Research Methodology

Lecture 9Farha Hassan

Analysis of Variance (ANOVA)

• Used to compare the means of two or more populations

• It was developed by R. A. Fisher

One Way Anova

Observations A B C

1 5 3 10

2 6 5 13

3 8 2 7

4 1 10 13

5 5 0 17

PROBLEM 1

The following is the sales revenue of three salesmen taken on five occasions. Test at 5% level whether there is any difference between the performances of three salesmen.

Observations A B C

1 5 3 10

2 6 5 13

3 8 2 7

4 1 10 13

5 5 0 17

TOTAL 25 20 60

Reproduce the table with Column Total

SS (Treatment)

Observations

A Ya 2 B Yb 2 C Yc

2

1 5 25 3 9 10 100

2 6 36 5 25 13 169

3 8 64 2 4 7 49

4 1 1 10 100 13 169

5 5 25 0 0 17 289

TOTAL 25 151 20 138 60 776

Reproduce the table with sum of squares

SS (Total)

Find the Correction Factor Y2/N (A + B + C )2 / N

SS (Total) = Ya 2 + Yb 2 + Yc

2 _ Y2/ N

SS (Treatment) = A/ CN + B/ CN + C/ CN - Y2/ N

SS (Error) = SS (Total) - SS (Treatment)

ANOVA TABLE

Sources of Variances

S S D F Mean Computed F Tabulated F

C-1

N-C

N-1

PROBLEM 2

A company has deputed A, B, C and D to four different training programmes. Check whether there is any significant difference between the training programmes of A, B, C, and D at 5% level of significance.

Employees A B C D

1 80 70 65 90

2 90 60 50 89

3 96 55 58 85

4 85 85 55 95

5 70 90 40 80