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paper/paper.bib

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@@ -149,4 +149,34 @@ @article{bollen1989structural
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author={Bollen, Kenneth A},
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journal={New York},
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year={1989}
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}
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@book{cramer1946mathematical,
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title={Mathematical Methods of Statistics},
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author={Cram{\'e}r, Harald},
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year={1946},
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publisher={Princeton: Princeton University Press}
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}
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@article{kelley1935unbiased,
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title={An unbiased correlation ratio measure},
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author={Kelley, Truman L},
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journal={Proceedings of the National Academy of Sciences of the United States of America},
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volume={21},
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number={9},
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pages={554},
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year={1935},
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publisher={National Academy of Sciences}
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}
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@article{friedman1982simplified,
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title={Simplified determinations of statistical power, magnitude of effect and research sample sizes},
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author={Friedman, Herbert},
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journal={Educational and Psychological Measurement},
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volume={42},
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number={2},
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pages={521--526},
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year={1982},
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publisher={Sage Publications Sage CA: Thousand Oaks, CA}
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}

paper/paper.md

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@@ -42,7 +42,7 @@ In both theoretical and applied research, it is often of interest to assess the
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**effectsize**'s functionality is in part comparable to packages like **lm.beta** [@behrendt2014lmbeta], **MOTE** [@buchanan2019MOTE] or **MBESS** [@kelley2020MBESS]. Yet, there are some notable differences, e.g.:
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- **lm.beta** provides standardized regression coefficients for linear models, based on post-hoc model matrix standardization. However, the functionality is available only for a limited number of models (models inheriting from the `lm` class), whereas **effectsize** provides support for many types of models, including (generalized) linear mixed models, Bayesian models, and more. Additionally, in additional to post-hoc model matrix standardization, **effectsize** offers other methods of standardization (see below).
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- Both **MOTE** and **MBESS** provide functions for computing effect sizes such as Cohen's *d* and effect sizes for ANOVAs, and their confidence intervals. However, both require manual input of *F*- or *t*-statistics, *degrees of freedom*, and *Sums of Squares* for the computation the effect sizes, whereas **effectsize** can automatically extract this information from the provided models, thus allowing for better ease-of-use as well as reducing any potential for error.
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- Both **MOTE** and **MBESS** provide functions for computing effect sizes such as Cohen's *d* and effect sizes for ANOVAs [@cohen1988statistical], and their confidence intervals. However, both require manual input of *F*- or *t*-statistics, *degrees of freedom*, and *Sums of Squares* for the computation the effect sizes, whereas **effectsize** can automatically extract this information from the provided models, thus allowing for better ease-of-use as well as reducing any potential for error.
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- Finally, in **base R**, the function `scale()` can be used to standardize vectors, matrices and data frame, which can be used to standardize data prior to model fitting. The coefficients of a linear model fit on such data are in effect standardized regression coefficients. **effectsize** expands an this, allowing for robust standardization (using the median and the MAD, instead of the mean and SD), post-hoc parameter standardization, and more.
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# Examples of Features
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### Contingency Tables
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Pearson's $\phi$ (`phi()`) and Cramér's *V* (`cramers_v()`) can be used to estimate the strength of association between two categorical variables, while Cohen's *g* (`cohens_g()`) estimates the deviance between paired categorical variables.
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Pearson's $\phi$ (`phi()`) and Cramér's *V* (`cramers_v()`) can be used to estimate the strength of association between two categorical variables [@cramer1946mathematical], while Cohen's *g* (`cohens_g()`) estimates the deviance between paired categorical variables [@cohen1988statistical].
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``` r
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M <- rbind(c(150, 130, 35, 55),
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## Effect Sizes for ANOVAs
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Unlike standardized parameters, the effect sizes reported in the context of ANOVAs (analysis of variance) or ANOVA-like tables represent the amount of variance explained by each of the model's terms, where each term can be represented by one or more parameters. `eta_squared()` can produce such popular effect sizes as Eta-squared ($\eta^2$), its partial version ($\eta^2_p$), as well as the generalized $\eta^2_G$ [@olejnik2003generalized]:
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Unlike standardized parameters, the effect sizes reported in the context of ANOVAs (analysis of variance) or ANOVA-like tables represent the amount of variance explained by each of the model's terms, where each term can be represented by one or more parameters. `eta_squared()` can produce such popular effect sizes as Eta-squared ($\eta^2$), its partial version ($\eta^2_p$), as well as the generalized $\eta^2_G$ [@cohen1988statistical; @olejnik2003generalized]:
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``` r
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#> Chick:Time | Diet:Time | 0.03 | [0.00, 0.00]
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```
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**effectsize** also offers the unbiased estimates of $\epsilon^2_p$ (`epsilon_squared()`) and $\omega^2_p$ (`omega_squared()`). For more details about the various effect size measures and their applications, see the [*Effect sizes for ANOVAs* vignette](https://easystats.github.io/effectsize/articles/anovaES.html).
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**effectsize** also offers $\epsilon^2_p$ (`epsilon_squared()`) and $\omega^2_p$ (`omega_squared()`), which are less biased estimates of the variance explained in the population [@kelley1935unbiased; @olejnik2003generalized]. For more details about the various effect size measures and their applications, see the [*Effect sizes for ANOVAs* vignette](https://easystats.github.io/effectsize/articles/anovaES.html).
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## Effect Size Conversion
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### From Test Statistics
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In many real world applications there are no straightforward ways of obtaining standardized effect sizes. However, it is possible to get approximations of most of the effect size indices (*d*, *r*, $\eta^2_p$...) with the use of test statistics. These conversions are based on the idea that test statistics are a function of effect size and sample size (or more often of degrees of freedom). Thus it is possible to reverse-engineer indices of effect size from test statistics (*F*, *t*, $\chi^2$, and *z*).
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In many real world applications there are no straightforward ways of obtaining standardized effect sizes. However, it is possible to get approximations of most of the effect size indices (*d*, *r*, $\eta^2_p$...) with the use of test statistics [@friedman1982simplified]. These conversions are based on the idea that test statistics are a function of effect size and sample size (or more often of degrees of freedom). Thus it is possible to reverse-engineer indices of effect size from test statistics (*F*, *t*, $\chi^2$, and *z*).
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``` r
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F_to_eta2(f = c(40.72, 33.77),

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