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Visualize a Standardized Mean Difference With Overlapping Distributions

Source: R/plot_smd.R
plot_smd.Rd

Creates a publication-quality plot showing two normal distributions separated by the standardized mean difference (d). The plot includes a confidence interval for the population effect size and sample size annotations, both shown by default.

Usage

plot_smd(
  smd = NULL,
  n_1 = NULL,
  n_2 = NULL,
  group_1 = NULL,
  group_2 = NULL,
  conf_level = 0.95,
  show_ci = TRUE,
  show_n = TRUE,
  title = NULL,
  group_labels = c("Group 1", "Group 2"),
  palette = "okabe_ito",
  colors = NULL
)

Arguments

smd

The standardized mean difference (Cohen's d).

n_1

Sample size for Group 1.

n_2

Sample size for Group 2.

group_1

Raw data for Group 1. When provided, smd, n_1, and n_2 are computed from the data.

group_2

Raw data for Group 2.

conf_level

Confidence level for the confidence interval (default 0.95).

show_ci

Logical. If TRUE (the default), a confidence interval for the population standardized mean difference is displayed beneath the distributions. Requires both n_1 and n_2.

show_n

Logical. If TRUE (the default), per-group sample sizes are annotated on the plot.

title

Optional character string for the plot title. Defaults to "Standardized Mean Difference".

group_labels

Character vector of length 2 giving labels for the two groups. Defaults to c("Group 1", "Group 2").

palette

Character string naming the color palette used when colors is NULL. Defaults to "okabe_ito", base R's colorblind-safe Okabe-Ito palette; "tableau" is also available.

colors

Optional character vector of length 2 giving fill colors for the two groups. When NULL (the default), the first two colors of palette are used.

Value

A ggplot2 object that can be further customized with standard ggplot2 layers, scales, and themes.

Details

Two unit-variance normal distributions are drawn, centered at 0 (Group 2 / reference) and d (Group 1 / focal). The semi-transparent fills make the overlap visible, giving a direct visual impression of how much the distributions differ.

When show_ci = TRUE and both n_1 and n_2 are available, the function calls ci_smd to compute the noncentral t based confidence interval and displays it as a horizontal bar beneath the curves. A filled dot marks the point estimate and vertical caps mark the confidence bounds.

Note

Requires ggplot2 (listed in Suggests). Install it with install.packages("ggplot2") if needed.

References

Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale, NJ: Lawrence Erlbaum.

Kelley, K. (2007). Confidence intervals for standardized effect sizes: Theory, application, and implementation. Journal of Statistical Software, 20(8), 1–24. doi:10.18637/jss.v020.i08

See also

smd, ci_smd, plot_ci, plot_R2

Other plotting: plot_R2(), plot_cfa_k(), plot_ci(), plot_equivalence(), plot_forest(), plot_irt_information(), plot_mediation_mbco(), plot_randomization_test(), plot_regions_of_significance(), plot_trajectories(), plot_trajectories_fitted(), power_equivalence_md_plot()

Other confidence intervals for effect sizes: ci_R2(), ci_c(), ci_c_ancova(), ci_c_ancova_bp(), ci_correlation, ci_cv(), ci_eta_squared(), ci_eta_squared_generalized(), ci_eta_squared_partial(), ci_mahalanobis(), ci_omega_squared(), ci_pvaf(), ci_rc(), ci_reg_coef(), ci_rmsea(), ci_sc(), ci_sc_ancova(), ci_sm(), ci_smd(), ci_smd_c(), ci_snr(), ci_src(), ci_srsnr(), contrast_adjusted()

Author

Ken Kelley kkelley@nd.edu

Examples

# From a known effect size and sample sizes.
plot_smd(smd = 0.50, n_1 = 50, n_2 = 50)


# The variations below are not run, since the call above already shows
# the default display and each additional figure has to be drawn. From
# raw data, where the standardized mean difference and both sample
# sizes are taken from the data:
# set.seed(113)
# g1 <- rnorm(40, mean = 0.6, sd = 1)
# g2 <- rnorm(40, mean = 0.0, sd = 1)
# plot_smd(group_1 = g1, group_2 = g2)

# Without the confidence interval or the sample size annotations:
# plot_smd(smd = 0.80, show_ci = FALSE, show_n = FALSE)

# Custom group labels and title:
# plot_smd(smd = 0.45, n_1 = 75, n_2 = 75,
#          group_labels = c("Treatment", "Control"),
#          title = "Treatment Effect on Reading Scores")