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Factorial Analysis of variance

Factorial Analysis of variance. Factorial Analysis of variance. Orthogonal. Is the property that every level of one factor is present in the experiment in combination with every level of the other factor.

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Factorial Analysis of variance

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  1. Factorial Analysis of variance

  2. Factorial Analysis of variance

  3. Orthogonal • Is the property that every level of one factor is present in the experiment in combination with every level of the other factor

  4. Effects of season (winter/spring and summer/fall) and adult density (8,15, 30 y 45 animales/225 cm2) on egg production of Siphonariadiemenensis

  5. Spring-30 Summer- 15 Summer- 45 Summer- 30 Spring-8 Spring-15 Summer- 15 Summer- 8 Spring-15 Summer- 8 Spring-40 Summer- 45 Spring-40 Summer- 45 Spring-30 Summer- 30 Spring-8 Spring-40 Spring-15 Summer- 15 Spring-8 Summer- 8 Summer- 30 Spring-30

  6. Two single-factor design

  7. Null hypothesis • No effects of treatment A • No effects of treatment B • No effects of the interaction

  8. Data Density

  9. Consider the entire analysis as though it were a single factor factorial experiment with ab experimental treatments

  10. Now start again and ignore any differences among the data that might be due to factor B. Equivalent to a single-factor analysis of variance of means of the levels of factor A (with a treatments each replicated bn times) A symmetrical argument can be made to analyze the data as a single factor B

  11. Not all the differences among means of the ab combinations of treatments have been accounted for by the two single factor analyses • The remaining differences can be identified empirically as • SS among all treatments- SS factorA- SS factorB= ΣiaΣjb(Xij-Xi-Xj+X)2

  12. Expected mean squares for test of null hypothesis for twofactorial analysis (A fixed, B fixed)

  13. Expected mean squares for test of null hypothesis for twofactorial analysis (A random, B random)

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