Use one-way ANOVA to determine whether there are statistically significant differences among the means of several populations. The null hypothesis for the test is that all population means (level means) are the same. The alternative hypothesis is that one or more population means differ from the others.

A one-way analysis of variance requires the following:

·    a response, or measurement taken from the units sampled.

·    a factor, or discrete variable that is altered systematically. The different values chosen for the factor variable are called levels of the factor. Each level of the factor in the analysis corresponds to a larger population with its own mean. The sample mean is an estimate of the level mean for the whole population.

In addition to helping you evaluate whether all the level means are the same, Minitab also provides output to help you determine which level means are different when differences exist.

Investigators compared the hardness of four different blends of paint. Six samples of each paint blend were applied to a small piece of metal, then cured, and measured for hardness.

Data: PaintHardness.MTW (available in the Sample Data folder).