We show examples for comparing the magnitude of two
*r*_{rm} values. Correlations are compared using
the cocor package (Diedenhofen and Musch
2015):

R
package

Web
Version

In the first example, we compare *r*_{rm}
values from two distinct, independent datasets. That is, they do not
have the same participants. This is a nonsense example because the two
datasets are from completely different experimental designs that do not
share common measures.

Note the two
*r*_{rm} values are similar in magnitude and
have large overlap in their confidence intervals:
*r*_{rm} = -0.58, 95% CI [-0.74, -0.38] and
*r*_{rm} = -0.40, 95% CI [-0.66, -0.07]. Thus,
they are not significantly different.

```
#1) Run rmcorr on two different datasets
model1.marusich2016_exp2 <- rmcorr(Pair, HVT_capture, MARS, marusich2016_exp2)
#> Warning in rmcorr(Pair, HVT_capture, MARS, marusich2016_exp2): 'Pair' coerced
#> into a factor
model1.marusich2016_exp2
#>
#> Repeated measures correlation
#>
#> r
#> -0.5890471
#>
#> degrees of freedom
#> 55
#>
#> p-value
#> 1.434929e-06
#>
#> 95% confidence interval
#> -0.7365623 -0.3880381
model2.gilden2010 <- rmcorr(sub, rt, acc, gilden2010 )
#> Warning in rmcorr(sub, rt, acc, gilden2010): 'sub' coerced into a factor
model2.gilden2010
#>
#> Repeated measures correlation
#>
#> r
#> -0.406097
#>
#> degrees of freedom
#> 32
#>
#> p-value
#> 0.01716871
#>
#> 95% confidence interval
#> -0.6543958 -0.07874527
#2) Extract relevant parameters
#Model 1
rmcorr1 <- model1.marusich2016_exp2$r
rmcorr1
#> [1] -0.5890471
n1 <- model1.marusich2016_exp2$df + 2 #note the same kludge as power above
n1 #this is the effective sample size
#> [1] 57
#Model 2
rmcorr2 <- model2.gilden2010$r
rmcorr2
#> [1] -0.406097
n2 <- model2.gilden2010$df + 2
n2
#> [1] 34
#3) Compare the two indendent rmcorr coefficients
cocor.indep.groups(rmcorr1, rmcorr2, n1, n2,
var.labels = c(model1.marusich2016_exp2$var[2:3],
model2.gilden2010$vars[2:3]))
#>
#> Results of a comparison of two correlations based on independent groups
#>
#> Comparison between r1.jk (HVT_capture, MARS) = -0.589 and r2.hm (rt, acc) = -0.4061
#> Difference: r1.jk - r2.hm = -0.183
#> Data: j = HVT_capture, k = MARS, h = rt, m = acc
#> Group sizes: n1 = 57, n2 = 34
#> Null hypothesis: r1.jk is equal to r2.hm
#> Alternative hypothesis: r1.jk is not equal to r2.hm (two-sided)
#> Alpha: 0.05
#>
#> fisher1925: Fisher's z (1925)
#> z = -1.0885, p-value = 0.2764
#> Null hypothesis retained
#>
#> zou2007: Zou's (2007) confidence interval
#> 95% confidence interval for r1.jk - r2.hm: -0.5420 0.1365
#> Null hypothesis retained (Interval includes 0)
```