BIOM301 Chapter 12 ANOVA Analysis of Variance So Far Statistical test have all been about COMPARISIONS o 1 Population Tests Does the Parameter some value o 2 Population Tests Does Pop A Pop B Conceptually for a 2 Sample t test We asked if the difference between the means was large relative to the pooled variability If you show the distribution of 2 samples from 2 different populations Based on the distributions would you conclude both samples came from populations with same mean More than 2 means Same idea but with a different approach If the means are so close together relative to the total variability we probably won t be able to say the samples came from population with significantly different means Some cases one or more means are not so close thus some samples may have come from populations with different means o F Ratio F Variability among treatment means Average variability within a treatment NOTE We could Just do multiple t tests If comparing 3 means X Y and Z then compare o 1st X to Y o 2nd Y to Z o 3rd Z to X BUT REMEMBER THERE IS A 5 chance of making a Type I error with each o So if you do 3 tests the probability of that error has greatly increased past 5 Actual Equation F MS Trt MS Error o Variance among samples due to treatment effects MS Trt which is the average squared deviation associated with treatment effect o Variance within samples due to variability in the populations sampled MS Error which is the average squared deviation associated with variability ANOVA TABLE Tukey s Means Comparison Test Allows you to compare every mean to every other mean while keeping 0 05 We will use a computer program to do this in discussion you do NOT need to be able to calculate yourself but DO need to be able to interpret results o You only do a Tukey s comparison test IF you reject the Ho p 0 05 There ARE assumptions o ASSUMPTION OF NORMALITY population is normal or sample size is 30 o HOMOGENEITY OF VARIANCES the spread of data around each sample mean is similar USE standard error bars on graphs 1
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