STAT 2050 Midterm: Midterm #2 (ANOVA) Formula Sheet
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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 u’s equal; Ha = ot all u’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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Related notes for STAT 2050
