Questions: A researcher obtains t(20)=2.00 and MD=9 for a repeated-measures study. If the researcher measures effect size using the percentage of variance accounted for, what value will be obtained for r^2 ? 4 / 13 9/20 4/24 9/29

Solution Steps

To find the value of $r^2$, which represents the percentage of variance accounted for, we use the formula for $r^2$ in the context of a t-test:

$$r^2 = \frac{t^2}{t^2 + df}$$

where $t$ is the t-value and $df$ is the degrees of freedom. In this case, $t = 2.00$ and $df = 20$.

First, we calculate $t^2$: $$t^2 = (2.00)^2 = 4.00$$

Next, we compute $t^2 + df$: $$t^2 + df = 4.00 + 20 = 24.00$$

Now, we can find $r^2$ using the formula: $$r^2 = \frac{t^2}{t^2 + df} = \frac{4.00}{24.00} = \frac{1}{6} \approx 0.1667$$

Final Answer