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2. Chi-Square Test-Goodness of Fit
A number of marketing problems involve decision situations in which it is important for a marketing manager to know whether the pattern of frequencies that are observed fit well with the expected ones. The appropriate test is the c2 test of goodness of fit. The illustration given below will clarify the role of c2
Problem: In consumer marketing, a common problem that any marketing manager faces is the selection of appropriate colors for package design. Assume that a marketing manager wishes to compare five different colors of package design. He is interested in knowing which of the five is the most preferred one so that it can be introduced in the market. A random sample of 400 consumers reveals the following:
| Package Color |
Preference
by
Consumers |
| Red |
70 |
| Blue |
106 |
| Green |
80 |
| Pink |
70 |
| Orange |
74 |
| Total |
400 |
Do the consumer preferences for package colors show any significant difference?
Solution: If you look at the data, you may be tempted to infer that Blue is the most preferred color. Statistically, you have to find out whether this preference could have arisen due to chance. The appropriate test statistic is the c2 test of goodness of fit.
Null Hypothesis: All colors are equally preferred.
Alternative Hypothesis: They are not equally preferred.
| Package Color |
Observed
Frequencies (O)
|
Expected
Frequencies (E)
|
 |
 |
| Red |
70 |
80 |
100 |
1.250 |
| Blue |
106 |
80 |
676 |
8.450 |
| Green |
80 |
80 |
0 |
0.000 |
| Pink |
70 |
80 |
100 |
1.250 |
| Orange |
74 |
80 |
36 |
0.450 |
| Total |
400 |
400 |
|
11.400 |
Please note that under the null hypothesis of equal preference for all colors being true, the expected frequencies for all the colors will be equal to 80. Applying the formula,
we get the computed value of chi-square ( c2 ) = 11.400.
The critical value of c2 at 5% level of significance for 4 degrees of freedom is 9.488. So, the null hypothesis is rejected. The inference is that all colors are not equally preferred by the consumers. In particular, Blue is the most preferred one. The marketing manager can introduce blue color package in the market.
Next.....Chi-Square Test of Independence
* Prof. P.K. Viswanathan is an Adjunct Professor and Management Consultant based in Chennai, India.
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