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Stat 513 – Day 18

Explore the advantages of factorial design & two-variable analysis in ensuring validity. Learn about conditions for sample size, symmetry, equal standard deviations, and random assignment of units. Check for residual normality and treatment variability.

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Stat 513 – Day 18

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  1. Stat 513 – Day 18 Interactions

  2. Last Time – Multifactor Experiment • Advantages of factorial design and two variable analysis

  3. Validity conditions • Either the sample size is at least 20 for all of the treatments, without strong skewness or outliers; or if the sample size is less than 20, then the distribution of the response variable is approximately symmetric for all treatments (examine dotplots or normal probability plots for strong skewness or outliers) • The standard deviations of the response variable in each treatment are approximately equal to each other (the largest standard deviation is not more than twice the value of the smallest standard deviation) • The experimental units are randomly assigned to each treatment combination.

  4. Validity conditions • Either the sample size is at least 20 for all of the treatments, without strong skewness or outliers; or if the sample size is less than 20, then the distribution of the response variable is approximately symmetric for all treatments (examine dotplots or normal probability plots for strong skewness or outliers) • The standard deviations of the response variable in each treatment are approximately equal to each other (the largest standard deviation is not more than twice the value of the smallest standard deviation) • The experimental units are randomly assigned to each treatment combination.

  5. Checking validity conditions • The residuals follow a normal distribution • The residuals vs. the treatments do now show large differences in variability

  6. Follow-up confidence intervals

  7. To Do • HW • Project • Section 3.2…

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