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One Way ANOVA:

k = number of groups

i = group number;

j = number of samples in ith group (group size)

Yij follows a normal distribution

Assumptions:

Normal distribution for Yij

Distribution of Yij has common variance and equal variance

Observations are independent

5 steps:

1. Ho = all î…µuâ€™s equal; Ha = î…¶ot all î…µuâ€™s equal

2. State Alpha

3. F Test (F~FI-1,n-I under the null)

4. Interpret (e.g. Given Fobs > F*, we reject the Ho)

5. Conclusion (e.g. That is, there is strong evidence to suggest Group A > Group B)

Pairwise Test: Comparing two groups within an ANOVA

H0: mu2=mu3 vs HA: mu2 =/= mu3

If using CI, reject Ho if CI does not cover 0

CI=

Calculate variance, standard deviation using all groups (group pooled sd or variance)

(Continue until all groups are covered, not just the compared groups, and subtract by # of group)

Df still = n-1

Linear Combination

Gamma:

SE(Gamma):

H0: gamma = 0 vs Ha: gamma =/= 0

Number of pairs for comparison: Where I = number of groups

Standard Deviation:

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