Analysis of Variance

What is Variance? Think….think…

Variance First, this is the Sums of Squares µ

Variance

Next: T Test When do we use a T-Test? What is the dependent variable? Independent variable?

Analysis of Variance This is what we use when we want to know whether three or more samples have different means from one another Dependent Variable: Continuous Independent Variable: 2 or more categories But, we have to ask the question in a slightly different way

Grand Mean One Way to do Variance

Another Way to do Variance

What ANOVA is really asking Do we need one mean (the grand mean) or do we need one for each sample? Does it make a difference? The way we are forced to ask this: Is the first variance significantly different from the second variance? The null hypothesis: That the ratio=1

We Have Technical Names For these Variances Within Treatment This is just the sum of how a sample varies from its sample mean Between Treatments This is the sum of how sample means vary from the grand mean (adjusted for N size of each sample)

Within Treatment

Between Treatment

F Test

Degrees of Freedom Numerator = Groups-1 Denominator= N-Groups

F Distribution

Assumptions Independence of Observations Normally distributed values Equality of variance (between samples)

The Big Picture Ok…so there’s a bunch of crazy terminology But…this is kind of powerful in what it lets you do. Any arbitrary number of samples can be tested for mean differences! This general idea of testing variances for differences becomes useful later.