To test whether there is significant difference between the row means as well as column means using R language

 

Aim:- To test whether there is significant difference between the row means as well as column

means.

Problem: The following data represent the number of units of production per day turned out by

different workers using 4 different types of machines.

Test whether the five men differ with respect to mean productivity and test whether the mean

productivity is the same for the four different machine types.

Null Hypothesis (H0)

: There is no significant difference between men and machines.

Alternate Hypothesis (H1)

: There is significant difference between men and machines.

R – Code:-

> data=c(44,38,47,36,46,40,52,43,34,36,44,32,43,38,46,33,38,42,49,39)

>data

[1] 44 38 47 36 46 40 52 43 34 36 44 32 43 38 46 33 38 42 49 39

>workers=gl(5,4)

>workers

[1] 1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4 5 5 5 5

Levels: 1 2 3 4 5

>machine=gl(4,1,20)

>machine

[1] 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

Levels: 1 2 3 4

>Twoway_Anova=aov(data~workers+machine)

>summary(Twoway_Anova)

Df

Sum Sq

Mean Sq

F value

Pr(>F)

workers

4

161.5

40.37

6.574

0.00485 **

machine

3

338.8

112.93

18.388

8.78e-05 ***

Residuals

12

73.7

6.14

>qf(.95, df1=4, df2=12)

[1] 3.259167

>qf(.95, df1=3, df2=12)

[1] 3.490295