Analysis of Variance Designs I. Systematic Designs II. Randomized designs with one treatment a. Experimental units not subdivided on any bases other than randomization prior to assignment to treatment levels; no restriction on random assignment other than the option of assigning the same number of objects to each treatment level 1. Completely randomized design b. Experimental units divided on some nonrandom basis or one or more restrictions on random assignment other than assigning the same number of subjects to each treatment level 1. Balanced incomplete block design 2. Cross-over design 3. Generalized Randomized block design 4. Graeco-Latin square design 5. Hyper-Graeco-Latin square design 6. Latin square design 7. Partially balanced incomplete block design 8. Randomized block design 9. Youden square design III. Randomized designs with two or more treatments a. Factorial experiments: designs in which all treatment levels are crossed 1. Designs without confounding i. Completely randomized factorial design ii. Generalized randomized block factorial design iii. Randomized block factorial design 2. Design with group treatment confounding i. Split-plot factorial design 3. Desings with group interaction confounding i. Latin square confounded factorial design ii. Randomized block completely confounded factorial design iii. Randomized block partially confounded factorial design 4. Designs with treatment interaction confounding i. Completely randomized fractional factorial design ii. Graeco-Latin square fractional factorial design iii. Latin square fractional factorial design iv. Randomized block fractional factorial design b. Hierarchical experiments: designs in which one or more treatments are nested 1. Designs with complete nesting i. Completely randomized hierarchical design ii. Randomized block hierarchical design 2. Designs with partial nesting i. Completely randomized partial hierarchical nesting ii. Randomized block partial hierarchical nesting IV. Randomized designs with one or more covariates a. A covariate can be used with all the designs listed above 1. Completely randomized analysis of covariance design 2. Completely randomized factorial analysis of covariance design 3. Latin square analysis of covariance design 4. Randomized block analysis of covariance design 5. Split-plot analysis of covariance design V. Response surface designs Kirk, 1996.
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