Statistical modelling/Sample size estimation

Finally let us investigate the suitability of the sample size used in Experiment 1 with six buds and 15 fields of view. We observed that bud length was not significant. We shall therefore repeat the analysis of variance but fit instead the model:

pgerm = bud+sucros+slide / bud

to the data contained in CS9Data1a. Here we specify bud to be block and slide to be whole plot in the split-plot analysis of variance. By doing so we obtain an extra mean square to represent the residual term for field of view within slide (bud.slide*Units* Stratum). 

Note that the mean square for slide within bud (bud.slide.stratum Residual) is now 1438.1 compared with 95.87 in the first analysis based on means. This is 15 times larger. Why? Nevertheless, note that the standard error of the difference between means has remained at 5.653. Again why?

***** Analysis of variance ***** Variate: pgerm Source of variation d.f. (m.v.) s.s. m.s. v.r. bud stratum bud.slide stratum 5 10123.9 2024.8 1.41 sucros 7 233218.1 33316.9 23.17 Residual 35 50333.6 1438.1 4.95 bud.slide.stratum *Units*  667(5) 193767.9 290.5   Total 714(5) 486830.5     ***** Tables of means ***** Variate: pgerm sucros 0.0 5.0 10.0 15.0 20.0 25.0 30.0   5.3 19.9 36.1 52.6 58.3 50.7 58.3 sucros 35.0             45.6           *** Standard errors of differences of means *** Table sucros rep. 90 d.f. 35 s.e.d. 5.653