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Chapter 16: One-Way Analysis of Variance
example, one will not be certain if the probability of a Type I error will
remain fix for the overall comparisons of the means. As a matter of fact, for
a series of pairwise comparisons, the level of significance will accumulate
and can be quite large. There is a way to overcome this issue since ANOVA
allows the researcher to compare all of the population means in a single
hypothesis test using a single level of significance (
) and thereby keeping
the probability of a Type I error in check
no matter how many
population
means are being compared
16-2 Comparing Population Means Graphically
The objective in comparing several population means is to determine
whether there is a statistical significant difference between them. So when
random samples are obtained from these populations, the respective sample
means can be computed to help determine whether there is a significant
difference between the population means. If the samples are truly random
and the sample means are very different, then it is likely that the true or
population means will be different. The question is: “How large a difference
is needed between a sample mean and the corresponding population mean to
conclude that there is a statistical significant difference between these
population means?” Also, we need to determine whether the differences are
due to random variations in the sample data or if there really are differences
between the population means.
One simple way of analyzing the differences of population means is to
display the data through box plots and to study them for any differences.
Example 16-1:
A random sample of undergraduate students on a college
campus was asked to record their classification and the number of credit
hours in which they were enrolled. The summary information is shown in
Table 16-1
.