To examine development in the pedagogical content knowledge (PCK) of new teachers, 12 novice teachers are measured on their PCK at the beginning of their teaching career, at the end of the first semester, and at the end of the first school year. The scale that measures PCK ranges from 0 to 45, with higher scores reflecting greater levels of PCK. The data are shown below. Conduct a one-factor repeated measures ANOVA to determine the mean differences across time, using $\alpha$ = .05. Use the Bonferroni method to detect exactly where the differences are among the time points (if they are different).

$\begin{array}{|c|c|c|c|}
\hline \text { Subject } & \text { Time 1 } & \text { Time 2 } & \text { Time } 3 \
\hline 1 & 16 & 17 & 28 \
\hline 2 & 17 & 23 & 32 \
\hline 3 & 11 & 21 & 30 \
\hline 4 & 15 & 23 & 35 \
\hline 5 & 21 & 32 & 40 \
\hline 6 & 14 & 22 & 31 \
\hline 7 & 12 & 19 & 31 \
\hline 8 & 17 & 21 & 25 \
\hline 9 & 11 & 16 & 24 \
\hline 10 & 8 & 14 & 20 \
\hline 11 & 14 & 24 & 28 \
\hline 12 & 12 & 19 & 25 \
\hline
\end{array}$

Question

To examine development in the pedagogical content knowledge (PCK) of new teachers, 12 novice teachers are measured on their PCK at the beginning of their teaching career, at the end of the first semester, and at the end of the first school year. The scale that measures PCK ranges from 0 to 45, with higher scores reflecting greater levels of PCK. The data are shown below. Conduct a one-factor repeated measures ANOVA to determine the mean differences across time, using $\alpha$ = .05. Use the Bonferroni method to detect exactly where the differences are among the time points (if they are different).

$\begin{array}{|c|c|c|c|}
\hline \text { Subject } & \text { Time 1 } & \text { Time 2 } & \text { Time } 3 \
\hline 1 & 16 & 17 & 28 \
\hline 2 & 17 & 23 & 32 \
\hline 3 & 11 & 21 & 30 \
\hline 4 & 15 & 23 & 35 \
\hline 5 & 21 & 32 & 40 \
\hline 6 & 14 & 22 & 31 \
\hline 7 & 12 & 19 & 31 \
\hline 8 & 17 & 21 & 25 \
\hline 9 & 11 & 16 & 24 \
\hline 10 & 8 & 14 & 20 \
\hline 11 & 14 & 24 & 28 \
\hline 12 & 12 & 19 & 25 \
\hline
\end{array}$

Quizplus · Accepted Answer

The Answer is Procedure:
Create a data set with three variables: Time 1, Time 2, and Time 3. The data set should have 12 cases, representing 12 teachers.

1. Go to Analyze

ightarrow

General Linear Model

ightarrow

Repeated Measures.
"2. For Within-Subject Factor Name, enter ""Time.""
For Number of Levels, enter 3 (i.e., 3 time points). Click Add.
For Measure Name, enter ""PCK."" Click Add."
3. Click Define. Move Time1 through Time3 in the left box to Within-Subjects Variables (Time).
4. Click Options. Move "Time" to Display Means for. Select Compare main effects. Select Bonferroni under Confidence interval adjustment. Select Descriptive statistics, Estimates of effect size, and Observed power. Click Continue.
5. To get profile plots, click Plots. Move "Time" to the box under Horizontal Axis. Click Add. Click Continue.
"6. Click OK.
Selected SPSS Output:
$Procedure: Create a data set with three variables: Time 1, Time 2, and Time 3. The data set should have 12 cases, representing 12 teachers. 1. Go to Analyze ightarrow General Linear Model ightarrow Repeated Measures. 2. For Within-Subject Factor Name, enter Time. For Number of Levels, enter 3 (i.e., 3 time points). Click Add. For Measure Name, enter PCK. Click Add. 3. Click Define. Move Time1 through Time3 in the left box to Within-Subjects Variables (Time). 4. Click Options. Move Time to Display Means for. Select Compare main effects. Select Bonferroni under Confidence interval adjustment. Select Descriptive statistics, Estimates of effect size, and Observed power. Click Continue. 5. To get profile plots, click Plots. Move Time to the box under Horizontal Axis. Click Add. Click Continue. 6. Click OK. Selected SPSS Output: Pairwise Comparisons: Bonferroni Method Measure: PCK \begin{array}{r} \hline95 \% ext { Confidence Interval for }\ ext { Difference } \quad\quad\quad\quad \ \begin{array}{ccccccc} \hline ext {(I) }& ext {(J) }& ext {Mean}& ext { Std}\ ext { Time}& ext { Time }& ext { Difference (I-J)}& ext { Error}& ext { Sig }& ext { Lower Bound }& ext { Upper Bound }\ \hline {1} & 2 & -6.917^{*} & .811 & .000 & -9.205 & -4.628 \ & 3 & -15.083^{*} & 1.076 & .000 & -18.119 & -12.048 \ \hline {2} & 1 & 6.917^{*} & .811 & .000 & 4.628 & 9.205 \ & 3 & -8.167^{*} & .796 & .000 & -10.412 & -5.922 \ \hline {3} & 1 & 15.083^{*} & 1.076 & .000 & 12.048 & 18.119 \ & 2 & 8.167^{*} & .796 & .000 & 5.922 & 10.412 \ \hline \end{array}\end{array} The results of the test of sphericity give no evidence against the assumption of sphericity (Mauchly's W = .825, \chi 2 = 1.925, df = 2, p = .382). Based on the results of the one-factor repeated measures ANOVA, the effect of the within-subjects factor, Time, is significant at the .05 level (F2,22 = 139.556, p < .001) with large effect size (partial \eta 2 = .927) and maximum observed power, implying that the novice teachers' average level of PCK has changed significantly across three time points. Results of MCP, using the Bonferroni method, reveal significant differences among all pairs of time points. Specifically, the level of PCK increased significantly from Time 1 (i.e., the beginning of the school year) to Time 2 (i.e., the end of the first semester), from Time 2 to Time 3 (i.e., the end of the school year), and from Time 1 to Time 3. The results therefore suggest that the novice teachers' pedagogical content knowledge increases substantially in their first two semesters of teaching.$

Pairwise Comparisons: Bonferroni Method
Measure: PCK

\begin{array}{r}\hline95 \% ext { Confidence Interval for }\ ext { Difference } \quad\quad\quad\quad \\begin{array}{ccccccc}\hline ext {(I) }& ext {(J) }& ext {Mean}& ext { Std}\ ext { Time}& ext { Time }& ext { Difference (I-J)}& ext { Error}& ext { Sig }& ext { Lower Bound }& ext { Upper Bound }\\hline {1} & 2 & -6.917^{*} & .811 & .000 & -9.205 & -4.628 \& 3 & -15.083^{*} & 1.076 & .000 & -18.119 & -12.048 \\hline {2} & 1 & 6.917^{*} & .811 & .000 & 4.628 & 9.205 \& 3 & -8.167^{*} & .796 & .000 & -10.412 & -5.922 \\hline {3} & 1 & 15.083^{*} & 1.076 & .000 & 12.048 & 18.119 \& 2 & 8.167^{*} & .796 & .000 & 5.922 & 10.412 \\hline\end{array}\end{array}

The results of the test of sphericity give no evidence against the assumption of sphericity (Mauchly's W = .825,

\chi

²= 1.925, df = 2, p = .382).
Based on the results of the one-factor repeated measures ANOVA, the effect of the within-subjects factor, Time, is significant at the .05 level (F₂_,₂₂ = 139.556, p < .001) with large effect size (partial

\eta

²= .927) and maximum observed power, implying that the novice teachers' average level of PCK has changed significantly across three time points.

Results of MCP, using the Bonferroni method, reveal significant differences among all pairs of time points. Specifically, the level of PCK increased significantly from Time 1 (i.e., the beginning of the school year) to Time 2 (i.e., the end of the first semester), from Time 2 to Time 3 (i.e., the end of the school year), and from Time 1 to Time 3. The results therefore suggest that the novice teachers' pedagogical content knowledge increases substantially in their first two semesters of teaching."

To Examine Development in the Pedagogical Content Knowledge (PCK) of New