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