Problem 1

Using the following summary data, perform a oneway analysis of variance using \(\alpha=.05\). Perform all pairwise contrasts (i.e., group1 vs group2, group2 vs group3, and group1 vs group3). The Bonferroni-corrected alpha should be \(\frac{.05}{3}=.0167\), but you should use \(\alpha_{corrected}=.02\) since that’s the closest value in the book’s table.

\[\begin{equation} \begin{bmatrix} \textbf{n} & \textbf{mean} & \textbf{sd} \\ 20 & 46.87 & 11.6 \\ 20 & 50.92 & 10.33 \\ 20 & 45.82 & 9.18 \\ \end{bmatrix} \end{equation}\]

Problem 2

Using the following summary data, perform a oneway analysis of variance using \(\alpha=.05\). Perform all pairwise contrasts. The Bonferroni-corrected alpha should be \(\frac{.05}{3}=.0167\), but you should use \(\alpha_{corrected}=.02\) since that’s the closest value in the book’s table.

\[\begin{equation} \begin{bmatrix} \textbf{n} & \textbf{mean} & \textbf{sd} \\ 10 & 104.9 & 14.7 \\ 10 & 107.4 & 16.5 \\ 10 & 105.8 & 15.4 \\ \end{bmatrix} \end{equation}\]

Problem 3

Using the following summary data, perform a oneway analysis of variance using \(\alpha=.05\). Perform all pairwise contrasts and a corrected \(\alpha\) of .01 for the contrasts.

\[\begin{equation} \begin{bmatrix} \textbf{n} & \textbf{mean} & \textbf{sd} \\ 15 & 8.8 & 3 \\ 15 & 5.6 & 3.4 \\ 15 & 12.2 & 3.3 \\ 15 & 9.9 & 3.2 \\ \end{bmatrix} \end{equation}\]

Problem 4

Using the following summary data, perform a oneway analysis of variance using \(\alpha=.05\). Perform all pairwise contrasts using the Bonferroni correction to control the familywise error rate.

\[\begin{equation} \begin{bmatrix} \textbf{n} & \textbf{mean} & \textbf{sd} \\ 30 & 22.8 & 3 \\ 30 & 22.3 & 5.6 \\ 30 & 20.2 & 4.9 \\ \end{bmatrix} \end{equation}\]