Question

A volleyball coach noted that players who practiced jumping during practice time seemed to be able to jump higher in games. For 6 weeks prior to the start of the season he randomly divided his team into three groups of 10 players each. Group 1 practiced regularly without any special jumping or weight training, group 2 spent at least 20 minutes per practice jumping and group 3 spent at least 20 minutes per practice weight training. Determine if there are significant effects of the treatments. The obtained statistic: 5.55

What type of test should you use?

b. Please provide, in words, the null and alternative hypotheses.

c. Using an alpha level of .05 identify the critical value(s).

d. Using the above test statistic, alpha level and critical value(s) what is your statistical decision?

e. State your conclusion regarding the results from this test in language that a friend of yours with no knowledge of statistics could understand

Answer 1

Three groups are
Group-I : practiced regularly without any special jumping or weight training
Group-II : spent at least 20 minutes per practice jumping
Group-III : spent at least 20 minutes per practice weight training.
[Basically, the three groups are three treatments.]

Each group has 10 players i.e. n(Group-I)=n(Group-II)=n(Group-III)=10
Total number of observations(N)=10+10+10=30
The obtained (calculated) statistic is F0, F0=5.55.

One-way anova:

• The one-way analysis of variance (ANOVA) is used to determine whether there are any statistically significant differences between the means of two or more independent (unrelated) groups.
• The one-way ANOVA test statistic cannot tell which specific groups are statistically significantly different from each other; it only tells you that at least two groups were different.

TYPE OF TEST TO BE USED
Here, one-way ANOVA-Analysis of Varinace technique should be used.The test statistic is F-tat, so the test is F-test.

b.
Null Hypotheis-H0: There are no significant effects of the treatments.
Alternatively, H0 can be written as:
H0: mu1=mu2=mu3 (All treatment(group) means are equal)

Similarly,
Alternative Hypotheis-H1: There are significant effects of the treatments.
H1: at least two mui's is different from the others (At least two treatments are different)

c.
# df=degrees of freedom, k=number of treatments (groups)=3
df(Treatment)=k-1=3-1=2
df(Error)=N-k=30-3=27
df(Total)=N-1=30-1=29
# df(Treatment)+df(Error)=df(Total)
# Critical value(Fc) is the value such that P(F>Fc)=alpha, where F ~ F(df(Treatment),df(Error)) distribution.
Critical value of F is obtained using R-Software as:
alpha=0.05
qf(1-alpha,2,27)
[1] 3.354131

d.
calcualted value of test statistic(5.55) is greater than critical value(3.35), we Reject H0. and hence conclude that There are significant effects of the treatments.

e.
Players are able to jump higher when alongwith regular practise, they also do practise either special jumping or weight training. That is, special jumping and/or weight training help jump higher rather than regular exercise only.