effectsize: Indices of Effect Size and Standardized Parameters, Study Guides, Projects, Research of Statistics for Psychologists

Download effectsize: Indices of Effect Size and Standardized Parameters and more Study Guides, Projects, Research Statistics for Psychologists in PDF only on Docsity! Package ‘effectsize’ May 26, 2022 Type Package Title Indices of Effect Size and Standardized Parameters Version 0.7.0 Maintainer Mattan S. Ben-Shachar <matanshm@post.bgu.ac.il> Description Provide utilities to work with indices of effect size and standardized parameters for a wide variety of models (see list of supported models using the function 'insight::supported_models()'), allowing computation of and conversion between indices such as Cohen's d, r, odds, etc. License GPL-3 URL https://easystats.github.io/effectsize/ BugReports https://github.com/easystats/effectsize/issues/ Depends R (>= 3.4) Imports bayestestR (>= 0.12.1), insight (>= 0.17.0), parameters (>= 0.18.0), performance (>= 0.9.0), datawizard (>= 0.4.1), stats, utils Suggests correlation (>= 0.8.0), see (>= 0.6.9), afex, BayesFactor, biglm, boot, brms, car, covr, emmeans, gamm4, knitr, lavaan, lm.beta, lme4, lmerTest, MASS, mediation, mgcv, pscl, rmarkdown, rms, rstanarm, rstantools, spelling, testthat, tidymodels VignetteBuilder knitr Encoding UTF-8 Language en-US RoxygenNote 7.2.0 Config/testthat/edition 3 Config/testthat/parallel true NeedsCompilation no 1 2 R topics documented: Author Mattan S. Ben-Shachar [aut, cre] (<https://orcid.org/0000-0002-4287-4801>, @mattansb), Dominique Makowski [aut] (<https://orcid.org/0000-0001-5375-9967>, @Dom_Makowski), Daniel Lüdecke [aut] (<https://orcid.org/0000-0002-8895-3206>, @strengejacke), Indrajeet Patil [aut] (<https://orcid.org/0000-0003-1995-6531>, @patilindrajeets), Brenton M. Wiernik [aut] (<https://orcid.org/0000-0001-9560-6336>, @bmwiernik), Ken Kelley [ctb], David Stanley [ctb], Jessica Burnett [rev] (<https://orcid.org/0000-0002-0896-5099>), Johannes Karreth [rev] (<https://orcid.org/0000-0003-4586-7153>) Repository CRAN Date/Publication 2022-05-26 13:20:02 UTC R topics documented: chisq_to_phi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 cles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 cohens_d . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 d_to_cles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 d_to_r . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 effectsize.BFBayesFactor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 effectsize_API . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 effectsize_CIs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 effectsize_deprecated . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 equivalence_test.effectsize_table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 eta2_to_f2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 eta_squared . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 format_standardize . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 F_to_eta2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 hardlyworking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 interpret . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 interpret_bf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 interpret_cohens_d . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 interpret_cohens_g . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 interpret_direction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 interpret_ess . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 interpret_gfi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 interpret_icc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 interpret_kendalls_w . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 interpret_oddsratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 interpret_omega_squared . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 interpret_p . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 interpret_pd . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 chisq_to_phi 5 Details These functions use the following formulae: φ = √ χ2/n Cramer′sV = φ/ √ min(nrow, ncol)− 1 Pearson′sC = √ χ2/(χ2 + n) χNormalized = w × √ q 1− q Where q is the smallest of the expected probabilities. For adjusted versions of phi and V, see Bergsma, 2013. Value A data frame with the effect size(s), and confidence interval(s). See cramers_v(). Confidence (Compatibility) Intervals (CIs) Unless stated otherwise, confidence (compatibility) intervals (CIs) are estimated using the non- centrality parameter method (also called the "pivot method"). This method finds the noncentrality parameter ("ncp") of a noncentral t, F, or χ2 distribution that places the observed t, F, or χ2 test statistic at the desired probability point of the distribution. For example, if the observed t statistic is 2.0, with 50 degrees of freedom, for which cumulative noncentral t distribution is t = 2.0 the .025 quantile (answer: the noncentral t distribution with ncp = .04)? After estimating these confidence bounds on the ncp, they are converted into the effect size metric to obtain a confidence interval for the effect size (Steiger, 2004). For additional details on estimation and troubleshooting, see effectsize_CIs. CIs and Significance Tests "Confidence intervals on measures of effect size convey all the information in a hypothesis test, and more." (Steiger, 2004). Confidence (compatibility) intervals and p values are complementary summaries of parameter uncertainty given the observed data. A dichotomous hypothesis test could be performed with either a CI or a p value. The 100 (1 - α)% confidence interval contains all of the parameter values for which p > α for the current data and model. For example, a 95% confidence interval contains all of the values for which p > .05. Note that a confidence interval including 0 does not indicate that the null (no effect) is true. Rather, it suggests that the observed data together with the model and its assumptions combined do not pro- vided clear evidence against a parameter value of 0 (same as with any other value in the interval), 6 chisq_to_phi with the level of this evidence defined by the chosen α level (Rafi & Greenland, 2020; Schweder & Hjort, 2016; Xie & Singh, 2013). To infer no effect, additional judgments about what parameter values are "close enough" to 0 to be negligible are needed ("equivalence testing"; Bauer & Kiesser, 1996). References • Cumming, G., & Finch, S. (2001). A primer on the understanding, use, and calculation of confidence intervals that are based on central and noncentral distributions. Educational and Psychological Measurement, 61(4), 532-574. • Bergsma, W. (2013). A bias-correction for Cramer’s V and Tschuprow’s T. Journal of the Korean Statistical Society, 42(3), 323-328. • Johnston, J. E., Berry, K. J., & Mielke Jr, P. W. (2006). Measures of effect size for chi-squared and likelihood-ratio goodness-of-fit tests. Perceptual and motor skills, 103(2), 412-414. • Rosenberg, M. S. (2010). A generalized formula for converting chi-square tests to effect sizes for meta-analysis. PloS one, 5(4), e10059. See Also Other effect size from test statistic: F_to_eta2(), t_to_d() Examples contingency_table <- as.table(rbind(c(762, 327, 468), c(484, 239, 477), c(484, 239, 477))) # chisq.test(contingency_table) #> #> Pearson's Chi-squared test #> #> data: contingency_table #> X-squared = 41.234, df = 4, p-value = 2.405e-08 chisq_to_cohens_w(41.234, n = sum(contingency_table), nrow = nrow(contingency_table), ncol = ncol(contingency_table) ) Smoking_ASD <- as.table(c(ASD = 17, ASP = 11, TD = 640)) # chisq.test(Smoking_ASD, p = c(0.015, 0.010, 0.975)) #> #> Chi-squared test for given probabilities #> #> data: Smoking_ASD #> X-squared = 7.8521, df = 2, p-value = 0.01972 chisq_to_normalized( cles 7 7.8521, n = sum(Smoking_ASD), nrow = 1, ncol = 3, p = c(0.015, 0.010, 0.975) ) cles Estimate Common Language Effect Sizes (CLES) Description cohens_u3(), p_superiority(), and p_overlap() give only one of the CLESs. Usage cles( x, y = NULL, data = NULL, mu = 0, ci = 0.95, alternative = "two.sided", parametric = TRUE, verbose = TRUE, iterations = 200, ... ) common_language( x, y = NULL, data = NULL, mu = 0, ci = 0.95, alternative = "two.sided", parametric = TRUE, verbose = TRUE, iterations = 200, ... ) cohens_u3(...) p_superiority(...) p_overlap(...) 10 cohens_d Usage cohens_d( x, y = NULL, data = NULL, pooled_sd = TRUE, mu = 0, paired = FALSE, ci = 0.95, alternative = "two.sided", verbose = TRUE, ... ) hedges_g( x, y = NULL, data = NULL, pooled_sd = TRUE, mu = 0, paired = FALSE, ci = 0.95, alternative = "two.sided", verbose = TRUE, ... ) glass_delta( x, y = NULL, data = NULL, mu = 0, ci = 0.95, alternative = "two.sided", verbose = TRUE, ... ) Arguments x A formula, a numeric vector, or a character name of one in data. y A numeric vector, a grouping (character / factor) vector, a or a character name of one in data. Ignored if x is a formula. data An optional data frame containing the variables. pooled_sd If TRUE (default), a sd_pooled() is used (assuming equal variance). Else the mean SD from both groups is used instead. cohens_d 11 mu a number indicating the true value of the mean (or difference in means if you are performing a two sample test). paired If TRUE, the values of x and y are considered as paired. This produces an effect size that is equivalent to the one-sample effect size on x - y. ci Confidence Interval (CI) level alternative a character string specifying the alternative hypothesis; Controls the type of CI returned: "two.sided" (default, two-sided CI), "greater" or "less" (one- sided CI). Partial matching is allowed (e.g., "g", "l", "two"...). See One-Sided CIs in effectsize_CIs. verbose Toggle warnings and messages on or off. ... Arguments passed to or from other methods. When x is a formula, these can be subset and na.action. Details Set pooled_sd = FALSE for effect sizes that are to accompany a Welch’s t-test (Delacre et al, 2021). Value A data frame with the effect size ( Cohens_d, Hedges_g, Glass_delta) and their CIs (CI_low and CI_high). Confidence (Compatibility) Intervals (CIs) Unless stated otherwise, confidence (compatibility) intervals (CIs) are estimated using the non- centrality parameter method (also called the "pivot method"). This method finds the noncentrality parameter ("ncp") of a noncentral t, F, or χ2 distribution that places the observed t, F, or χ2 test statistic at the desired probability point of the distribution. For example, if the observed t statistic is 2.0, with 50 degrees of freedom, for which cumulative noncentral t distribution is t = 2.0 the .025 quantile (answer: the noncentral t distribution with ncp = .04)? After estimating these confidence bounds on the ncp, they are converted into the effect size metric to obtain a confidence interval for the effect size (Steiger, 2004). For additional details on estimation and troubleshooting, see effectsize_CIs. CIs and Significance Tests "Confidence intervals on measures of effect size convey all the information in a hypothesis test, and more." (Steiger, 2004). Confidence (compatibility) intervals and p values are complementary summaries of parameter uncertainty given the observed data. A dichotomous hypothesis test could be performed with either a CI or a p value. The 100 (1 - α)% confidence interval contains all of the parameter values for which p > α for the current data and model. For example, a 95% confidence interval contains all of the values for which p > .05. Note that a confidence interval including 0 does not indicate that the null (no effect) is true. Rather, it suggests that the observed data together with the model and its assumptions combined do not pro- vided clear evidence against a parameter value of 0 (same as with any other value in the interval), with the level of this evidence defined by the chosen α level (Rafi & Greenland, 2020; Schweder 12 cohens_d & Hjort, 2016; Xie & Singh, 2013). To infer no effect, additional judgments about what parameter values are "close enough" to 0 to be negligible are needed ("equivalence testing"; Bauer & Kiesser, 1996). Note The indices here give the population estimated standardized difference. Some statistical packages give the sample estimate instead (without applying Bessel’s correction). References • Algina, J., Keselman, H. J., & Penfield, R. D. (2006). Confidence intervals for an effect size when variances are not equal. Journal of Modern Applied Statistical Methods, 5(1), 2. • Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd Ed.). New York: Routledge. • Delacre, M., Lakens, D., Ley, C., Liu, L., & Leys, C. (2021, May 7). Why Hedges’ g*s based on the non-pooled standard deviation should be reported with Welch’s t-test. https://doi.org/10.31234/osf.io/tu6mp • Hedges, L. V. & Olkin, I. (1985). Statistical methods for meta-analysis. Orlando, FL: Aca- demic Press. • Hunter, J. E., & Schmidt, F. L. (2004). Methods of meta-analysis: Correcting error and bias in research findings. Sage. See Also d_to_cles() sd_pooled() Other effect size indices: cles(), effectsize.BFBayesFactor(), eta_squared(), phi(), rank_biserial() Examples data(mtcars) mtcars$am <- factor(mtcars$am) # Two Independent Samples ---------- (d <- cohens_d(mpg ~ am, data = mtcars)) # Same as: # cohens_d("mpg", "am", data = mtcars) # cohens_d(mtcars$mpg[mtcars$am=="0"], mtcars$mpg[mtcars$am=="1"]) # More options: cohens_d(mpg ~ am, data = mtcars, pooled_sd = FALSE) cohens_d(mpg ~ am, data = mtcars, mu = -5) cohens_d(mpg ~ am, data = mtcars, alternative = "less") hedges_g(mpg ~ am, data = mtcars) glass_delta(mpg ~ am, data = mtcars) # One Sample ---------- d_to_r 15 d_to_r Convert between d, r and Odds ratio Description Enables a conversion between different indices of effect size, such as standardized difference (Co- hen’s d), correlation r or (log) odds ratios. Usage d_to_r(d, ...) r_to_d(r, ...) oddsratio_to_d(OR, log = FALSE, ...) logoddsratio_to_d(OR, log = TRUE, ...) d_to_oddsratio(d, log = FALSE, ...) oddsratio_to_r(OR, log = FALSE, ...) logoddsratio_to_r(OR, log = TRUE, ...) r_to_oddsratio(r, log = FALSE, ...) Arguments d Standardized difference value (Cohen’s d). ... Arguments passed to or from other methods. r Correlation coefficient r. OR Odds ratio values in vector or data frame. log Take in or output the log of the ratio (such as in logistic models). Details Conversions between d and OR or r is done through these formulae. • d = 2∗r√ 1−r2 • r = d√ d2+4 • d = log(OR)× √ 3 π • log(OR) = d ∗ π√ (3) The conversion from d to r assumes equally sized groups. The resulting r is also called the binomial effect size display (BESD; Rosenthal et al., 1982). 16 effectsize.BFBayesFactor Value Converted index. References • Sánchez-Meca, J., Marín-Martínez, F., & Chacón-Moscoso, S. (2003). Effect-size indices for dichotomized outcomes in meta-analysis. Psychological methods, 8(4), 448. • Borenstein, M., Hedges, L. V., Higgins, J. P. T., & Rothstein, H. R. (2009). Converting among effect sizes. Introduction to meta-analysis, 45-49. • Rosenthal, R., & Rubin, D. B. (1982). A simple, general purpose display of magnitude of experimental effect. Journal of educational psychology, 74(2), 166. See Also Other convert between effect sizes: d_to_cles(), eta2_to_f2(), odds_to_probs(), oddsratio_to_riskratio() Examples r_to_d(0.5) d_to_oddsratio(1.154701) oddsratio_to_r(8.120534) d_to_r(1) r_to_oddsratio(0.4472136, log = TRUE) oddsratio_to_d(1.813799, log = TRUE) effectsize.BFBayesFactor Effect Size Description This function tries to return the best effect-size measure for the provided input model. See details. Usage ## S3 method for class 'BFBayesFactor' effectsize(model, type = NULL, verbose = TRUE, test = NULL, ...) effectsize(model, ...) ## S3 method for class 'aov' effectsize(model, type = NULL, ...) ## S3 method for class 'htest' effectsize(model, type = NULL, verbose = TRUE, ...) effectsize.BFBayesFactor 17 Arguments model An object of class htest, or a statistical model. See details. type The effect size of interest. See details. verbose Toggle warnings and messages on or off. test The indices of effect existence to compute. Character (vector) or list with one or more of these options: "p_direction" (or "pd"), "rope", "p_map", "equivalence_test" (or "equitest"), "bayesfactor" (or "bf") or "all" to compute all tests. For each "test", the corresponding bayestestR function is called (e.g. rope() or p_direction()) and its results included in the summary output. ... Arguments passed to or from other methods. See details. Details • For an object of class htest, data is extracted via insight::get_data(), and passed to the relevant function according to: – A t-test depending on type: "cohens_d" (default), "hedges_g", or "cles". – A Chi-squared tests of independence, depending on type: "cramers_v" (default), "phi", "cohens_w", "pearsons_c", "cohens_h", "oddsratio", or "riskratio". – A Chi-squared tests of goodness-of-fit, depending on type: "normalized_chi" (de- fault) "cohens_w", "pearsons_c" – A One-way ANOVA test, depending on type: "eta" (default), "omega" or "epsilon" -squared, "f", or "f2". – A McNemar test returns Cohen’s g. – A Wilcoxon test depending on type: returns "rank_biserial" correlation (default) or "cles". – A Kruskal-Wallis test returns rank Epsilon squared. – A Friedman test returns Kendall’s W. (Where applicable, ci and alternative are taken from the htest if not otherwise provided.) • For an object of class BFBayesFactor, using bayestestR::describe_posterior(), – A t-test depending on type: "cohens_d"(default) or"cles"‘. – A correlation test returns r. – A contingency table test, depending on type: "cramers_v" (default), "phi", "cohens_w", "pearsons_c", "cohens_h", "oddsratio", or "riskratio". – A proportion test returns p. • Objects of class anova, aov, or aovlist, depending on type: "eta" (default), "omega" or "epsilon" -squared, "f", or "f2". • Other objects are passed to parameters::standardize_parameters(). For statistical models it is recommended to directly use the listed functions, for the full range of options they provide. Value A data frame with the effect size (depending on input) and and its CIs (CI_low and CI_high). 20 effectsize_CIs Arguments aov_table Input data frame type Which effect size to compute? partial, generalized, ci, alternative, verbose See eta_squared(). include_intercept Should the intercept ((Intercept)) be included? DV_names A character vector with the names of all the predictors, including the grouping variable (e.g., "Subject"). effectsize_CIs Confidence (Compatibility) Intervals Description More information regarding Confidence (Compatibiity) Intervals and how they are computed in effectsize. Confidence (Compatibility) Intervals (CIs) Unless stated otherwise, confidence (compatibility) intervals (CIs) are estimated using the non- centrality parameter method (also called the "pivot method"). This method finds the noncentrality parameter ("ncp") of a noncentral t, F, or χ2 distribution that places the observed t, F, or χ2 test statistic at the desired probability point of the distribution. For example, if the observed t statistic is 2.0, with 50 degrees of freedom, for which cumulative noncentral t distribution is t = 2.0 the .025 quantile (answer: the noncentral t distribution with ncp = .04)? After estimating these confidence bounds on the ncp, they are converted into the effect size metric to obtain a confidence interval for the effect size (Steiger, 2004). For additional details on estimation and troubleshooting, see effectsize_CIs. CIs and Significance Tests "Confidence intervals on measures of effect size convey all the information in a hypothesis test, and more." (Steiger, 2004). Confidence (compatibility) intervals and p values are complementary summaries of parameter uncertainty given the observed data. A dichotomous hypothesis test could be performed with either a CI or a p value. The 100 (1 - α)% confidence interval contains all of the parameter values for which p > α for the current data and model. For example, a 95% confidence interval contains all of the values for which p > .05. Note that a confidence interval including 0 does not indicate that the null (no effect) is true. Rather, it suggests that the observed data together with the model and its assumptions combined do not pro- vided clear evidence against a parameter value of 0 (same as with any other value in the interval), with the level of this evidence defined by the chosen α level (Rafi & Greenland, 2020; Schweder & Hjort, 2016; Xie & Singh, 2013). To infer no effect, additional judgments about what parameter values are "close enough" to 0 to be negligible are needed ("equivalence testing"; Bauer & Kiesser, 1996). effectsize_CIs 21 One-Sided CIs Typically, CIs are constructed as two-tailed intervals, with an equal proportion of the cumulative probability distribution above and below the interval. CIs can also be constructed as one-sided in- tervals, giving only a lower bound or upper bound. This is analogous to computing a 1-tailed p value or conducting a 1-tailed hypothesis test. Significance tests conducted using CIs (whether a value is inside the interval) and using p val- ues (whether p < alpha for that value) are only guaranteed to agree when both are constructed using the same number of sides/tails. Most effect sizes are not bounded by zero (e.g., r, d, g), and as such are generally tested using 2-tailed tests and 2-sided CIs. Some effect sizes are strictly positive–they do have a minimum value, of 0. For example, R2, η2, and other variance-accounted-for effect sizes, as well as Cramer’s V and multiple R, range from 0 to 1. These typically involve F- or χ2-statistics and are generally tested using 1-tailed tests which test whether the estimated effect size is larger than the hypothesized null value (e.g., 0). In order for a CI to yield the same significance decision it must then by a 1-sided CI, estimating only a lower bound. This is the default CI computed by effectsize for these effect sizes, where alternative = "greater" is set. This lower bound interval indicates the smallest effect size that is not significantly different from the observed effect size. That is, it is the minimum effect size compatible with the observed data, background model assumptions, and α level. This type of interval does not indicate a maximum effect size value; anything up to the maximum possible value of the effect size (e.g., 1) is in the interval. One-sided CIs can also be used to test against a maximum effect size value (e.g., is R2 significantly smaller than a perfect correlation of 1.0?) can by setting alternative = "less". This estimates a CI with only an upper bound; anything from the minimum possible value of the effect size (e.g., 0) up to this upper bound is in the interval. We can also obtain a 2-sided interval by setting alternative = "two-sided". These intervals can be interpreted in the same way as other 2-sided intervals, such as those for r, d, or g. An alternative approach to aligning significance tests using CIs and 1-tailed p values that can often be found in the literature is to construct a 2-sided CI at a lower confidence level (e.g., 100(1-2α)% = 100 - 2*5% = 90%. This estimates the lower bound and upper bound for the above 1-sided intervals simultaneously. These intervals are commonly reported when conducting equivalence tests. For example, a 90% 2-sided interval gives the bounds for an equivalence test with α = .05. However, be aware that this interval does not give 95% coverage for the underlying effect size parameter value. For that, construct a 95% 2-sided CI. data("hardlyworking") fit <- lm(salary ~ n_comps + age, data = hardlyworking) eta_squared(fit) # default, ci = 0.95, alternative = "greater" ## # Effect Size for ANOVA (Type I) 22 effectsize_CIs ## ## Parameter | Eta2 (partial) | 95% CI ## ----------------------------------------- ## n_comps | 0.21 | [0.16, 1.00] ## age | 0.10 | [0.06, 1.00] ## ## - One-sided CIs: upper bound fixed at [1.00]. eta_squared(fit, alternative = "less") # Test is eta is smaller than some value ## # Effect Size for ANOVA (Type I) ## ## Parameter | Eta2 (partial) | 95% CI ## ----------------------------------------- ## n_comps | 0.21 | [0.00, 0.26] ## age | 0.10 | [0.00, 0.14] ## ## - One-sided CIs: lower bound fixed at [0.00]. eta_squared(fit, alternative = "two.sided") # 2-sided bounds for alpha = .05 ## # Effect Size for ANOVA (Type I) ## ## Parameter | Eta2 (partial) | 95% CI ## ----------------------------------------- ## n_comps | 0.21 | [0.15, 0.27] ## age | 0.10 | [0.06, 0.15] eta_squared(fit, ci = 0.9, alternative = "two.sided") # both 1-sided bounds for alpha = .05 ## # Effect Size for ANOVA (Type I) ## ## Parameter | Eta2 (partial) | 90% CI ## ----------------------------------------- ## n_comps | 0.21 | [0.16, 0.26] ## age | 0.10 | [0.06, 0.14] CI Does Not Contain the Estimate For very large sample sizes or effect sizes, the width of the CI can be smaller than the tolerance of the optimizer, resulting in CIs of width 0. This can also result in the estimated CIs excluding the point estimate. For example: t_to_d(80, df_error = 4555555) ## d | 95% CI ## ------------------- ## 0.07 | [0.08, 0.08] equivalence_test.effectsize_table 25 • "bayes" - The Bayesian approach, as put forth by Kruschke: – If the CI does is completely outside the ROPE - Reject H0 – Else, If the CI is completely within the ROPE - Accept H0 – Else - Undecided Value A data frame with the results of the equivalence test. References • Campbell, H., & Gustafson, P. (2018). Conditional equivalence testing: An alternative remedy for publication bias. PLOS ONE, 13(4), e0195145. https://doi.org/10.1371/journal.pone.0195145 • Kruschke, J. K. (2014). Doing Bayesian data analysis: A tutorial with R, JAGS, and Stan. Academic Press • Kruschke, J. K. (2018). Rejecting or accepting parameter values in Bayesian estimation. Ad- vances in Methods and Practices in Psychological Science, 1(2), 270-280. doi: 10.1177/2515245918771304 • Lakens, D. (2017). Equivalence Tests: A Practical Primer for t Tests, Correlations, and Meta- Analyses. Social Psychological and Personality Science, 8(4), 355–362. https://doi.org/10.1177/1948550617697177 See Also For more details, see bayestestR::equivalence_test(). Examples model <- aov(mpg ~ hp + am * factor(cyl), data = mtcars) es <- eta_squared(model, ci = 0.9, alternative = "two.sided") equivalence_test(es, range = 0.30) # TOST RCT <- matrix(c(71, 101, 50, 100), nrow = 2) OR <- oddsratio(RCT, alternative = "greater") equivalence_test(OR, range = 1) ds <- t_to_d( t = c(0.45, -0.65, 7, -2.2, 2.25), df_error = c(675, 525, 2000, 900, 1875), ci = 0.9, alternative = "two.sided" # TOST ) # Can also plot if (require(see)) plot(equivalence_test(ds, range = 0.2)) if (require(see)) plot(equivalence_test(ds, range = 0.2, rule = "cet")) if (require(see)) plot(equivalence_test(ds, range = 0.2, rule = "bayes")) 26 eta2_to_f2 eta2_to_f2 Convert between ANOVA effect sizes Description Convert between ANOVA effect sizes Usage eta2_to_f2(es) eta2_to_f(es) f2_to_eta2(f2) f_to_eta2(f) Arguments es Any measure of variance explained such as Eta-, Epsilon-, Omega-, or R-Squared, partial or otherwise. See details. f, f2 Cohen’s f or f -squared. Details Any measure of variance explained can be converted to a corresponding Cohen’s f via: f2 = η2 1− η2 η2 = f2 1 + f2 If a partial Eta-Squared is used, the resulting Cohen’s f is a partial-Cohen’s f ; If a less biased estimate of variance explained is used (such as Epsilon- or Omega-Squared), the resulting Cohen’s f is likewise a less biased estimate of Cohen’s f. References • Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd Ed.). New York: Routledge. • Steiger, J. H. (2004). Beyond the F test: Effect size confidence intervals and tests of close fit in the analysis of variance and contrast analysis. Psychological Methods, 9, 164-182. eta_squared 27 See Also eta_squared() for more details. Other convert between effect sizes: d_to_cles(), d_to_r(), odds_to_probs(), oddsratio_to_riskratio() eta_squared Effect size for ANOVA Description Functions to compute effect size measures for ANOVAs, such as Eta- (η), Omega- (ω) and Epsilon- (ε) squared, and Cohen’s f (or their partialled versions) for ANOVA tables. These indices represent an estimate of how much variance in the response variables is accounted for by the explanatory variable(s). When passing models, effect sizes are computed using the sums of squares obtained from anova(model) which might not always be appropriate. See details. Usage eta_squared( model, partial = TRUE, generalized = FALSE, ci = 0.95, alternative = "greater", verbose = TRUE, ... ) omega_squared( model, partial = TRUE, ci = 0.95, alternative = "greater", verbose = TRUE, ... ) epsilon_squared( model, partial = TRUE, ci = 0.95, alternative = "greater", verbose = TRUE, ... ) 30 eta_squared Cohen’s f can take on values between zero, when the population means are all equal, and an in- definitely large number as standard deviation of means increases relative to the average standard deviation within each group. When comparing two models in a sequential regression analysis, Cohen’s f for R-square change is the ratio between the increase in R-square and the percent of unexplained variance. Cohen has suggested that the values of 0.10, 0.25, and 0.40 represent small, medium, and large effect sizes, respectively. Eta Squared from Posterior Predictive Distribution: For Bayesian models (fit with brms or rstanarm), eta_squared_posterior() simulates data from the posterior predictive distribution (ppd) and for each simulation the Eta Squared is com- puted for the model’s fixed effects. This means that the returned values are the population level effect size as implied by the posterior model (and not the effect size in the sample data). See rstantools::posterior_predict() for more info. Value A data frame with the effect size(s) between 0-1 (Eta2, Epsilon2, Omega2, Cohens_f or Cohens_f2, possibly with the partial or generalized suffix), and their CIs (CI_low and CI_high). For eta_squared_posterior(), a data frame containing the ppd of the Eta squared for each fixed effect, which can then be passed to bayestestR::describe_posterior() for summary stats. A data frame containing the effect size values and their confidence intervals. Confidence (Compatibility) Intervals (CIs) Unless stated otherwise, confidence (compatibility) intervals (CIs) are estimated using the non- centrality parameter method (also called the "pivot method"). This method finds the noncentrality parameter ("ncp") of a noncentral t, F, or χ2 distribution that places the observed t, F, or χ2 test statistic at the desired probability point of the distribution. For example, if the observed t statistic is 2.0, with 50 degrees of freedom, for which cumulative noncentral t distribution is t = 2.0 the .025 quantile (answer: the noncentral t distribution with ncp = .04)? After estimating these confidence bounds on the ncp, they are converted into the effect size metric to obtain a confidence interval for the effect size (Steiger, 2004). For additional details on estimation and troubleshooting, see effectsize_CIs. CIs and Significance Tests "Confidence intervals on measures of effect size convey all the information in a hypothesis test, and more." (Steiger, 2004). Confidence (compatibility) intervals and p values are complementary summaries of parameter uncertainty given the observed data. A dichotomous hypothesis test could be performed with either a CI or a p value. The 100 (1 - α)% confidence interval contains all of the parameter values for which p > α for the current data and model. For example, a 95% confidence interval contains all of the values for which p > .05. Note that a confidence interval including 0 does not indicate that the null (no effect) is true. Rather, eta_squared 31 it suggests that the observed data together with the model and its assumptions combined do not pro- vided clear evidence against a parameter value of 0 (same as with any other value in the interval), with the level of this evidence defined by the chosen α level (Rafi & Greenland, 2020; Schweder & Hjort, 2016; Xie & Singh, 2013). To infer no effect, additional judgments about what parameter values are "close enough" to 0 to be negligible are needed ("equivalence testing"; Bauer & Kiesser, 1996). References • Albers, C., \& Lakens, D. (2018). When power analyses based on pilot data are biased: In- accurate effect size estimators and follow-up bias. Journal of experimental social psychology, 74, 187-195. • Allen, R. (2017). Statistics and Experimental Design for Psychologists: A Model Comparison Approach. World Scientific Publishing Company. • Carroll, R. M., & Nordholm, L. A. (1975). Sampling Characteristics of Kelley’s epsilon and Hays’ omega. Educational and Psychological Measurement, 35(3), 541-554. • Kelley, T. (1935) An unbiased correlation ratio measure. Proceedings of the National Academy of Sciences. 21(9). 554-559. • Olejnik, S., & Algina, J. (2003). Generalized eta and omega squared statistics: measures of effect size for some common research designs. Psychological methods, 8(4), 434. • Steiger, J. H. (2004). Beyond the F test: Effect size confidence intervals and tests of close fit in the analysis of variance and contrast analysis. Psychological Methods, 9, 164-182. See Also F_to_eta2() Other effect size indices: cles(), cohens_d(), effectsize.BFBayesFactor(), phi(), rank_biserial() Examples data(mtcars) mtcars$am_f <- factor(mtcars$am) mtcars$cyl_f <- factor(mtcars$cyl) model <- aov(mpg ~ am_f * cyl_f, data = mtcars) (eta2 <- eta_squared(model)) # More types: eta_squared(model, partial = FALSE) eta_squared(model, generalized = "cyl_f") omega_squared(model) epsilon_squared(model) cohens_f(model) if (require(see)) plot(eta2) model0 <- aov(mpg ~ am_f + cyl_f, data = mtcars) # no interaction cohens_f_squared(model0, model2 = model) 32 eta_squared ## Interpretation of effect sizes ## ------------------------------ interpret_omega_squared(0.10, rules = "field2013") interpret_eta_squared(0.10, rules = "cohen1992") interpret_epsilon_squared(0.10, rules = "cohen1992") interpret(eta2, rules = "cohen1992") # Recommended: Type-2 or -3 effect sizes + effects coding # ------------------------------------------------------- contrasts(mtcars$am_f) <- contr.sum contrasts(mtcars$cyl_f) <- contr.sum model <- aov(mpg ~ am_f * cyl_f, data = mtcars) model_anova <- car::Anova(model, type = 3) eta_squared(model_anova) # afex takes care of both type-3 effects and effects coding: data(obk.long, package = "afex") model <- afex::aov_car(value ~ treatment * gender + Error(id / (phase)), data = obk.long, observed = "gender") eta_squared(model) epsilon_squared(model) omega_squared(model) eta_squared(model, generalized = TRUE) # observed vars are pulled from the afex model. ## Approx. effect sizes for mixed models ## ------------------------------------- model <- lme4::lmer(mpg ~ am_f * cyl_f + (1 | vs), data = mtcars) omega_squared(model) ## Bayesian Models (PPD) ## --------------------- ## Not run: fit_bayes <- rstanarm::stan_glm( mpg ~ factor(cyl) * wt + qsec, data = mtcars, family = gaussian(), refresh = 0 ) es <- eta_squared_posterior(fit_bayes, verbose = FALSE, ss_function = car::Anova, type = 3) bayestestR::describe_posterior(es, test = NULL) F_to_eta2 35 ... ) t_to_f(t, df_error, ci = 0.95, alternative = "greater", squared = FALSE, ...) F_to_f2( f, df, df_error, ci = 0.95, alternative = "greater", squared = TRUE, ... ) t_to_f2(t, df_error, ci = 0.95, alternative = "greater", squared = TRUE, ...) Arguments df, df_error Degrees of freedom of numerator or of the error estimate (i.e., the residuals). ci Confidence Interval (CI) level alternative a character string specifying the alternative hypothesis; Controls the type of CI returned: "greater" (default) or "less" (one-sided CI), or "two.sided" (default, two-sided CI). Partial matching is allowed (e.g., "g", "l", "two"...). See One-Sided CIs in effectsize_CIs. ... Arguments passed to or from other methods. t, f The t or the F statistics. squared Return Cohen’s f or Cohen’s f -squared? Details These functions use the following formulae: η2p = F × dfnum F × dfnum + dfden ε2p = (F − 1)× dfnum F × dfnum + dfden ω2 p = (F − 1)× dfnum F × dfnum + dfden + 1 fp = √ η2p 1− η2p 36 F_to_eta2 For t, the conversion is based on the equality of t2 = F when dfnum = 1. Choosing an Un-Biased Estimate: Both Omega and Epsilon are unbiased estimators of the population Eta. But which to choose? Though Omega is the more popular choice, it should be noted that: 1. The formula given above for Omega is only an approximation for complex designs. 2. Epsilon has been found to be less biased (Carroll & Nordholm, 1975). Value A data frame with the effect size(s) between 0-1 (Eta2_partial, Epsilon2_partial, Omega2_partial, Cohens_f_partial or Cohens_f2_partial), and their CIs (CI_low and CI_high). (Note that for ω2 p and ε2p it is possible to compute a negative number; even though this doesn’t make any practical sense, it is recommended to report the negative number and not a 0). Confidence (Compatibility) Intervals (CIs) Unless stated otherwise, confidence (compatibility) intervals (CIs) are estimated using the non- centrality parameter method (also called the "pivot method"). This method finds the noncentrality parameter ("ncp") of a noncentral t, F, or χ2 distribution that places the observed t, F, or χ2 test statistic at the desired probability point of the distribution. For example, if the observed t statistic is 2.0, with 50 degrees of freedom, for which cumulative noncentral t distribution is t = 2.0 the .025 quantile (answer: the noncentral t distribution with ncp = .04)? After estimating these confidence bounds on the ncp, they are converted into the effect size metric to obtain a confidence interval for the effect size (Steiger, 2004). For additional details on estimation and troubleshooting, see effectsize_CIs. CIs and Significance Tests "Confidence intervals on measures of effect size convey all the information in a hypothesis test, and more." (Steiger, 2004). Confidence (compatibility) intervals and p values are complementary summaries of parameter uncertainty given the observed data. A dichotomous hypothesis test could be performed with either a CI or a p value. The 100 (1 - α)% confidence interval contains all of the parameter values for which p > α for the current data and model. For example, a 95% confidence interval contains all of the values for which p > .05. Note that a confidence interval including 0 does not indicate that the null (no effect) is true. Rather, it suggests that the observed data together with the model and its assumptions combined do not pro- vided clear evidence against a parameter value of 0 (same as with any other value in the interval), with the level of this evidence defined by the chosen α level (Rafi & Greenland, 2020; Schweder & Hjort, 2016; Xie & Singh, 2013). To infer no effect, additional judgments about what parameter values are "close enough" to 0 to be negligible are needed ("equivalence testing"; Bauer & Kiesser, 1996). Note Adjusted (partial) Eta-squared is an alias for (partial) Epsilon-squared. F_to_eta2 37 References • Albers, C., & Lakens, D. (2018). When power analyses based on pilot data are biased: Inac- curate effect size estimators and follow-up bias. Journal of experimental social psychology, 74, 187-195. doi: 10.31234/osf.io/b7z4q • Carroll, R. M., & Nordholm, L. A. (1975). Sampling Characteristics of Kelley’s epsilon and Hays’ omega. Educational and Psychological Measurement, 35(3), 541-554. • Cumming, G., & Finch, S. (2001). A primer on the understanding, use, and calculation of confidence intervals that are based on central and noncentral distributions. Educational and Psychological Measurement, 61(4), 532-574. • Friedman, H. (1982). Simplified determinations of statistical power, magnitude of effect and research sample sizes. Educational and Psychological Measurement, 42(2), 521-526. doi: 10.1177/001316448204200214 • Mordkoff, J. T. (2019). A Simple Method for Removing Bias From a Popular Measure of Standardized Effect Size: Adjusted Partial Eta Squared. Advances in Methods and Practices in Psychological Science, 2(3), 228-232. doi: 10.1177/2515245919855053 • Morey, R. D., Hoekstra, R., Rouder, J. N., Lee, M. D., & Wagenmakers, E. J. (2016). The fallacy of placing confidence in confidence intervals. Psychonomic bulletin & review, 23(1), 103-123. • Steiger, J. H. (2004). Beyond the F test: Effect size confidence intervals and tests of close fit in the analysis of variance and contrast analysis. Psychological Methods, 9, 164-182. See Also eta_squared() for more details. Other effect size from test statistic: chisq_to_phi(), t_to_d() Examples mod <- aov(mpg ~ factor(cyl) * factor(am), mtcars) anova(mod) (etas <- F_to_eta2( f = c(44.85, 3.99, 1.38), df = c(2, 1, 2), df_error = 26 )) if (require(see)) plot(etas) # Compare to: eta_squared(mod) fit <- lmerTest::lmer(extra ~ group + (1 | ID), sleep) # anova(fit) # #> Type III Analysis of Variance Table with Satterthwaite's method # #> Sum Sq Mean Sq NumDF DenDF F value Pr(>F) # #> group 12.482 12.482 1 9 16.501 0.002833 ** 40 interpret_bf interpret(eta2, rules = "field2013") X <- chisq.test(mtcars$am, mtcars$cyl == 8) interpret(oddsratio(X), rules = "chen2010") interpret(cramers_v(X), "lovakov2021") interpret_bf Interpret Bayes Factor (BF) Description Interpret Bayes Factor (BF) Usage interpret_bf( bf, rules = "jeffreys1961", log = FALSE, include_value = FALSE, protect_ratio = TRUE, exact = TRUE ) Arguments bf Value or vector of Bayes factor (BF) values. rules Can be "jeffreys1961" (default), "raftery1995" or custom set of rules() (for the absolute magnitude of evidence). log Is the bf value log(bf)? include_value Include the value in the output. protect_ratio Should values smaller than 1 be represented as ratios? exact Should very large or very small values be reported with a scientific format (e.g., 4.24e5), or as truncated values (as "> 1000" and "< 1/1000"). Details Argument names can be partially matched. Rules Rules apply to BF as ratios, so BF of 10 is as extreme as a BF of 0.1 (1/10). • Jeffreys (1961) ("jeffreys1961"; default) – BF = 1 - No evidence – 1 < BF <= 3 - Anecdotal interpret_cohens_d 41 – 3 < BF <= 10 - Moderate – 10 < BF <= 30 - Strong – 30 < BF <= 100 - Very strong – BF > 100 - Extreme. • Raftery (1995) ("raftery1995") – BF = 1 - No evidence – 1 < BF <= 3 - Weak – 3 < BF <= 20 - Positive – 20 < BF <= 150 - Strong – BF > 150 - Very strong References • Jeffreys, H. (1961), Theory of Probability, 3rd ed., Oxford University Press, Oxford. • Raftery, A. E. (1995). Bayesian model selection in social research. Sociological methodology, 25, 111-164. • Jarosz, A. F., & Wiley, J. (2014). What are the odds? A practical guide to computing and reporting Bayes factors. The Journal of Problem Solving, 7(1), 1. Examples interpret_bf(1) interpret_bf(c(5, 2)) interpret_cohens_d Interpret standardized differences Description Interpretation of standardized differences using different sets of rules of thumb. Usage interpret_cohens_d(d, rules = "cohen1988", ...) interpret_hedges_g(g, rules = "cohen1988") interpret_glass_delta(delta, rules = "cohen1988") Arguments d, g, delta Value or vector of effect size values. rules Can be "cohen1988" (default), "gignac2016", "sawilowsky2009", "lovakov2021" or a custom set of rules(). ... Not directly used. 42 interpret_cohens_d Rules Rules apply to equally to positive and negative d (i.e., they are given as absolute values). • Cohen (1988) ("cohen1988"; default) – d < 0.2 - Very small – 0.2 <= d < 0.5 - Small – 0.5 <= d < 0.8 - Medium – d >= 0.8 - Large • Sawilowsky (2009) ("sawilowsky2009") – d < 0.1 - Tiny – 0.1 <= d < 0.2 - Very small – 0.2 <= d < 0.5 - Small – 0.5 <= d < 0.8 - Medium – 0.8 <= d < 1.2 - Large – 1.2 <= d < 2 - Very large – d >= 2 - Huge • Lovakov & Agadullina (2021) ("lovakov2021") – d < 0.15 - Very small – 0.15 <= d < 0.36 - Small – 0.36 <= d < 0.65 - Medium – d >= 0.65 - Large • Gignac & Szodorai (2016) ("gignac2016", based on the d_to_r() conversion, see interpret_r()) – d < 0.2 - Very small – 0.2 <= d < 0.41 - Small – 0.41 <= d < 0.63 - Moderate – d >= 0.63 - Large References • Lovakov, A., & Agadullina, E. R. (2021). Empirically Derived Guidelines for Effect Size Interpretation in Social Psychology. European Journal of Social Psychology. • Gignac, G. E., & Szodorai, E. T. (2016). Effect size guidelines for individual differences researchers. Personality and individual differences, 102, 74-78. • Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd Ed.). New York: Routledge. • Sawilowsky, S. S. (2009). New effect size rules of thumb. Examples interpret_cohens_d(.02) interpret_cohens_d(c(.5, .02)) interpret_cohens_d(.3, rules = "lovakov2021") interpret_gfi 45 Rules ESS: • Bürkner, P. C. (2017) ("burkner2017"; default) – ESS < 1000 - Insufficient – ESS >= 1000 - Sufficient Rhat: • Vehtari et al. (2019) ("vehtari2019"; default) – Rhat < 1.01 - Converged – Rhat >= 1.01 - Failed • Gelman & Rubin (1992) ("gelman1992") – Rhat < 1.1 - Converged – Rhat >= 1.1 - Failed References • Bürkner, P. C. (2017). brms: An R package for Bayesian multilevel models using Stan. Journal of Statistical Software, 80(1), 1-28. • Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple se- quences. Statistical science, 7(4), 457-472. • Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2019). Rank-normalization, folding, and localization: An improved Rhat for assessing convergence of MCMC. arXiv preprint arXiv:1903.08008. Examples interpret_ess(1001) interpret_ess(c(852, 1200)) interpret_rhat(1.00) interpret_rhat(c(1.5, 0.9)) interpret_gfi Interpret of indices of CFA / SEM goodness of fit Description Interpretation of indices of fit found in confirmatory analysis or structural equation modelling, such as RMSEA, CFI, NFI, IFI, etc. 46 interpret_gfi Usage interpret_gfi(x, rules = "default") interpret_agfi(x, rules = "default") interpret_nfi(x, rules = "byrne1994") interpret_nnfi(x, rules = "byrne1994") interpret_cfi(x, rules = "default") interpret_rmsea(x, rules = "default") interpret_srmr(x, rules = "default") interpret_rfi(x, rules = "default") interpret_ifi(x, rules = "default") interpret_pnfi(x, rules = "default") ## S3 method for class 'lavaan' interpret(x, ...) ## S3 method for class 'performance_lavaan' interpret(x, ...) Arguments x vector of values, or an object of class lavaan. rules Can be "default" or custom set of rules(). ... Currently not used. Details Indices of fit: • Chisq: The model Chi-squared assesses overall fit and the discrepancy between the sample and fitted covariance matrices. Its p-value should be > .05 (i.e., the hypothesis of a perfect fit cannot be rejected). However, it is quite sensitive to sample size. • GFI/AGFI: The (Adjusted) Goodness of Fit is the proportion of variance accounted for by the estimated population covariance. Analogous to R2. The GFI and the AGFI should be > .95 and > .90, respectively. • NFI/NNFI/TLI: The (Non) Normed Fit Index. An NFI of 0.95, indicates the model of interest improves the fit by 95\ NNFI (also called the Tucker Lewis index; TLI) is preferable for smaller samples. They should be > .90 (Byrne, 1994) or > .95 (Schumacker & Lomax, 2004). interpret_gfi 47 • CFI: The Comparative Fit Index is a revised form of NFI. Not very sensitive to sample size (Fan, Thompson, & Wang, 1999). Compares the fit of a target model to the fit of an independent, or null, model. It should be > .90. • RMSEA: The Root Mean Square Error of Approximation is a parsimony-adjusted index. Values closer to 0 represent a good fit. It should be < .08 or < .05. The p-value printed with it tests the hypothesis that RMSEA is less than or equal to .05 (a cutoff sometimes used for good fit), and thus should be not significant. • RMR/SRMR: the (Standardized) Root Mean Square Residual represents the square-root of the difference between the residuals of the sample covariance matrix and the hypothesized model. As the RMR can be sometimes hard to interpret, better to use SRMR. Should be < .08. • RFI: the Relative Fit Index, also known as RHO1, is not guaranteed to vary from 0 to 1. However, RFI close to 1 indicates a good fit. • IFI: the Incremental Fit Index (IFI) adjusts the Normed Fit Index (NFI) for sample size and degrees of freedom (Bollen’s, 1989). Over 0.90 is a good fit, but the index can exceed 1. • PNFI: the Parsimony-Adjusted Measures Index. There is no commonly agreed-upon cutoff value for an acceptable model for this index. Should be > 0.50. See the documentation for fitmeasures(). What to report: For structural equation models (SEM), Kline (2015) suggests that at a minimum the following indices should be reported: The model chi-square, the RMSEA, the CFI and the SRMR. Note When possible, it is recommended to report dynamic cutoffs of fit indices. See https://dynamicfit.app/cfa/. References • Awang, Z. (2012). A handbook on SEM. Structural equation modeling. • Byrne, B. M. (1994). Structural equation modeling with EQS and EQS/Windows. Thousand Oaks, CA: Sage Publications. • Tucker, L. R., \& Lewis, C. (1973). The reliability coefficient for maximum likelihood factor analysis. Psychometrika, 38, 1-10. • Schumacker, R. E., \& Lomax, R. G. (2004). A beginner’s guide to structural equation mod- eling, Second edition. Mahwah, NJ: Lawrence Erlbaum Associates. • Fan, X., B. Thompson, \& L. Wang (1999). Effects of sample size, estimation method, and model specification on structural equation modeling fit indexes. Structural Equation Model- ing, 6, 56-83. • Kline, R. B. (2015). Principles and practice of structural equation modeling. Guilford publi- cations. Examples interpret_gfi(c(.5, .99)) interpret_agfi(c(.5, .99)) interpret_nfi(c(.5, .99)) 50 interpret_oddsratio interpret_oddsratio Interpret Odds ratio Description Interpret Odds ratio Usage interpret_oddsratio(OR, rules = "chen2010", log = FALSE, ...) Arguments OR Value or vector of (log) odds ratio values. rules Can be "chen2010" (default), "cohen1988" (through transformation to stan- dardized difference, see oddsratio_to_d()) or custom set of rules(). log Are the provided values log odds ratio. ... Currently not used. Rules Rules apply to OR as ratios, so OR of 10 is as extreme as a OR of 0.1 (1/10). • Chen et al. (2010) ("chen2010"; default) – OR < 1.68 - Very small – 1.68 <= OR < 3.47 - Small – 3.47 <= OR < 6.71 - Medium – **OR >= 6.71 ** - Large • Cohen (1988) ("cohen1988", based on the oddsratio_to_d() conversion, see interpret_cohens_d()) – OR < 1.44 - Very small – 1.44 <= OR < 2.48 - Small – 2.48 <= OR < 4.27 - Medium – **OR >= 4.27 ** - Large References • Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd Ed.). New York: Routledge. • Chen, H., Cohen, P., & Chen, S. (2010). How big is a big odds ratio? Interpreting the magni- tudes of odds ratios in epidemiological studies. Communications in Statistics-Simulation and Computation, 39(4), 860-864. • Sánchez-Meca, J., Marín-Martínez, F., & Chacón-Moscoso, S. (2003). Effect-size indices for dichotomized outcomes in meta-analysis. Psychological methods, 8(4), 448. interpret_omega_squared 51 Examples interpret_oddsratio(1) interpret_oddsratio(c(5, 2)) interpret_omega_squared Interpret ANOVA effect size Description Interpret ANOVA effect size Usage interpret_omega_squared(es, rules = "field2013", ...) interpret_eta_squared(es, rules = "field2013", ...) interpret_epsilon_squared(es, rules = "field2013", ...) Arguments es Value or vector of eta / omega / epsilon squared values. rules Can be "field2013" (default), "cohen1992" or custom set of rules(). ... Not used for now. Rules • Field (2013) ("field2013"; default) – ES < 0.01 - Very small – 0.01 <= ES < 0.06 - Small – 0.16 <= ES < 0.14 - Medium – **ES >= 0.14 ** - Large • Cohen (1992) ("cohen1992") applicable to one-way anova, or to partial eta / omega / epsilon squared in multi-way anova. – ES < 0.02 - Very small – 0.02 <= ES < 0.13 - Small – 0.13 <= ES < 0.26 - Medium – ES >= 0.26 - Large References • Field, A (2013) Discovering statistics using IBM SPSS Statistics. Fourth Edition. Sage:London. • Cohen, J. (1992). A power primer. Psychological bulletin, 112(1), 155. 52 interpret_p See Also https://imaging.mrc-cbu.cam.ac.uk/statswiki/FAQ/effectSize/ Examples interpret_eta_squared(.02) interpret_eta_squared(c(.5, .02), rules = "cohen1992") interpret_p Interpret p-values Description Interpret p-values Usage interpret_p(p, rules = "default") Arguments p Value or vector of p-values. rules Can be "default", "rss" (for Redefine statistical significance rules) or custom set of rules(). Rules • Default – p >= 0.05 - Not significant – p < 0.05 - Significant • Benjamin et al. (2018) ("rss") – p >= 0.05 - Not significant – 0.005 <= p < 0.05 - Suggestive – p < 0.005 - Significant References • Benjamin, D. J., Berger, J. O., Johannesson, M., Nosek, B. A., Wagenmakers, E. J., Berk, R., ... & Cesarini, D. (2018). Redefine statistical significance. Nature Human Behaviour, 2(1), 6-10. Examples interpret_p(c(.5, .02, 0.001)) interpret_p(c(.5, .02, 0.001), rules = "rss") interpret_r 55 – r >= 0.5 - Large • Lovakov & Agadullina (2021) ("lovakov2021") – r < 0.12 - Very small – 0.12 <= r < 0.24 - Small – 0.24 <= r < 0.41 - Moderate – r >= 0.41 - Large • Evans (1996) ("evans1996") – r < 0.2 - Very weak – 0.2 <= r < 0.4 - Weak – 0.4 <= r < 0.6 - Moderate – 0.6 <= r < 0.8 - Strong – r >= 0.8 - Very strong Note As φ can be larger than 1 - it is recommended to compute and interpret Cramer’s V instead. References • Lovakov, A., & Agadullina, E. R. (2021). Empirically Derived Guidelines for Effect Size Interpretation in Social Psychology. European Journal of Social Psychology. • Funder, D. C., & Ozer, D. J. (2019). Evaluating effect size in psychological research: sense and nonsense. Advances in Methods and Practices in Psychological Science. • Gignac, G. E., & Szodorai, E. T. (2016). Effect size guidelines for individual differences researchers. Personality and individual differences, 102, 74-78. • Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd Ed.). New York: Routledge. • Evans, J. D. (1996). Straightforward statistics for the behavioral sciences. Thomson Brooks/Cole Publishing Co. See Also Page 88 of APA’s 6th Edition. Examples interpret_r(.015) interpret_r(c(.5, -.02)) interpret_r(.3, rules = "lovakov2021") 56 interpret_r2 interpret_r2 Interpret coefficient of determination (R2) Description Interpret coefficient of determination (R2) Usage interpret_r2(r2, rules = "cohen1988") Arguments r2 Value or vector of R2 values. rules Can be "cohen1988" (default), "falk1992", "chin1998", "hair2011", or cus- tom set of rules()]. Rules For Linear Regression: • Cohen (1988) ("cohen1988"; default) – R2 < 0.02 - Very weak – 0.02 <= R2 < 0.13 - Weak – 0.13 <= R2 < 0.26 - Moderate – R2 >= 0.26 - Substantial • Falk & Miller (1992) ("falk1992") – R2 < 0.1 - Negligible – R2 >= 0.1 - Adequate For PLS / SEM R-Squared of latent variables: • Chin, W. W. (1998) ("chin1998") – R2 < 0.19 - Very weak – 0.19 <= R2 < 0.33 - Weak – 0.33 <= R2 < 0.67 - Moderate – R2 >= 0.67 - Substantial • Hair et al. (2011) ("hair2011") – R2 < 0.25 - Very weak – 0.25 <= R2 < 0.50 - Weak – 0.50 <= R2 < 0.75 - Moderate – R2 >= 0.75 - Substantial interpret_rope 57 References • Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd Ed.). New York: Routledge. • Falk, R. F., & Miller, N. B. (1992). A primer for soft modeling. University of Akron Press. • Chin, W. W. (1998). The partial least squares approach to structural equation modeling. Mod- ern methods for business research, 295(2), 295-336. • Hair, J. F., Ringle, C. M., & Sarstedt, M. (2011). PLS-SEM: Indeed a silver bullet. Journal of Marketing theory and Practice, 19(2), 139-152. Examples interpret_r2(.02) interpret_r2(c(.5, .02)) interpret_rope Interpret Bayesian diagnostic indices Description Interpretation of Bayesian indices of percentage in ROPE. Usage interpret_rope(rope, ci = 0.9, rules = "default") Arguments rope Value or vector of percentages in ROPE. ci The Credible Interval (CI) probability, corresponding to the proportion of HDI, that was used. Can be 1 in the case of "full ROPE". rules A character string (see details) or a custom set of rules(). Rules • Default – For CI < 1 * Rope = 0 - Significant * 0 < Rope < 1 - Undecided * Rope = 1 - Negligible – For CI = 1 * Rope < 0.01 - Significant * 0.01 < Rope < 0.025 - Probably significant * 0.025 < Rope < 0.975 - Undecided * 0.975 < Rope < 0.99 - Probably negligible * Rope > 0.99 - Negligible 60 odds_to_probs References Grant, R. L. (2014). Converting an odds ratio to a range of plausible relative risks for better com- munication of research findings. Bmj, 348, f7450. See Also Other convert between effect sizes: d_to_cles(), d_to_r(), eta2_to_f2(), odds_to_probs() Examples p0 <- 0.4 p1 <- 0.7 (OR <- probs_to_odds(p1) / probs_to_odds(p0)) (RR <- p1 / p0) riskratio_to_oddsratio(RR, p0 = p0) oddsratio_to_riskratio(OR, p0 = p0) m <- glm(am ~ factor(cyl), data = mtcars, family = binomial()) oddsratio_to_riskratio(m) odds_to_probs Convert between Odds and Probabilities Description Convert between Odds and Probabilities Usage odds_to_probs(odds, log = FALSE, ...) ## S3 method for class 'data.frame' odds_to_probs(odds, log = FALSE, select = NULL, exclude = NULL, ...) probs_to_odds(probs, log = FALSE, ...) ## S3 method for class 'data.frame' probs_to_odds(probs, log = FALSE, select = NULL, exclude = NULL, ...) Arguments odds The Odds (or log(odds) when log = TRUE) to convert. log Take in or output log odds (such as in logistic models). ... Arguments passed to or from other methods. phi 61 select When a data frame is passed, character or list of of column names to be trans- formed. exclude When a data frame is passed, character or list of column names to be excluded from transformation. probs Probability values to convert. Value Converted index. See Also stats::plogis() Other convert between effect sizes: d_to_cles(), d_to_r(), eta2_to_f2(), oddsratio_to_riskratio() Examples odds_to_probs(3) odds_to_probs(1.09, log = TRUE) probs_to_odds(0.95) probs_to_odds(0.95, log = TRUE) phi Effect size for contingency tables Description Compute Cramer’s V, phi (φ), Cohen’s w, normalized Chi (χ), Pearson’s contingency coefficient, Odds ratios, Risk ratios, Cohen’s h and Cohen’s g for contingency tables or goodness-of-fit. See details. Usage phi(x, y = NULL, ci = 0.95, alternative = "greater", adjust = FALSE, ...) cohens_w(x, y = NULL, ci = 0.95, alternative = "greater", ...) cramers_v(x, y = NULL, ci = 0.95, alternative = "greater", adjust = FALSE, ...) normalized_chi(x, y = NULL, ci = 0.95, alternative = "greater", ...) pearsons_c( x, y = NULL, ci = 0.95, alternative = "greater", 62 phi adjust = FALSE, ... ) oddsratio(x, y = NULL, ci = 0.95, alternative = "two.sided", log = FALSE, ...) riskratio(x, y = NULL, ci = 0.95, alternative = "two.sided", log = FALSE, ...) cohens_h(x, y = NULL, ci = 0.95, alternative = "two.sided", ...) cohens_g(x, y = NULL, ci = 0.95, alternative = "two.sided", ...) Arguments x a numeric vector or matrix. x and y can also both be factors. y a numeric vector; ignored if x is a matrix. If x is a factor, y should be a factor of the same length. ci Confidence Interval (CI) level alternative a character string specifying the alternative hypothesis; Controls the type of CI returned: "greater" (two-sided CI; default for Cramer’s V, phi (φ), and Cohen’s w), "two.sided" (default for OR, RR, Cohen’s h and Cohen’s g) or "less" (one-sided CI). Partial matching is allowed (e.g., "g", "l", "two"...). See One-Sided CIs in effectsize_CIs. adjust Should the effect size be bias-corrected? Defaults to FALSE. ... Arguments passed to stats::chisq.test(), such as p for goodness-of-fit. Ig- nored for cohens_g(). log Take in or output the log of the ratio (such as in logistic models). Details Cramer’s V, phi (φ), Cohen’s w, and Pearson’s C are effect sizes for tests of independence in 2D contingency tables. For 2-by-2 tables, Cramer’s V, phi and Cohen’s w are identical, and are equal to the simple correlation between two dichotomous variables, ranging between 0 (no dependence) and 1 (perfect dependence). For larger tables, Cramer’s V or Pearson’s C should be used, as they are bounded between 0-1. Cohen’s w can also be used, but since it is not bounded at 1 (can be larger) its interpretation is more difficult. For goodness-of-fit in 1D tables Cohen’s W, normalized Chi (χ) or Pearson’s C can be used. Co- hen’s w has no upper bound (can be arbitrarily large, depending on the expected distribution). Nor- malized Chi is an adjusted Cohen’s w, accounting for the expected distribution, making it bounded between 0-1. Pearson’s C is also bounded between 0-1. To summarize, for correlation-like effect sizes, we recommend: • For a 2x2 table, use phi() • For larger tables, use cramers_v() phi 65 cohens_h(RCT) ## Larger tables ## ------------- M <- matrix(c(150, 100, 165, 130, 50, 65, 35, 10, 2, 55, 40, 25), nrow = 4, dimnames = list( Music = c("Pop", "Rock", "Jazz", "Classic"), Study = c("Psych", "Econ", "Law"))) M cohens_w(M) cramers_v(M) pearsons_c(M) ## Goodness of fit ## --------------- Smoking_ASD <- as.table(c(ASD = 17, ASP = 11, TD = 640)) normalized_chi(Smoking_ASD) cohens_w(Smoking_ASD) pearsons_c(Smoking_ASD) # Use custom expected values: normalized_chi(Smoking_ASD, p = c(0.015, 0.010, 0.975)) cohens_w(Smoking_ASD, p = c(0.015, 0.010, 0.975)) pearsons_c(Smoking_ASD, p = c(0.015, 0.010, 0.975)) ## Dependent (Paired) Contingency Tables ## ------------------------------------- Performance <- matrix(c(794, 150, 86, 570), nrow = 2, dimnames = list( "1st Survey" = c("Approve", "Disapprove"), "2nd Survey" = c("Approve", "Disapprove"))) Performance 66 plot.effectsize_table cohens_g(Performance) plot.effectsize_table Methods for effectsize tables Description Printing, formatting and plotting methods for effectsize tables. Usage ## S3 method for class 'effectsize_table' plot(x, ...) ## S3 method for class 'effectsize_table' print(x, digits = 2, ...) ## S3 method for class 'effectsize_table' print_md(x, digits = 2, ...) ## S3 method for class 'effectsize_table' print_html(x, digits = 2, ...) ## S3 method for class 'effectsize_table' format(x, digits = 2, output = c("text", "markdown", "html"), ...) ## S3 method for class 'effectsize_difference' print(x, digits = 2, append_CLES = FALSE, ...) Arguments x Object to print. ... Arguments passed to or from other functions. digits Number of digits for rounding or significant figures. May also be "signif" to return significant figures or "scientific" to return scientific notation. Control the number of digits by adding the value as suffix, e.g. digits = "scientific4" to have scientific notation with 4 decimal places, or digits = "signif5" for 5 significant figures (see also signif()). output Which output is the formatting intended for? Affects how title and footers are formatted. append_CLES Should the Common Language Effect Sizes be printed as well? Only applicable to Cohen’s d, Hedges’ g for independent samples of equal variance (pooled sd) or for the rank-biserial correlation for independent samples (See d_to_cles()) rank_biserial 67 See Also insight::display() rank_biserial Effect size for non-parametric (rank sum) tests Description Compute the rank-biserial correlation (rrb), Cliff’s delta (δ), rank epsilon squared (ε2), and Kendall’s W effect sizes for non-parametric (rank sum) tests. Usage rank_biserial( x, y = NULL, data = NULL, mu = 0, ci = 0.95, alternative = "two.sided", paired = FALSE, verbose = TRUE, ..., iterations ) cliffs_delta( x, y = NULL, data = NULL, mu = 0, ci = 0.95, alternative = "two.sided", verbose = TRUE, ... ) rank_epsilon_squared( x, groups, data = NULL, ci = 0.95, alternative = "greater", iterations = 200, ... ) 70 rank_biserial • Cliff, N. (1993). Dominance statistics: Ordinal analyses to answer ordinal questions. Psycho- logical bulletin, 114(3), 494. • Tomczak, M., & Tomczak, E. (2014). The need to report effect size estimates revisited. An overview of some recommended measures of effect size. See Also Other effect size indices: cles(), cohens_d(), effectsize.BFBayesFactor(), eta_squared(), phi() Examples data(mtcars) mtcars$am <- factor(mtcars$am) mtcars$cyl <- factor(mtcars$cyl) # Rank Biserial Correlation # ========================= # Two Independent Samples ---------- (rb <- rank_biserial(mpg ~ am, data = mtcars)) # Same as: # rank_biserial("mpg", "am", data = mtcars) # rank_biserial(mtcars$mpg[mtcars$am=="0"], mtcars$mpg[mtcars$am=="1"]) # More options: rank_biserial(mpg ~ am, data = mtcars, mu = -5) print(rb, append_CLES = TRUE) # One Sample ---------- rank_biserial(wt ~ 1, data = mtcars, mu = 3) # same as: # rank_biserial("wt", data = mtcars, mu = 3) # rank_biserial(mtcars$wt, mu = 3) # Paired Samples ---------- dat <- data.frame(Cond1 = c(1.83, 0.5, 1.62, 2.48, 1.68, 1.88, 1.55, 3.06, 1.3), Cond2 = c(0.878, 0.647, 0.598, 2.05, 1.06, 1.29, 1.06, 3.14, 1.29)) (rb <- rank_biserial(Pair(Cond1, Cond2) ~ 1, data = dat, paired = TRUE)) # same as: # rank_biserial(dat$Cond1, dat$Cond2, paired = TRUE) interpret_rank_biserial(0.78) interpret(rb, rules = "funder2019") # Rank Epsilon Squared # ==================== rules 71 rank_epsilon_squared(mpg ~ cyl, data = mtcars) # Kendall's W # =========== dat <- data.frame(cond = c("A", "B", "A", "B", "A", "B"), ID = c("L", "L", "M", "M", "H", "H"), y = c(44.56, 28.22, 24, 28.78, 24.56, 18.78)) (W <- kendalls_w(y ~ cond | ID, data = dat, verbose = FALSE)) interpret_kendalls_w(0.11) interpret(W, rules = "landis1977") rules Interpretation Grid Description Create a container for interpretation rules of thumb. Usually used in conjunction with interpret. Usage rules(values, labels = NULL, name = NULL, right = TRUE) is.rules(x) Arguments values Vector of reference values (edges defining categories or critical values). labels Labels associated with each category. If NULL, will try to infer it from values (if it is a named vector or a list), otherwise, will return the breakpoints. name Name of the set of rules (will be printed). right logical, for threshold-type rules, indicating if the thresholds themselves should be included in the interval to the right (lower values) or in the interval to the left (higher values). x An arbitrary R object. See Also interpret 72 sd_pooled Examples rules(c(0.05), c("significant", "not significant"), right = FALSE) rules(c(0.2, 0.5, 0.8), c("small", "medium", "large")) rules(c("small" = 0.2, "medium" = 0.5), name = "Cohen's Rules") sd_pooled Pooled Standard Deviation Description The Pooled Standard Deviation is a weighted average of standard deviations for two or more groups, assumed to have equal variance. It represents the common deviation among the groups, around each of their respective means. Usage sd_pooled(x, y = NULL, data = NULL, verbose = TRUE, ...) mad_pooled(x, y = NULL, data = NULL, constant = 1.4826, verbose = TRUE, ...) Arguments x A formula, a numeric vector, or a character name of one in data. y A numeric vector, a grouping (character / factor) vector, a or a character name of one in data. Ignored if x is a formula. data An optional data frame containing the variables. verbose Toggle warnings and messages on or off. ... Arguments passed to or from other methods. When x is a formula, these can be subset and na.action. constant scale factor. Details The standard version is calculated as: √∑ (xi − x̄)2 n1 + n2 − 2 The robust version is calculated as: 1.4826×Median(| {x−Medianx, y −Mediany} |) Value Numeric, the pooled standard deviation. t_to_d 75 Confidence (Compatibility) Intervals (CIs) Unless stated otherwise, confidence (compatibility) intervals (CIs) are estimated using the non- centrality parameter method (also called the "pivot method"). This method finds the noncentrality parameter ("ncp") of a noncentral t, F, or χ2 distribution that places the observed t, F, or χ2 test statistic at the desired probability point of the distribution. For example, if the observed t statistic is 2.0, with 50 degrees of freedom, for which cumulative noncentral t distribution is t = 2.0 the .025 quantile (answer: the noncentral t distribution with ncp = .04)? After estimating these confidence bounds on the ncp, they are converted into the effect size metric to obtain a confidence interval for the effect size (Steiger, 2004). For additional details on estimation and troubleshooting, see effectsize_CIs. CIs and Significance Tests "Confidence intervals on measures of effect size convey all the information in a hypothesis test, and more." (Steiger, 2004). Confidence (compatibility) intervals and p values are complementary summaries of parameter uncertainty given the observed data. A dichotomous hypothesis test could be performed with either a CI or a p value. The 100 (1 - α)% confidence interval contains all of the parameter values for which p > α for the current data and model. For example, a 95% confidence interval contains all of the values for which p > .05. Note that a confidence interval including 0 does not indicate that the null (no effect) is true. Rather, it suggests that the observed data together with the model and its assumptions combined do not pro- vided clear evidence against a parameter value of 0 (same as with any other value in the interval), with the level of this evidence defined by the chosen α level (Rafi & Greenland, 2020; Schweder & Hjort, 2016; Xie & Singh, 2013). To infer no effect, additional judgments about what parameter values are "close enough" to 0 to be negligible are needed ("equivalence testing"; Bauer & Kiesser, 1996). References • Friedman, H. (1982). Simplified determinations of statistical power, magnitude of effect and research sample sizes. Educational and Psychological Measurement, 42(2), 521-526. doi: 10.1177/001316448204200214 • Wolf, F. M. (1986). Meta-analysis: Quantitative methods for research synthesis (Vol. 59). Sage. • Rosenthal, R. (1994) Parametric measures of effect size. In H. Cooper and L.V. Hedges (Eds.). The handbook of research synthesis. New York: Russell Sage Foundation. • Steiger, J. H. (2004). Beyond the F test: Effect size confidence intervals and tests of close fit in the analysis of variance and contrast analysis. Psychological Methods, 9, 164-182. • Cumming, G., & Finch, S. (2001). A primer on the understanding, use, and calculation of confidence intervals that are based on central and noncentral distributions. Educational and Psychological Measurement, 61(4), 532-574. See Also Other effect size from test statistic: F_to_eta2(), chisq_to_phi() 76 t_to_d Examples ## t Tests res <- t.test(1:10, y = c(7:20), var.equal = TRUE) t_to_d(t = res$statistic, res$parameter) t_to_r(t = res$statistic, res$parameter) t_to_r(t = res$statistic, res$parameter, alternative = "less") res <- with(sleep, t.test(extra[group == 1], extra[group == 2], paired = TRUE)) t_to_d(t = res$statistic, res$parameter, paired = TRUE) t_to_r(t = res$statistic, res$parameter) t_to_r(t = res$statistic, res$parameter, alternative = "greater") ## Linear Regression model <- lm(rating ~ complaints + critical, data = attitude) (param_tab <- parameters::model_parameters(model)) (rs <- t_to_r(param_tab$t[2:3], param_tab$df_error[2:3])) if (require(see)) plot(rs) # How does this compare to actual partial correlations? if (require("correlation")) { correlation::correlation(attitude[, c(1, 2, 6)], partial = TRUE)[1:2, c(2, 3, 7, 8)] } Index ∗ convert between effect sizes d_to_cles, 13 d_to_r, 15 eta2_to_f2, 26 odds_to_probs, 60 oddsratio_to_riskratio, 59 ∗ data hardlyworking, 38 ∗ effect size from test statistic chisq_to_phi, 3 F_to_eta2, 34 t_to_d, 73 ∗ effect size indices cles, 7 cohens_d, 9 effectsize.BFBayesFactor, 16 eta_squared, 27 phi, 61 rank_biserial, 67 .es_aov_simple (effectsize_API), 19 .es_aov_strata (effectsize_API), 19 .es_aov_table (effectsize_API), 19 anova(), 29 bayestestR::describe_posterior(), 17, 30 bayestestR::equivalence_test(), 25 bayestestR::overlap(), 8 chisq_to_cohens_w (chisq_to_phi), 3 chisq_to_cramers_v (chisq_to_phi), 3 chisq_to_normalized (chisq_to_phi), 3 chisq_to_pearsons_c (chisq_to_phi), 3 chisq_to_phi, 3, 37, 75 chisq_to_phi(), 64 cles, 7, 12, 18, 31, 64, 70 cliffs_delta (rank_biserial), 67 cohens_d, 9, 9, 18, 31, 64, 70 cohens_d(), 8, 14, 24, 73, 74 cohens_f (eta_squared), 27 cohens_f_squared (eta_squared), 27 cohens_g (phi), 61 cohens_h (phi), 61 cohens_u3 (cles), 7 cohens_w (phi), 61 common_language (cles), 7 convert_d_to_common_language (d_to_cles), 13 convert_d_to_oddsratio (d_to_r), 15 convert_d_to_r (d_to_r), 15 convert_logoddsratio_to_d (d_to_r), 15 convert_logoddsratio_to_r (d_to_r), 15 convert_odds_to_probs (odds_to_probs), 60 convert_oddsratio_to_d (d_to_r), 15 convert_oddsratio_to_r (d_to_r), 15 convert_probs_to_odds (odds_to_probs), 60 convert_r_to_d (d_to_r), 15 convert_r_to_oddsratio (d_to_r), 15 convert_rb_to_common_language (d_to_cles), 13 cramers_v (phi), 61 cramers_v(), 5 d_to_cles, 13, 16, 27, 60, 61 d_to_cles(), 8, 9, 12, 66 d_to_common_language (d_to_cles), 13 d_to_oddsratio (d_to_r), 15 d_to_r, 14, 15, 27, 60, 61 d_to_r(), 42 effectsize (effectsize.BFBayesFactor), 16 effectsize.BFBayesFactor, 9, 12, 16, 31, 64, 70 effectsize_API, 19 effectsize_CIs, 4, 5, 8, 11, 20, 20, 28, 30, 35, 36, 62, 63, 68, 74, 75 77