Statistics Sunday: Converting Between Effect Sizes for Meta-Analysis


(This article was first published on Deeply Trivial,and kindly contributed to 188bet appR-bloggers)

Converting Between Effect Sizes I'm currently working on mypromised video on mixed effects meta-analysis,and was planning on covering this particular topic in that video – converting betweeneffect sizes.But I decided to do this as a separate post that I can reference in the video,which I hope to post next week.

As a brief refresher,,meta-analysisis aimed at estimating the true effect (or effects) in an area of study by combining findings from multiple studies on that topic.Effect sizes,the most frequently used beingCohen's d,,Pearson's r,andlog odds ratio,根据研究报告和报告中的信息进行估计。There's a lot of variation in how clearly reports and documents describe the findings and the information given to estimate the study's overall effect.但是当你进行荟萃分析时,是否使用固定,随机的,或混合效应分析,you need to use only one type of effect size.也就是说,有时,studies will give you a different type of effect size than you plan to use.Fortunately,there are ways to convert between effect sizes and use different types of statistical information to generate your estimates.

首先,在这些关键效果大小之间转换。在我在研究生院进行的荟萃分析中,I examined the effect of pretrial publicity on guilt.在这项研究中,犯罪经常有两种方式被操作:作为有罪/无罪判决或作为一个持续的犯罪率。For those outcomes,we would likely use,分别log odds ratio and Cohen's d.metafor包中的escalc函数可以计算有罪/无罪计数的对数优势比,科恩的D是犯罪率的平均值和标准差。但是,在展示研究结果时,研究可能会使用不同类型的信息,so you may not be able to simply compute those effect sizes.

例如,a study using verdict may present achi-squareand one of its effect sizes,克莱默的V,which is very similar to a correlation coefficient.How can I convert that into log odds ratio??

要从一种效果大小转换为另一种效果大小,你需要跟着指定的路径,如下图所示。What this diagram tells you is which effect sizes you can convert between directly: you can directly convert between log odds ratio and Cohen's d,and between Cohen's d and Pearson's r.If you wanted to convert between Pearson's r and log odds ratio,you'll first need to convert to Cohen's d.对于方差,您需要做同样的事情——根据本机效果大小度量计算它,然后将其转换为新的效果大小度量。

让我们从设置在我们的效果大小之间转换的函数开始,从科恩的D和对数优势比开始。Then we'll demonstrate with some real data.

#Convert log odds ratio to d
ltod < functionlor) {
d = lor * sqrt3/pi)
VLtoVVD < function虚拟现实) {
vd = 虚拟现实 * 3/pi^2

DTOL < functiond) {
lor = d*(PI)/sqrt3
vdtovl < functionvd) {
虚拟现实 = vd*(PI)^2/3

You'll notice a mathematical symmetry in these equations – the numerators and denominators switch between the equations.现在让我们建立R和D的方程。这些方程稍微复杂一些,需要一些额外的参数。例如,将r的方差转换为d的方差需要r和r本身的方差。从D到R的转换需要组样本大小,称为n1和n2。

#Convert r to d
RTOD < functionr) {
d = 2*r)/sqrt-r^2
vrtovd < functionvr,,r) {
vd = *虚拟现实)/-r^2^3

#Convert d to r
dtor < functionN1,,N2,,d) {
a = (N1)+N2)^2/(N1)*N2)
r = d/sqrt(d^2+a))
vdtovr < functionN1,,N2,,vd,,d) {
a = (N1)+N2)^2/(N1)*N2)
vr = a^2*vd/(d^2+a)^3

Remember that the metafor package can compute effect sizes and variances for you,so you might want to run the escalc on the native effect sizes so that you have the estimates and variances you need to run these functions.But if you ever find yourself having to compute those variances by hand,这是方程式,我们将在下一步中使用。

瓦德 < functionN1,,N2,,d) {
vd = ((N1)+N2)/(N1)*n2)) + (d^2/2*(N1)+N2)))

varr < functionr,,n) {
vr = -r^2^2/(n)-

varlor < functiona,,,,c,,d) {
虚拟现实 = /a)+/b)+/c)+/d)

One of the studies I included in my meta-analysis gave Cramer's V.样本大小为42,每组21人。I'd like to convert that effect size to log odds ratio.我可以这样做。

克拉梅夫 < 零点六七
studyd < RTOD(克拉梅罗)
studyvr < varr零点六七,,四十二
学习VD < vrtovd(studyvr,cramerv)
## [1] 0.5824038

I can now include this study in my meta-analysis of log odds ratios.

如果我的研究给出了不同的信息呢?例如,它可能给了我一个卡方或者一个T值。This在线效果大小计算器,created by David Wilson,coauthor of实用元分析,可以从许多不同类型的信息中为您计算效果大小。In fact,spoiler alert: I used an earlier version of this calculator extensively for my meta-analysis.注意,这个计算器返回优势比,so you'll need to convert those values into a log odds ratio.

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