Exercise 8.16 on page 554 looks at possible differences in ratings of closeness to a group after doing a physical activity that involves either high or low levels of synchronization (HS or LS) and high or low levels of exertion (HE or LE). Students were randomly assigned to one of four groups with different combinations of these variables, and the change in their ratings of closeness to their group (on a 1 to 7 scale) were recorded. The data are stored in SynchronizedMovement and the means for each treatment group are given below, along with an ANOVA table that indicates a significant difference in the means at a \(5 \%\) level.

\begin{array}{llrr}
Group & N & Mean & StDev \\
HS+HE & 72 & 0.319 & 1.852 \\
HS+LE & 64 & 0.328 & 1.861 \\
LS+HE & 66 & 0.379 & 1.838 \\
LS+LE & 58 & -0.431 & 1.623  \end{array}

Analysis of Variance \begin{array}{lrrrrr}
Source & DF & SS & MS & F-Value & P-Value \\
Group & 3 & 27.04 & 9.012 & 2.77 & 0.042 \\
Error & 256 & 831.52 & 3.248 & & \\
Total & 259 & 858.55 & & &
\end{array}

The first three means look very similar, but the LS+LE group looks quite a bit different from the others. Is that a significant difference? Test this by comparing the mean difference in change in closeness ratings between the synchronized, high exertion activity group (HS+HE) and the nonsynchronized, low exertion activity group (LS+LE).

Data From Exercise 8.16:

A study designed to examine the effect of doing synchronized movements (such as marching in step or doing synchronized dance steps) and the effect of exertion on many different variables, including how close participants feel to others in their group. In the study, high school students in Brazil were randomly assigned to an exercise with either high synchronization (HS) or low synchronization (LS) and also either to high exertion (HE) or low exertion (LE). Thus, there are four groups: HS+HE, HS+LE, \(\mathrm{LS}+\mathrm{HE}\), and LS+LE. Closeness is measured on a 7-point Likert scale (1=least close to \(7=\) most close), and the response variable is the change in how close participants feel to those in their group using the rating after the exercise minus the rating before the exercise. The data are stored in Synchronized Movement and output for an ANOVA test is shown below, along with some summary statistics.

\begin{array}{lrrrrr}
Analysis of Variance & & & \\
Source & DF & SS & MS & F-Value & P-Value \\
Group & 3 & 27.04 & 9.012 & 2.77 & 0.042 \\
Error & 256 & 831.52 & 3.248 & & \\
Total & 259 & 858.55 & & & \\
& & & & & \\
Group & N & Mean & StDev & & \\
HS+HE & 72 & 0.319 & 1.852 & & \\
HS+LE & 64 & 0.328 & 1.861 & & \\
LS+HE & 66 & 0.379 & 1.838 & & \\
LS+LE & 58 & -0.431 & 1.623 & &
\end{array}