Background Elite athletes have honed their skills over years, but their performance ultimately comes down to a brief win

[answerhappygod]

Background
Elite athletes have honed their skills over years, but their
performance ultimately comes down to a brief window during the
actual competition. As a sports psychologist, you have worked with
elite athletes to manage their stress and anxiety leading up to and
during competition to help them reach their true potential. The
specific interventions you’ve relied on have been individualised to
each athlete, depending on the ‘pain points’ you’ve witnessed
around competitions for that person.
You have become interested in the effectiveness of these
techniques for managing competition stress and anxiety for
non-elite young athletes. You have partnered with the GPS
schools in Brisbane to test the efficacy of three common types of
sports psychology interventions for these budding competitors –
relaxation techniques to help athletes control their
nerves leading up to and during competition, a focusing
intervention to help athletes ignore distractions, and a
positive self-talk intervention teaching athletes
how to enhance motivation (e.g., “I’ve got this!”) to manage the
stress of the competition.
You run an experiment to provide a preliminary test of the
relative effectiveness of these interventions to improve young
athletes’ performance during competition. To enable a single
measure of performance, this particular study includes boys (12 and
under) competing in the 100m freestyle in the GPS swimming
competition, using their competition time (in seconds) as a measure
of performance. Your experiment has four conditions:
Before collecting any data, you formulate three experimental
hypotheses:
The data below represent the time (in seconds) in the 100m
freestyle competition for the 60 young athletes in your experiment.
Athletes were randomly assigned to one of the four experimental
conditions, with n = 15 in each group.
The table below displays each young
athlete’s time by condition:
Control
Relaxation
Focusing
Positive
self-talk
120.59
126.81
109.21
121.58
131.42
115.14
114.91
138.34
115.98
115.46
111.57
134.84
124.32
126.14
112.23
110.78
129.23
130.78
120.48
113.76
124.04
139.80
110.90
119.89
150.49
124.34
116.63
128.29
144.22
117.90
109.36
113.71
117.79
112.68
117.89
140.78
148.32
118.74
118.81
125.24
133.64
114.38
108.89
124.08
119.91
132.88
110.85
125.76
132.29
131.96
123.18
131.04
141.09
136.82
122.77
123.62
123.01
115.57
119.32
136.57
Use these data to address the following question;-
QUESTION
Form an appropriate set of contrast coefficients to test the
three contrasts.
Describe and justify whether these contrasts are orthogonal,
showing the results (including your calculations) of all checks of
orthogonality and your interpretation of the results of each
orthogonality check. You do not need to use a tree
diagram for this.