Using the following data, perform a oneway analysis of variance using \(\alpha=.05\). Write up the results in APA format.
\[\begin{equation} \begin{bmatrix} \textbf{Group1} \\ 51 \\ 45 \\ 33 \\ 45 \\ 67 \end{bmatrix} \begin{bmatrix} \textbf{Group2} \\ 23 \\ 43 \\ 23 \\ 43 \\ 45 \end{bmatrix} \begin{bmatrix} \textbf{Group3} \\ 56 \\ 76 \\ 74 \\ 87 \\ 56 \end{bmatrix} \end{equation}\]Using the following summary data, perform a oneway analysis of variance using \(\alpha=.01\).
\[\begin{equation} \begin{bmatrix} \textbf{n} & \textbf{mean} & \textbf{sd} \\ 30 & 50.26 & 10.45 \\ 30 & 45.32 & 12.76 \\ 30 & 53.67 & 11.47 \\ \end{bmatrix} \end{equation}\]A clinical psychologist has run a between-subjects experiment comparing two treatments for depression (cognitive-behavioral therapy (CBT) and client-centered therapy (CCT) against a control condition. Subjects were randomly assigned to the experimental condition. After 12 weeks, the subject’s depression scores were measured using the CESD depression scale. The data are summarized as follows:
\[\begin{equation} \begin{bmatrix} & \textbf{n} & \textbf{mean} & \textbf{sd} \\ \textbf{control} & 40 & 21.4 & 4.5 \\ \textbf{CBT} & 40 & 16.9 & 5.5 \\ \textbf{CCT} & 40 & 19.1 & 5.8 \\ \end{bmatrix} \end{equation}\]Use a oneway ANOVA with \(\alpha=.01\) for the test.
An education researcher is comparing four different algebra curricula. Eighth grade students are randomly assigned to one one of the four groups. Their state achievement test scores are compared at the end of the year. Use the appropriate statistical procedure to determine whether the curricula differ with respect to math achievement. An alpha criterion of .05 should be used for the test.
\[\begin{equation} \begin{bmatrix} & \textbf{n} & \textbf{mean} & \textbf{sd} \\ \textbf{curriculum 1} & 50 & 170.5 & 14.5 \\ \textbf{curriculum 2} & 50 & 168.3 & 12.8 \\ \textbf{curriculum 3} & 50 & 167.6 & 17.7 \\ \textbf{curriculum 4} & 50 & 172.8 & 16.8 \\ \end{bmatrix} \end{equation}\]