Question

A researcher obtains a random sample of NCSS division 1 men's basketball game data giving player position (center, power forward, small forward, shooting guard, and point guard) as well as the number of fouls in the game for that player. The researcher plans to use ANOVA to answer, "Is there an association between player position and the number of fouls committed in the game?"
a. What conditions need to be checked in to use ANOVA?

Answer 1

One way ANOVA here is used to check the assumption that whether 5 group means are same or not

k=5

k=enter, power forward, small forward, shooting guard, and point guard

Conditions:

(1)Each of the k populations normally distributed or not

(2)The variances of the populations are all equal

(3)The sample are independently drawn

For assumption(1) check with normal probability plot ,if the points fall on straight line then that particular sample follows normal distibution

For(2) Check with residual plot ..there should be no pattern seen .If there is no pattern,Homoscedasticity assumption is satisfied.

Also check levene test or bartlett's test to check this assumption.

if we get p>0.05

Do not reject Ho and conclude that the 5 group variances are same.