1

I am working in R. I am doing some simulations of sample sizes by drawing random samples from two normal distributions.

I am calculating Cohen's $d$ effect size with:

library(esc)

esc_mean_sd(grp1m = ..., grp1sd = ..., grp1n = ..., # mean, sd, n of group CONTROL
            grp2m = ..., grp2sd = ..., grp2n = ..., # mean, sd, n of group TEST
            es.type = "d")

Note: from package documentation https://cran.r-project.org/web/packages/esc/esc.pdf: $d$ is standardized mean difference effect size $d$. From the function's source code: (grp1m - grp2m)/sd_pooled.

Then I am calculating sample size with: 

library(pwr)

pwr.t.test(n=NULL, d=..., sig.level=0.05, power=0.8)

It happens that I get the following error:

Error in uniroot(function(n) eval(p.body) - power, c(2 + 1e-10, 1e+09)) :    f() values at end points not of opposite sign

By trial and error, I found it throws the error when $d > 5.65348...$ Anything below is fine. I also noticed sample size at this effect size (and sig.level=0.05, power=0.8) is exactly $2$.

My current solution is to artificially bring down to $5.6$ any effect size higher than that, and report $2$ as sample size. Is $2$ the theoretical smallest sample size anyway? Is this an accurate fix?

Reproducible example

library(esc)
library(pwr)

Case1: $d=2$: does not throw an error

ESC <- esc_mean_sd(grp1m = 3, grp1sd = 1, grp1n = 20,
                   grp2m = 1, grp2sd = 1, grp2n = 20,
                   es.type = "d")

pwr.t.test(n=NULL, d=ESC$es, sig.level=0.05, power=0.8)

Case2: $d=6$: throws an error

ESC <- esc_mean_sd(grp1m = 7, grp1sd = 1, grp1n = 20,
                   grp2m = 1, grp2sd = 1, grp2n = 20,
                   es.type = "d")

pwr.t.test(n=NULL, d=ESC$es, sig.level=0.05, power=0.8)
kjetil b halvorsen
  • 63,378
  • 26
  • 142
  • 467
francoiskroll
  • 427
  • 1
  • 4
  • 12
  • 1
    Because there are great many different forms of Cohen's *d,* it is essential that you explain exactly *which* one this software is computing. In general there are mathematical bounds and they depend on the formula and the data counts. – whuber Mar 31 '20 at 13:00
  • I see. "*standardized mean difference effect size d*" from https://cran.r-project.org/web/packages/esc/esc.pdf. From source code of the function: `(grp1m - grp2m)/sd_pooled`. – francoiskroll Mar 31 '20 at 13:27
  • If readers must read source code in order to understand your question, it is unlikely you will get any answers. Please make the essential information plain within your post. – whuber Mar 31 '20 at 13:30
  • Sure. My question could be better formulated anyway. I am not directly asking about the mathematics behind the effect size, more how I should go about calculating sample sizes when $d > 5.6$. – francoiskroll Mar 31 '20 at 13:33
  • 1
    That's a very different question! In any conceivable situation (except, perhaps, for a finite population) there will be a sample size associated with any effect size. Indeed, the larger the effect size, the smaller the sample that will be needed to detect it. – whuber Mar 31 '20 at 13:38
  • That makes sense. Maybe I should think about the problem from the other end, is $2$ the theoretical minimum sample size? – francoiskroll Mar 31 '20 at 13:43
  • 1
    That's an interesting question. Its answer depends on how you plan to test the data. (That is, in part, why there are so many different formulas for Cohen's *d*.) For instance, in some cases a sample size of $1$ will work: see https://stats.stackexchange.com/a/1836/919. – whuber Mar 31 '20 at 13:47

0 Answers0