Understanding Statistics and Experimental Design by Michael H. Herzog & Gregory Francis & Aaron Clarke

Author:Michael H. Herzog & Gregory Francis & Aaron Clarke
Language: eng
Format: epub
ISBN: 9783030034993
Publisher: Springer International Publishing

Just as in the t-test, a criterion is chosen for statistical significance to set the Type I error rate to a desired rate (e.g., α = 0.05). When F exceeds the criterion, we conclude that there is a significant difference (i.e., we reject the null hypothesis of equality between the group means).

The tree example is a one-way ANOVA, where there is one factor (tree location) with three groups (regions) within the factor. The groups are also called levels and the factors are also called ways. There can be as many levels as you wish within a factor, e.g. many more regions, from which to sample trees. A special case is a one-way independent measures ANOVA with two levels, which compares two means as does the t-test. In fact, there is a close relationship between the two tests and in this case it holds that: F = t 2. The p-value here will be the same for the ANOVA and the two-tailed t-test. Hence, the ANOVA is a generalization of the t-test.

As with the t-test, the degrees of freedom play an important role in computing the p-value. For a one-way independent measures ANOVA with k levels, there are two types of degrees of freedom df 1 and df 2, respectively. In general, df 1 = k − 1 and df 2 = n − k where n is the total number of sampled scores pooled over all groups, e.g., all trees in the three groups. The total of the degrees of freedom is df 1 + df 2 = n − 1.

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