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Even more refs!
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mattansb committed Dec 10, 2020
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30 changes: 30 additions & 0 deletions paper/paper.bib
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Expand Up @@ -149,4 +149,34 @@ @article{bollen1989structural
author={Bollen, Kenneth A},
journal={New York},
year={1989}
}

@book{cramer1946mathematical,
title={Mathematical Methods of Statistics},
author={Cram{\'e}r, Harald},
year={1946},
publisher={Princeton: Princeton University Press}
}

@article{kelley1935unbiased,
title={An unbiased correlation ratio measure},
author={Kelley, Truman L},
journal={Proceedings of the National Academy of Sciences of the United States of America},
volume={21},
number={9},
pages={554},
year={1935},
publisher={National Academy of Sciences}
}


@article{friedman1982simplified,
title={Simplified determinations of statistical power, magnitude of effect and research sample sizes},
author={Friedman, Herbert},
journal={Educational and Psychological Measurement},
volume={42},
number={2},
pages={521--526},
year={1982},
publisher={Sage Publications Sage CA: Thousand Oaks, CA}
}
10 changes: 5 additions & 5 deletions paper/paper.md
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Expand Up @@ -42,7 +42,7 @@ In both theoretical and applied research, it is often of interest to assess the
**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.:

- **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).
- 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.
- 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.
- 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.

# Examples of Features
Expand All @@ -67,7 +67,7 @@ cohens_d(mpg ~ am, data = mtcars)

### Contingency Tables

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.
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].

``` r
M <- rbind(c(150, 130, 35, 55),
Expand Down Expand Up @@ -129,7 +129,7 @@ standardize_parameters(model, exponentiate = TRUE)

## Effect Sizes for ANOVAs

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]:
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]:


``` r
Expand Down Expand Up @@ -158,13 +158,13 @@ eta_squared(model, generalized = "Time")
#> Chick:Time | Diet:Time | 0.03 | [0.00, 0.00]
```

**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).
**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).

## Effect Size Conversion

### From Test Statistics

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*).
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*).

``` r
F_to_eta2(f = c(40.72, 33.77),
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