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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].
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]:
**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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