Aim:- To test whether there is significant difference between the row means (column means).
Problem:
As head of a department of a consumer’s research organization we have the responsibility of testing
and comparing life times of four brands of electric bulbs. Suppose we test the lifetime of three
electric bulbs each of 4 brands, the data is given below, each entry representing the lifetime of an
eclectic bulb, measured in hundreds of hours.
A B C D
38 40 41 39
45 42 49 36
40 38 42 42
Can we infer that the mean lifetime of the four brands of electric bulbs are equal?
Null Hypothesis (H0):
(I.e. Average lifetimes of four different bulbs are same)
Alternate Hypothesis (H1):
(I.e. Average lifetimes of four different bulbs are
different)
R – Code:-
>data
[1] 38 45 40 40 42 38 41 49 42 39 36 42
> brands=c("A","A","A","B","B","B","C","C","C","D","D","D")
>brands
[1] "A" "A" "A" "B" "B" "B" "C" "C" "C" "D" "D" "D"
>One_Way_Anova=aov(data~brands)
>summary(One_Way_Anova)
Df
Sum Sq
Mean Sq
F value
Pr(>F)
brands
3 42
14.00
1.244
0.356
Residuals 8 90
11.25
>qf(.95, df1=3, df2=8)
[1] 4.066181