Essential Statistics

Chapter 16: One-Way Analysis of Variance

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Solution:

Based on the display, we would expect the sample means to be

significantly different, as in this illustration. We would also expect the

variation among the sample means (between sample) to be large, relative to

the variation found around the individual sample means (within sample).

Thus one may infer that there would be a significant difference between the

population means.

Figure 16-5:

Samples from normal populations with

significantly different means

These examples provide us with a sense of whether or not there is a

significant difference among the population means. However, they cannot

help us evaluate how likely it is that any observed difference is due to

sampling variations or variations in the sample data. In this chapter, we will

present procedures which will help us determine how likely it is that the

observed differences among the sample means are due to sampling error and

whether this implies that there are significant differences among the

population means. Such procedures belong to a broad group of statistical

methods called

ANalysis Of VAriance (ANOVA)

Section Review