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Factorial Analysis of variance

Investigating the effects of season and adult density on egg production in Siphonariadiemenensis. Conducting two single-factor designs and estimating expected mean squares for factorial analyses.

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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-45 Summer- 45 Spring-45 Summer- 45 Spring-30 Summer- 30 Spring-8 Spring-45 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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