In this explanation, an animal identification code called subject, with nominal values 1, 2, and 3 for both foxes and coyotes. Then it was nested in species. Then subject[species] was selected as random effect, and then REML methos was selected.
1) In the below table,
subject[species] has 0.7013889 variance component. How can I interpret this? Does it mean the 70% error is coming from 'subject[species]' ?
For fixed effect test, species and season are significant respectively.
2) If I use simple two way ANOVA (species x season), in this case "subject" was considered as "block"
In this case, main effect was significant, whereas its interaction was not significant, and also block (subject-animal identification code) was also significant.
Even though I use ANOVA or Split Plot Design (or REML), the result is the same, why do we need to use Split Plot Design (or REML)? For what purpose?
1. No, it is not a proportion (relative) but the actual variance estimated by REML. Take the square root and you have the estimated standard deviation between subjects.
2. It is generally better to identify (and estimate) the between and within error when possible. The split-plot analysis is an example of such a model. You have two sources of variability that might be sampled at different rates. (This matter is about randomization and levels of experimental units.) If you include only one error term, then the estimate is some kind of average that can inflate the type I error of the hard to change factor and inflate the type II error of the easy to change factor.
It isn't a matter of trying different ways but understanding how the model terms and assumptions match the design and the way in which the data were collected.