One way anova examples
Following our manufacturing example, groups of products are independent if the selection of products for one group does not have any bearing on the selection of products for another group. (Note, then, that the samples need not necessarily have the same variance, although they should be similar if they are chosen properly.) Furthermore, proper use of ANOVA assumes that the samples are independent. Thus, careful consideration of the problem is always required (both for ANOVA and for Student's t-tests) to avoid blind (and erroneous) use of hypothesis testing.Īs with the Student's t-tests, one-way ANOVA assumes that the data are normally distributed and that the data groups have equivalent population variances. If these assumptions do not apply in a given situation, the analysis will be flawed. Although a thorough derivation of this test statistic is beyond the scope of this article, we have developed a sufficient foundation in statistics to facilitate a basic understanding of the statistic.Īs with the Student's t-tests that we studied in the preceding two articles, one-way ANOVA is based on several assumptions. One-way ANOVA differs from the Student's t-test primarily in the test statistic, which involves calculation of variances between and among the groups (or samples) under test. Thus, one-way ANOVA adds another tool to our statistical toolbox that we have developed. Using one-way ANOVA, however, the company could compare quality for any number of product groups. (In this case, the "factor" is product quality.) Such a comparison would be impossible using t-tests, which only allow examination of two groups (or products, in this case).
For instance, a manufacturing company might wish to compare the quality of several groups of products on the basis of a certain setting on a given machine.
Our study of ANOVA will be limited to so-called one-way ANOVA, which involves comparison of samples on the basis of only one factor (just as t-tests only involved one factor).