Page 254 - DMGT209_QUANTITATIVE_TECHNIQUES_II

Unit 13: Test of Significance

One-way ANOVA Notes

Following are the steps followed in ANOVA:
(a) Calculate the variance between samples.
(b) Calculate the variance within samples.
(c) Calculate F ratio using the formula.
F= Variance between the samples / Variance within the sample
(d) Compare the value of F obtained above in (c) with the critical value of F such as 5% level
of significance for the applicable degree of freedom.
(e) When the calculated value of F is less than the table value of F, the difference in sample
means is not significant and a null hypothesis is accepted. On the other hand, when the
calculated value of F is more than the critical value of F, the difference in sample means is
considered as significant and the null hypothesis is rejected.

Example: ANOVA is useful.
(1) To compare the mileage achieved by different brands of automotive fuel.
(2) Compare the first year earnings of graduates of half a dozen top business schools.

Application in Market Research

Consider the following pricing experiment. Three prices are considered for a new toffee box
introduced by Nutrine company. Price of three varieties of toffee boxes are 39, 44 and 49.
The idea is to determine the influence of price levels on sales. Five supermarkets are selected to
exhibit these toffee boxes. The sales are as follows:
Price ( ) 1 2 3 4 5 Total Sample mean x
39 8 12 10 9 11 50 10
44 7 10 6 8 9 40 8
49 4 8 7 9 7 35 7

What the manufacturer wants to know is: (1) Whether the difference among the means is significant?
If the difference is not significant, then the sale must be due to chance. (2) Do the means differ?
(3) Can we conclude that the three samples are drawn from the same population or not?

Two-way ANOVA

The procedure to be followed to calculate variance is the same as it is for the one-way classification.
The example of two-way classification of ANOVA is as follows:

Example: A firm has four types of machines – A , B, C and D. It has put four of its workers
on each machines for a specified period, say one week. At the end of one week, the average
output of each worker on each type of machine was calculated. These data are given below:

Average production by the type of machine
A B C D
Worker 1 25 26 23 28
Worker 2 23 22 24 27
Worker 3 27 30 26 32
Contd...
Worker 4 29 34 27 33

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