How report planned contrast test results

Question

I was reading through Andy Field's Discovering Statistics with SPSS. Following ANOVA, he ran several planned contrasts.

When he described how to report the planned contrast results, he wrote this:

“Planned contrasts revealed that having any dose of Viagra significantly increased libido compared to having a placebo, t(12) = 2.47, p =.029, r =.58, but having a high dose did not significantly increase libido compared to having a low dose, t(12) = 2.03, p =.065, r =.51.”

Where did the r come from??

Answer 1

The $r$-value converts the $t$-statistic into an effect size estimate. This is explained in Section 10.8.6 "Effect sizes for two independent means".

t <- 2.47
df <- 12
r <- sqrt(t^2 / (t^2 + df))
r
#> [1] 0.5805597

t <- 2.03
df <- 12
r <- sqrt(t^2 / (t^2 + df))
r
#> [1] 0.5055934
```