Using an ANOVA, we can simultaneously consider the effects of red, green, and blue light on 24 amplitude measurements and answer the question of whether color of light has an effect in general. (click to see data). In this example, the null hypothesis is that there is no difference among the mean responses for the three colors.
Table 16. Analysis of variance comparing effect of three colors of light on a roach eye
|
Source |
Degrees of freedom |
Sum of squares |
Mean square |
F ratio |
P |
|
Model |
2 |
857.2 |
428.6 |
14.8 |
4.44 x 10-6 |
|
Error |
69 |
1996.4 |
28.9 |
|
|
|
Total |
71 |
2853.6 |
|
|
|
These results in Table 16 show that the variance due to the effect of the three color treatments (model mean square) is much greater than the variance due to other factors (error mean square). This is reflected in the very small P-value. We can reject the null hypothesis and conclude that in general color has a significant effect on the response of cockroach retinas.
Notice that this test did not break the comparison down into individual pairs of colors. So it cannot say which particular colors are different from each other. It may be that some colors (e.g. blue and green) are not different, but at least one of the treatment categories is different from another category. To determine which particular treatments are different from others, a significant ANOVA can be followed by a posteriori ("after the fact") pairwise tests or by comparing 95% confidence intervals (a good method when there are many treatment categories).
