Analysis of variance in soil research: let the analysis fit the design

Sound design for experiments on soil is based on two fundamental principles: replication and randomization. Replication enables investigators to detect and measure contrasts between treatments against the backdrop of natural variation. Random allocation of experimental treatments to units enables effects to be estimated without bias and hypotheses to be tested. For inferential tests of effects to be valid an analysis of variance (anova) of the experimental data must match exactly the experimental design. Completely randomized designs are usually inefficient. Blocking will usually increase precision, and its role must be recognized as a unique entry in an anova table. Factorial designs enable questions on two or more factors and their interactions to be answered simultaneously, and split-plot designs may enable investigators to combine factors that require disparate amounts of land for each treatment. Each such design has its unique correct anova; no other anova will do. One outcome of an anova is a test of significance. If it turns out to be positive then the investigator may examine the contrasts between treatments to discover which themselves are significant. Those contrasts should have been ones in which the investigator was interested at the outset and which the experiment was designed to test. Post-hoc testing of all possible contrasts is deprecated as unsound, although the procedures may guide an investigator to further experimentation. Examples of the designs with simulated data and programs in GenStat and R for the analyses of variance are provided as File S1