what is the conceptual difference between independent sample 't' test statistic and cohen's d?
thanks in advance
The practical difference between Cohen's d and t is that for a given difference in means and pooled variance, t will vary with different sample sizes, but Cohen's d will not.
Cohen's d is the difference in means relative to the pooled variance, regardless of sample size, and so is an effect size.
The following is a table of results from t-tests and Cohen's d, for two samples (mean = 0, sd = 1; and mean = - 0.5 and sd =1) for a range of sample sizes. You can see that t and p change with sample size, while Cohen's d does not. R code below.
### Sample.size t p Cohen.d
### 10 1.4 0.17 0.64
### 20 2.1 0.04 0.66
### 50 3.3 0.001 0.67
### 100 4.7 < 0.0001 0.67
### 500 10.6 < 0.0001 0.67
####################################3
set.seed(45)
if(!require(lsr)){install.packages("lsr")}
Sample.size = 10
A = rep(rnorm(10), Sample.size/10)
B = A - 0.5
t.test(A,B, var.equal=TRUE)
library(lsr)
cohensD(A,B)
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