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# Ch 12 - Chapter 12 ANOVA Analysis of Variance So Far...

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Chapter 12 ANOVA Analysis of Variance

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So Far: Statistical tests have all been about COMPARISONS 1 population tests: Does the Parameter = ‘some value’? 2 population tests: Does Population A = Population B?
Conceptually for a 2 sample t- test We asked if the difference between the means was large relative to the pooled variability

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If show the distribution of 2 samples from 2 different populations Would you conclude these samples could have came from populations with same mean? What about these 2 samples? A A B B
What if you have more than 2 means? Same idea – slightly different approach Here the means are so close together relative to the total variability – so will probability NOT be able to say samples came from populations with significantly different means Variability among treatments Average variability within a sample

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But if there is a difference: Variability among treatments Average variability within a sample Here: looks like one sample came from a population with a significantly larger mean
F Ratio

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F Distribution CRI T CANNOT REJECT CAN REJECT
NOTE: We COULD… Just do multiple t -tests If comparing 3 means (X, Y and Z) then compare: 1st: X to Y 2nd: Y to Z 3rd: Z to X BUT REMEMBER THERE IS A 5% chance of making a Type I error with each == so if you do 3 tests, the probability of that error has greatly

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Variance among samples due to treatment effects = MS(Trt)
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