Data set: Tennis Repeat
Exercise 3 using Accuracy as the response instead of Speed. Notice that in this study there are several missing values. When a serve hit the net, no distance measurement could be made. Statistical software will account for missing values in the analysis. Thus, the p-values are still appropriate (assuming model assumptions are met) even though this is no longer a balanced design.
In exercise 3
a. Write the null and alternative hypotheses corresponding to the original research questions.
b. To avoid bias, all players used a Wilson K Factor KSix-One Tour 90 racquet (which has a recommended string tension of between 50 and 60 pounds).* In addition, each player used new balls each day and racquets were restrung after each day. Identify any questions or concerns you have about potential sources of bias in this study.
c. Use software to conduct an ANOVA to analyze the Tennis data set using a block design.
d. Create a main effects plot comparing the effects of Player and Racquet. Explain how the p-values correspond to what you see in the main effects plot.
e. The goals of this study did not include determining if there was a difference between the performance of Players. Based on the degrees of freedom, sum of squares, and p- value for Player provided in the ANOVA, do you believe that blocking was helpful in this study?
f. Create a probability plot or histogram of the residuals to determine if the residuals are consistent with data from a normal distribution.
g. State your conclusions for this study. Be sure to clearly identify the population for which these conclusions hold and also state whether causation has been shown.