Question

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, LS+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 output for an ANOVA test is shown below, along with some summary statistics.

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
(a) In both groups with high synchronization (HS), does mean closeness rating go up or down after the synchronized exercise?
(b) In the groups with low synchronization (LS), does mean closeness rating go up or down if the group engages in high exertion (HE) exercise? How about if the group engages in low exertion (LE) exercise?
(c) How many students were included in the analysis?
(d) At a 5% level, what is the conclusion of the test? If there is a difference in means, indicate where the difference is likely to be.
(e) At a 1% level, what is the conclusion of the test?

Answer 1

(a)

In both high synchronization group the mean of the variable is given positive which means that mean closeness rating has gone up after the synchronized excercise.

(b)

In the groups with low synchronization and high exertion the mean is given positive hence the mean closeness rating would go up after the synchronization excercise.

In the groups with low synhronization and low exertion the mean of the given variable is negative and hence the mean closeness rating after the synchronized excercise would go down.

(c)

Since the total degrees of freedom is 259, there would be 260 students in the analysis.

(d)

At 5% or 0.05 significance level the P-value is less than the signifcance level and hence we there must be a difference in the mean of the difference of before and after ratings for these combinations.

(e)

At 1% or 0.01 significance level the p-value is higher than signifcance level. Therefore the evidence indicates that the difference in the ratings after and before the synchronized excercise for all the four combinations is same.