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A Bestiary of ANOVA tables

A Bestiary of ANOVA tables. Randomized Block. Null hypotheses. No effects of treatment

gavin-hale
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A Bestiary of ANOVA tables

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  1. A Bestiary of ANOVA tables

  2. Randomized Block

  3. Null hypotheses • No effects of treatment • No effects of block B. However this hypothesis is usually not relevant because we are not interested in the differences among blocks per se. Formally, you also need to assume that the interaction is not present and you should consider the added variance due to restricted error.

  4. Randomized Block • Each set of treatments is physically grouped in a block, with each treatment represented exactly once in each block

  5. ANOVA table for randomized block design NOTE: the Expected Mean Square terms in brackets are assumed to be absent for the randomized block design

  6. Tribolium castaneum Mean dry weights (in milligrams) of 3 genotypes of beetles, reared at a density of 20 beetles per gram of flour. Four series of experiments represent blocks

  7. Tribolium castaneum

  8. ANOVA Table

  9. Relative efficiency • To compare two designs we compute the relative efficiency. This is a ratio of the variances resulting from the two designs • It is an estimate of the sensitivity of the original design to the one is compared • However other aspects should be considered as the relative costs of the two designs (Sokal and Rohlf 2000)

  10. Had we ignored differences among series and simply analyzed these data as four replicates for each genotype, what our variance would have been for a completely randomized design? • In the expression in the following slide • MSE(CR) = expected error mean square in the completely randomized design • MSE(RB) = observed error mean square in the randomized block design • MSB is the observed mean square among blocks

  11. Relative efficiency

  12. Nested analysis of variance

  13. Nested analysis of variance • Data are organized hierarchically, with one class of objects nested within another

  14. Null hypothesis • No effects of treatment • No effects of B nested within A

  15. E Enclosures C No enclosures PC Enclosures with openings E PC C E E C PC PC C E Effects of Insect Pollination PC PC C C E

  16. Data

  17. Expected mean squares for test of null hypothesis for two factor nested (A fixed, B random)

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