ANOVA

1) Test if there is a difference between the true average number of plate appearances by different salary tiers (where players making at least 10 million dollars per year are in one tier, those making at least 1 million dollars per year but less than 10 million dollars per year another, and those making less than 1 million dollars per year are in the bottom tier).

Hypotheses

Assumption Check

The samples are categorized in only one way and are independent. We should check to see if they have similar variances and distributions that are approximately normal to see if our assumptions hold. (Those these last requirements only need to be loosely met.) Comment by Dr. Ryan Sides: This is not done for you here, but as this was part of previous assignments, make sure you check this and show whether or not your assumptions truly hold.

Decision Rule

If the p-value is less than the pre-determined alpha of 0.05, we will reject the null hypothesis.

Descriptive Statistics

p-value

Decision

Because the p-value of 0.0132 is less than a pre-determined alpha of 0.05, we reject the null hypothesis.

Conclusion

We can conclude that at least one population mean number of plate appearances is different by salary tier when considering MLB players in 2008 who had at least 200 plate appearances.

Pairwise Comparisons

Of the three pairwise comparisons that can be made among the groups, we show statistical significance between both the filthy rice and not as rich players as well as the filthy rich and very rich players. Thus, it can be concluded that the filthy rich players actually have an average number of plate appearances different from the other two groups.

2) Test if there is a difference between the actual mean number of home runs hit by players in different speed categories (where players with at least 20 stolen bases are in one category, those with at least 10 stolen bases but less than 20 another, those with at least 5 stolen bases but less than 10 another, and those with less than 5 stolen bases are in the bottom category).

Hypotheses

Assumption Check

The samples are categorized in only one way and are independent. We should check to see if they have similar variances and distributions that are approximately normal to see if our assumptions hold, those these last requirements only need to be loosely met.

Decision Rule

If the p-value is less than the pre-determined alpha of 0.05, we will reject the null hypothesis.

Descriptive Statistics

p-value

Decision

Because the p-value of 0.374 is greater than a pre-determined alpha of 0.05, we fail to reject the null hypothesis.

Conclusion

We cannot conclude that at least one population mean number of home runs hit is different by speed category when considering MLB players in 2008 who had at least 200 plate appearances.

Code: