Two DQ and one activity questions. Dissertation correction.

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Week 14 DQ Guide: Suppose we have two chi squared random variables, then

Analysis of Variance (ANOVA): test homogeneity of mean across several groups

Assumptions: all groups are normally distributed with a common σ, elements of the sample will be independent from each other

Take a sample from each group

Size of sample from group i:

Sample from group i:

pooled sample mean

sample mean from group i

overall sum of squares of deviations

sum of squares of deviations within groups

sum of squares of deviations between groups

+

will have chi squared distribution

Dof of =

Distribution of test statistic under validity of H0

Area = ɑ

Critical value

Rejection region

If you reject H0, then Post hoc analysis, rank groups according to the order of the means

Pairwise right sided t tests in comparing the means

Suppose you want to compare mean of group i with mean of group l, suppose sample mean of group i is greater

Estimate of common variance () =

size of sample from group i

size of sample from group l