Question

4) While reading a journal article, you come across the results of an ANOVA, reported as F(3,32) = 4.61. Having read earlier that the groups were of equal size, and independent: (2 points each) a) How many groups were there, and why? b) How many observations were there per group, and why? c) How many observations were there in total, and why? d) Based on the reported statistic, what would you conclude about the groups, and why?

Answer 1

Solution

a)Number of groups are 4 because

Here F(3,32) , 3 indicates degrees of freedom for group so it is given by = Total number of group – 1 = 4- 1 =3

So Number of groups are 4

c) Observations were there in total are 36

Because total degrees of freedom are n-1

degrees of freedom = degrees of freedom group + degrees of freedom error

degrees of freedom = 3+32 = 35

so

n-1 = 35

n = 36

b)since groups are equal in size

so

there are total 4 groups so

n/4 = 36/4 = 9

Number of observations are 9

d) The p-value is .008618

As p-value < 0.05 level of significance so we conclude that all groups do not equal mean