Nested Designs - Scholar

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1. Model or or Hybrid 1 Pot 1(1) Pot 2(1) Pot 3(1) OOOO OOOO OOOO OOOO OOOO OOOO Hybrid 2 Pot 1(2) Pot 2(2) Pot 3(2) OOOO OOOO OOOO OOOO OOOO OOOO Hybrid 3 Pot 1(3) Pot 2(3) Pot 3(3) OOOO OOOO OOOO OOOO OOOO OOOO Hybrid 4 Pot 1(4) Pot 2(4) Pot 3(4) OOOO OOOO OOOO OOOO OOOO OOOO Hybrid 5 Pot 1(5) Pot 2(5) Pot 3(5) OOOO OOOO OOOO OOOO OOOO OOOO Figure 2. A nested design. Y B C e (1) , ijkl i j i k i j l ijk , Y B C B e ijkl i ij ijk ijkl nested01.docx 2 4/5/2012
Quantitative Response = Constant (grand mean) + where the quantitative response, Effects of Factor A nested01.docx 3 4/5/2012 + Effects of Factor B nested within A + Effects of Factor C nested within A and B + [possible additional nested factors] + Residual "error" Y ijkl is the transpiration rate (units unknown) on leaf l nested within plant k nested within pot j nested within hybrid i, i is the fixed effect of hybrid i , i = 1, 2, 3, 4, 5, B B is the random effect of pot j nested within hybrid i, j = 1, 2, 3, ji ij C C B is the random effect of plant k nested within hybrid i and pot j, k = 1, 2, and eijkl , , k i j ijk is the random effect of leaf l nested within hybrid i, pot j, and plant k, l = 1, 2, 3, 4. The variables that define the nested factors are categorical. The effects, moreover, can be fixed or random. Fixed effects are what we have dealt with so far in one- and two-factor Anova. With fixed effects, the levels of the factor used in the study are the specific levels we are interested in. Random effects are the effects of factor-levels that have been randomly selected as representatives of a larger population of factor-levels. Blocks are usually random. In the example above, the investigator is not interested specifically in the 15 pots that are used in the experiment, but he is interested in measuring the random variation in the response that is attributable to pots. The same can be said of the plants and leaves. The pots, the plants, and the leaves are random selected from the populations of pots, plants, and leaves. The hybrids, on the
Page 1: Nested Designs Nested designs, also
Page 5 and 6: Random effects are random variables
Page 7 and 8: o (dispersion) Yijkl iBjiCki, j
Page 9 and 10: Symbolically, H0: σplants = 0, ver
Page 11 and 12: 4. Design Significance level 0.05
Page 13 and 14: Alternative Allocation of Experimen
Page 15 and 16: Estimating Variance Components in J
Page 17 and 18: Least Squares Means Table Level Lea
Page 19 and 20: For random effects, the hypotheses
Page 21 and 22: Methods The effects on mean human f
Page 23 and 24: ANOVA Table ANOVA -----------------
Page 25: ii) Write a "results" paragraph. Do

Nested Designs - Scholar

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