By: M.A.Yulianto. *)

In this session will be explained about the test procedure used in quantitative data to determine whether there is a difference between the several averages of population. The name of the test is ANOVA (*analysis of variances*) derived based on the calculation that used a technique analyzes data to determine whether we can state that there is a difference between the average of the population we are thorough. In this module will be explained one-factor ANOVA testing.

This test is used when the sample is taken independently for each population. Average and variance of population is not known, for each sample can be calculated its average and variance. On this test assumes that the variable random follow a normal distribution and population variances are equal. If there is a violation of the assumptions, then ANOVA test can be replaced by Kruskal-Wallis test (this test will be discussed in another writing session). So did the normality and variance equality assumptions. The hypotheses of this test are written as follows:

If the decision is to reject the null hypothesis, then ANOVA testing can be followed by multiple comparisons procedures such as LSD and Tukey-Kramer procedures to see an average of the population which is different (this procedure will be discussed in another writing session).

ANOVA table below will explain testing procedure in more detail.

Example:

A company of Apple juice produced a new product. Marketing managers must decide how to market a new product. There are three ways of marketing approaches, namely:

- By emphasizing comfort such as no need of a wide place in the freezer.
- By emphasizing quality such as it tastes good.
- By emphasizing price.

Managers want to know whether the strategy in marketing provides a different level of sales with α = 0.05? Trials are applied in three different cities. Every week the products sold is recorded, and after 20 weeks of data is as follows (in cans):

Conclusion: At least there are two average populations that differ with the 95% level of confidence.

* *

See you in another writing session, have enjoying statistics.

If you have questions can be send to e-mail address: yuliantoyorki@yahoo.com

*) The writer is a lecturer in Institute of Statistics, Jakarta, Indonesia.

** **

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