatment effect on variability.

Usage

smd_c(
  group_T = NULL,
  group_C = NULL,
  mean_T = NULL,
  mean_C = NULL,
  s_C = NULL,
  n_C = NULL,
  unbiased = FALSE
)

Arguments

group_T

Raw data for the treatment group

group_C

Raw data for the control group

mean_T

The mean of the treatment group

mean_C

The mean of the control group

s_C

The standard deviation of the control group (i.e., the square root of the unbiased estimator of the population variance)

n_C

The sample size of the control group

unbiased

Returns the unbiased estimate of the standardized mean difference using the standard deviation of the control group

Value

A 1-row data.frame with columns term ("smd_c") and value (the estimated standardized mean difference using the control group standard deviation as the basis of standardization).

Details

When unbiased=TRUE, the unbiased estimate of the standardized mean difference (using the control group as the basis of standardization) is returned (Hedges, 1981). Although the unbiased estimate of the standardized mean difference is not often reported, at least at the present time, it is nevertheless made available to those who are interested in calculating this quantity.

References

Glass, G. V. (1976). Primary, secondary, and meta-analysis of research. Educational Researcher, 5, 3–8.

Hedges, L. V. (1981). Distribution theory for Glass's Estimator of effect size and related estimators. Journal of Educational Statistics, 6(2), 107–128.

Kelley, K., & Rausch, J. R. (2006). Sample size planning for the standardized mean difference: Accuracy in parameter estimation via narrow confidence intervals. Psychological Methods, 11(4), 363–385. doi:10.1037/1082-989X.11.4.363

Maxwell, S. E., Delaney, H. D., & Kelley, K. (2027). Designing experiments and analyzing data: A model comparison perspective (4th ed.). Routledge. (See Chapter 4 on individual comparisons and Chapter 3 on one-way ANOVA.)

See also

smd, conf_limits_nct

Author

Ken Kelley kkelley@nd.edu

Examples

# Generate sample data.
set.seed(113)
g.T <- rnorm(n = 25, mean = .5, sd = 1)
g.C <- rnorm(n = 25, mean = 0, sd = 1)
smd_c(group_T = g.T, group_C = g.C)
#>  term  value
#>  smd_c 0.37 

M.T <- .66745
M.C <- .24878
sd.c <- 1.1311
n.c <- 25
smd_c(mean_T = M.T, mean_C = M.C, s_C = sd.c)
#>  term  value
#>  smd_c 0.37 
smd_c(mean_T = M.T, mean_C = M.C, s_C = sd.c, n_C = n.c, unbiased = TRUE)
#>  term  value
#>  smd_c 0.358