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README.Rmd
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---
output: github_document
bibliography: "inst/REFERENCES.bib"
csl: "inst/apa-6th.csl"
---
# Cohen's $d_p$ library: Getting the Cohen's $d_p$ and its confidence interval in any design
<!-- badges: start -->
[](https://cran.r-project.org/package=CohensdpLibrary)
<!-- badges: end -->
This library computes the Cohen's $d_p$ and its confidence intervals in any experimental design. In the past,
researchers developed distinct versions of standardized mean difference for between and within-subject design.
The consequence is that these various estimators could not be compared between each others and more importantly,
across experimental design. @L0003-1 noted the existence of two different measures in within-subject design,
and @w16 noted the existence of at least 5 difference sorts of standardized mean difference. He concluded by
making this very important point: all these estimators ARE NOT Cohen's d measures.
The measure that J. Cohen [@c69] created is obtained from the mean difference standardized using the pooled
standard deviation. Hence, measures such as $d_a_v$, $d_z$, $d_a$, etc. are not Cohen's d and **more importantly**,
they cannot be compared! They all return different values because they measure different things. They are not just
different, they can be markedly different. As an example, a $d_z$, given the means and standard deviations,
can be _smaller_ **or** _larger_ than the Cohen's $d$ depending on the amount of correlation across the pairs
of data.
This whole mess implies lack of comparability and confusion as to what statistics was actually reported. For that
reason, I chose to call the true Cohen's $d$ with a distinct subscript $p$, as in $d_p$ so that (i) we clearly see the
difference (the reader is not left guessing what $d$ represents); (ii) is is clear that the pooled standard
deviation and only this statistic was used to standardized the mean difference. Further, by advocating a unique
statistic for standardized mean difference, it allows for comparisons across studies, whether they used within-subject
or between-subject design.
```{r, echo = FALSE, message = FALSE, results = 'hide', warning = FALSE}
cat("this will be hidden; use for general initializations.\n")
library(CohensdpLibrary)
options("CohensdpLibrary.SHOWWARNINGS" = FALSE) # shut down all messages
```
## Why this package?
`MBESS` is an excellent package which already computes standardized mean difference and returns confidence
intervals [@k22]. However, it does not compute confidence intervals in within-subject design directly. The
Algina and Keselman approximate method can be implemented within MBESS with some programming [@CG057-1].
This package, on the other hand, can be used with any experimental design. It only requires an argument
`design` which specifies the type of experimental design.
The confidence interval in within-subect design was unknown until recently. In recent work [@c22a;@c22b],
its exact expression was found when the population correlation is know and an approximation was
proposed when the sample correlation is known, but not the population correlation.
# Using ``CohensdpLibrary``
You can install this library on you computer from CRAN (note the uppercase C and uppercase L)
```{r, echo = TRUE, eval = FALSE}
install.packages("CohensdpLibrary")
```
or if the library devtools is installed with:
```{r, echo = TRUE, eval = FALSE}
devtools::install_github("dcousin3/CohensdpLibrary")
```
and before using it:
```{r, echo = TRUE}
library(CohensdpLibrary)
```
The main function is ``Cohensdp``, which returns the Cohen's $d_p$ and its
confidence intervals under various designs. For example, this returns the
triplet (lower 95% confidence interval bound, $d_p$, upper 95% confidence interval
bound) given the sample means, the sample standard deviations, and the correlation
```{r}
Cohensdp( statistics = list(m1=76, m2=72, n=20, s1=14.8, s2=18.8, r=0.2),
design = "within",
method = "adjustedlambdaprime"
)
```
You get a more readable output with ``summarize``, e.g.,
```{r}
summarize(Cohensdp( statistics = list(m1=76, m2=72, n=20, s1=14.8, s2=18.8, r=0.2),
design = "within",
method = "adjustedlambdaprime"
))
```
The design can be replaced with ``between`` for a between-subject design:
```{r}
summarize(Cohensdp( statistics = list(m1=76, m2=72, n1=10, n2=10, s1=14.8, s2=18.8),
design = "between")
)
```
(the statistic ``r`` is removed as there is no correlation in between-group design, and ``n`` is
provided separately for each group, ``n1`` and ``n2``).
Finally, it is also possible to get a Cohen's $d_p$ from a single group as long as you have an
hypothetical mean ``m0`` to compare the sample mean to, e.g.,
```{r}
summarize(Cohensdp( statistics = list(m=76, m0=72, n=20, s=14.8),
design = "single")
)
```
Replace ``summarize`` with ``explain`` for additional information on the result.
Check the web site [https://github.com/dcousin3/CohensdpLibrary](https://github.com/dcousin3/CohensdpLibrary) for more.
also, ``help(CohensdpLibrary)`` will get you started.
# References
\insertAllCited{}