Skip to contents

DMAR

DMAR (Design, Measurement, and Analysis in R, pronounced “Dee-Mar”) is a package for human-centered research: effect sizes, confidence intervals for effect sizes, sample size planning, reliability and agreement, mediation analysis (from the simple mediation model to likelihood ratio tests of arbitrary indirect effects, with moderated mediation probing), equivalence testing, meta-analysis, experimental and quasi-experimental designs, repeated measures, and model comparison-based inference. It draws on the psychometric and statistical traditions and reflects the methodological and applied research program of its author, Ken Kelley (University of Notre Dame). It aims to be methodologically sound and useful across psychology, sociology, education, management, marketing, and information systems, especially where the independent or dependent variables involve the person.

Installation 

# Once on CRAN:
install.packages("DMAR")

# Development version from GitHub:
# install.packages("remotes")
remotes::install_github("yelleKneK/DMAR")

R >= 4.0.0 is required. Most estimation, inference, and planning functions return a tidy data.frame(term, value) that composes naturally with dplyr / ggplot2 pipelines and with broom::tidy() / broom::glance(). Heavier dependencies (e.g., lavaan, lme4, OpenMx) are in Suggests and gated by requireNamespace(); install them only when you need the functions that use them.

Function families

DMAR is organized into a small number of stable function families:

Canonical examples

1. Standardized mean difference with a noncentral-t confidence interval 

library(DMAR)

# From summary statistics:
smd(mean_1 = 60, mean_2 = 55, s_1 = 10, s_2 = 10, n_1 = 30, n_2 = 30)
term value
smd 0.5 

# CI on the standardized mean difference (Cohen's d) via the noncentral t:
ci_smd(smd = 0.5, n_1 = 30, n_2 = 30, conf_level = 0.95)
term value
lower_limit -0.0162
smd 0.5
upper_limit 1.01

Confidence level: 95%

2. R² with a noncentral-F confidence interval and AIPE sample size 

ci_R2(R2 = 0.30, N = 100, p = 4, conf_level = 0.95)
term value prob_less prob_greater
lower_limit 0.13 0.025 0.975
R2 0.3 NA NA
upper_limit 0.43 0.975 0.025

Confidence level: 95%


# What N is needed so the 95% CI on R^2 has full width <= 0.20?
ss_aipe_R2(population_R2 = 0.30, width = 0.20, p = 4)
term value
necessary_N 228

Confidence level: 95%

3. AIPE planning with a sensitivity check 

# Plan N for a half-width of .10 on the SMD at delta = 0.40.
ss_aipe_smd(delta = 0.40, width = 0.20)
term value
necessary_n_per_group 784
supposed_smd 0.4
width 0.2

Confidence level: 95%


# How does that plan hold up if the truth is actually delta = 0.25?
set.seed(113)
ss_aipe_smd_sensitivity(
  true_delta      = 0.25,
  estimated_delta = 0.40,
  desired_width   = 0.20,
  G               = 200,
  print_iter      = FALSE
)
term value
mean_smd 0.253
median_smd 0.249
sd_smd 0.0516
mean_ci_width 0.199
median_ci_width 0.199
sd_ci_width 0.000324
mean_ci_width_lower 0.0994
mean_ci_width_upper 0.0994
pct_ci_less_w 1
pct_ci_miss_low 0.03
pct_ci_miss_high 0.025
total_type_I_error 0.055
n_per_group 784
total_N 1568
true_delta 0.25
estimated_delta 0.4
width 0.2
conf_level 0.95

Confidence level: 95%

4. Welch’s t test with a tidy return 

set.seed(113)
x <- rnorm(20, mean = 100, sd = 15)
y <- rnorm(20, mean = 110, sd = 25)
welch_t(x, y, conf_level = 0.95)
term value
mean_difference -16.9
t_statistic -2.41
df 28.3
p_value 0.0227
lower_limit -31.2
upper_limit -2.54
mean_x 100
mean_y 117
sd_x 14.3
sd_y 27.9
n_x 20
n_y 20

Confidence level: 95%

5. Reliability with a confidence interval 

# Cronbach's alpha plus the Bonett (2002) CI from a covariance matrix.
S <- matrix(
  c(1.0, 0.6, 0.5, 0.5,
    0.6, 1.0, 0.6, 0.5,
    0.5, 0.6, 1.0, 0.6,
    0.5, 0.5, 0.6, 1.0),
  nrow = 4)
reliability_alpha(S = S, N = 250, ci_method = "bonett")
term value
estimate 0.83
se 0.0176
se_transformed 0.104
lower_limit 0.792
upper_limit 0.861
conf_level 0.95
N 250
N_complete 250
J 4

6. Kish’s design effect in a clustered sample 

# 25 schools with attendance ranging from 0 (closed) to 30 (full class),
# ICC = .10. How much clustering information do we actually have?
sizes <- c(0, 0, 1, 1, 1, 2, 3, 5, 8, 10, 12, 15, 18, 20, 22,
           22, 25, 26, 28, 28, 30, 30, 30, 30, 30)
design_effect(cluster_sizes = sizes, icc = 0.10)
term value
design_effect 3.33
deft 1.82
effective_n 119
n_total 397
n_clusters_total 25
n_clusters_with_data 23
n_clusters_empty 2
n_clusters_singletons 3
n_clusters_informative 20
m_bar 17.3
m_kish 24.3
icc 0.1

Numerical validation

DMAR ships a dedicated numerical-correctness test suite (tests/testthat/test-numerical-correctness.R and companion files) that pins its output against authoritative reference implementations and published values, so results are reproducible and checkable:

Quantity Reference Agreement
Confidence intervals for R², SMD; noncentral t / F limits; AIPE sample sizes MBESS 1e-5 to 1e-6 (integer N)
Within-subjects sphericity epsilons; factorial ANOVA / ANCOVA car machine precision
CFA, coefficient omega, RMSEA lavaan, semTools machine precision
krippendorff_alpha(), gwet_ac() irr, irrCAC machine precision (validated designs)
R2_mixed_effects() (Nakagawa & Schielzeth), R2_mixed_effects_decomposition() (Rights & Sterba) r2mlm machine precision (validated model classes)
Multiple-comparison critical values and CIs multcomp, published tables published values

The machine-precision rows hold for the model and design classes the test suite pins, including the boundary cases the current tests add. The mixed-effects R-squared functions match r2mlm and the direct Johnson quadratic form across random-intercept, correlated random-slope, split (||) random-slope, multi-slope, and nested two-level models; on split random-slope models performance/insight omits the random-slope variance, so DMAR agrees with r2mlm and the Johnson form there and not with performance. The agreement procedures match irr and irrCAC on the ordinary rating designs and on the boundary cases the tests now cover: the zero-distance case of ratio-metric Krippendorff’s alpha, all-missing units in gwet_ac(), and incomplete category sets in cohen_kappa().

Learn more

Relation to MBESS

DMAR is the modern, more general reimplementation and expansion of the MBESS package (Kelley, 2007a, Journal of Statistical Software, 20(8), 1–24; 2007b, Behavior Research Methods, 39(4), 979–984), which has been on CRAN for about two decades. MBESS was originally framed for the behavioral, educational, and social sciences; its use has grown well beyond that scope, and DMAR reflects how the methods are now applied across disciplines. The notational and programming changes (uniform snake_case, tidy data.frame(term, value) returns, native ggplot2 plotting, broader coverage of within-subjects, multivariate, mixed-effects, and sequential-estimation methods) were too extensive to ship under the MBESS name without breaking compatibility, so the work ships under a new name. MBESS itself remains stable on CRAN; DMAR is the recommended path forward for new users. See NEWS.md for the MBESS → DMAR migration mapping.

Relation to Maxwell, Delaney, and Kelley (MDK, 4th ed.)

Many of the methods in DMAR are discussed in Maxwell, Delaney, and Kelley (2027), Designing Experiments and Analyzing Data: A Model Comparison Perspective (4th ed., Routledge). Functions cite the specific MDK chapter in their @references block where the underlying method is discussed in detail. DMAR is broader than MDK: it covers methods (e.g., minimum-risk sequential estimation, equivalence testing, mediation effect size CIs, design effects for cluster sampling) that are outside the scope of an experimental- design textbook. Conversely, MDK covers conceptual material that falls outside the scope of an R package. The two are complementary.

BUCSS (Bias-Corrected Uncertainty Adjusted Sample Size; Anderson, Kelley, and others) provides bias and uncertainty corrected sample size methods for several common designs, with overlap with DMAR’s AIPE family. Ken Kelley is a co-author of BUCSS; the two packages take complementary approaches to the small-sample sample size planning problem and reading them side by side is a good way to see where the AIPE and BUCSS traditions agree, where they diverge, and when each is most informative for a given planning question.

Citation

If you use DMAR in published work, please cite

Kelley, K. (2026). DMAR: Design, Measurement, and Analysis in R. R package version 1.0.0.

and, where appropriate, the original MBESS references for the methodological lineage:

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

Kelley, K. (2007). Methods for the Behavioral, Educational, and Social Sciences: An R package. Behavior Research Methods, 39(4), 979–984. doi:10.3758/BF03192993

citation("DMAR") reproduces the canonical BibTeX entry from R.

Feedback

Bug reports, feature requests, and suggestions for new methods are welcomed by email to Ken Kelley (please put “DMAR” in the subject line). See https://kenkelley.org and https://kenkelley.org/publications/ for related publications.