3.3 CROSS-FACTORED WITH NESTING MODEL Y = C|B(A) + e Analysis of settlement Density response in terms of: Recruit|Trtmnt + Trtmnt|Shore(Recruit) Data: Site Shore Recruit Trtmnt Density Cowes 1 High 2 0.386 Cowes 1 High 2 0.397 Cowes 1 High 2 0.432 Cowes 1 High 8 0.484 Cowes 1 High 8 0.482 Cowes 1 High 8 0.514 Cowes 1 High 32 0.484 Cowes 1 High 32 0.520 Cowes 1 High 32 0.569 Seaview 2 High 2 0.279 Seaview 2 High 2 0.411 Seaview 2 High 2 0.260 Seaview 2 High 8 0.625 Seaview 2 High 8 0.531 Seaview 2 High 8 0.478 Seaview 2 High 32 0.738 Seaview 2 High 32 0.570 Seaview 2 High 32 0.620 Totland 1 Low 2 0.190 Totland 1 Low 2 0.177 Totland 1 Low 2 0.300 Totland 1 Low 8 0.268 Totland 1 Low 8 0.261 Totland 1 Low 8 0.396 Totland 1 Low 32 0.384 Totland 1 Low 32 0.319 Totland 1 Low 32 0.334 Ventnor 2 Low 2 0.304 Ventnor 2 Low 2 0.302 Ventnor 2 Low 2 0.278 Ventnor 2 Low 8 0.402 Ventnor 2 Low 8 0.351 Ventnor 2 Low 8 0.254 Ventnor 2 Low 32 0.244 Ventnor 2 Low 32 0.401 Ventnor 2 Low 32 0.324 Model 3.3(i) Recruit and Trtmnt are fixed factors, Shore is a random factor: Restricted Unrestricted Source DF SS MS F P F P 1 Recruit 1 0.300852 0.300852 95.93 0.010* 95.93 0.010 2 Shore(Recruit) 2 0.006272 0.003136 0.82 0.453 0.31 0.748 3 Trtmnt 2 0.144142 0.072071 7.18 0.047 7.18 0.047 4 Trtmnt*Recruit 2 0.033243 0.016622 1.66 0.299 1.66 0.299 5 Trtmnt*Shore(Recruit) 4 0.040128 0.010032 2.62 0.060 2.62 0.060 6 Error 24 0.091985 0.003833 Total 35 0.616622 *Pooled error MS gives F(1,26) = 79.60, P < 0.001 COMMENT: The four study sites have been reclassified in the factor Shore as two shores nested in high recruitment, and two (different) shores nested in low recruitment. Model 3.3(v) Recruit is a fixed factor, Shore is a random factor, Trtment is a covariate of the response: Source DF Seq SS Seq MS F P 1 Recruit 1 0.300852 0.300852 95.93 0.010* 2 Shore(Recruit) 2 0.006272 0.003136 0.56 0.575 3 Trtmnt 1 0.097297 0.097297 6.30 0.129 4 Trtmnt*Recruit 1 0.025629 0.025629 1.66 0.327 5 Trtmnt*Shore(Recruit) 2 0.030891 0.015446 2.78 0.079 6 Error 28 0.155681 0.005560 Total 35 0.616622 *Pooled error MS gives F(1,30) = 55.73, P < 0.001 COMMENT: This example is balanced and therefore orthogonal, so uses Type I (sequential) SS. __________________________________________________________________ Doncaster, C. P. & Davey, A. J. H. (2007) Analysis of Variance and Covariance: How to Choose and Construct Models for the Life Sciences. Cambridge: Cambridge University Press. http://www.southampton.ac.uk/~cpd/anovas/datasets/