Things to know and formulas for Exam 1
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Three decisions.
Three sources of variability.
Three types of variability.
Control, Replication, and Randomization.
How to use the sample size tables.
How to interpret computer output.
Two independent Sample Problem
Equal Variance Condition
s 2p =
t=
(n1 − 1)s12 + (n2 − 1)s22 with df
(n1 + n2 − 2)
= n1 + n2 − 2
(Y1+ − Y2+ )
⎛ 1
1 ⎞
s p ⎜⎜ + ⎟⎟
⎝ n1 n2 ⎠
(Y1+ − Y2+ ) ± t * s p
⎛ 1
1 ⎞
⎜⎜ + ⎟⎟
⎝ n1 n2 ⎠
Analysis of Variance, 1-Factor with k levels
Source
df
Sums of Squares
Mean Square
F-Ratio
Factor
k–1
∑ ni (Yi + − Y+ + )
SS Factor
(k - 1)
MS Factor
MS Error
Error
N–k
∑ (ni − 1)si2
SS Error
(N - k )
C. Total
N–1
∑∑ (Yij − Y+ + )
2
2
1
Multiple Comparisons, LSD
t * has df = df Error and 95% confidence for each comparison
⎛1
1 ⎞⎟
LSD = t * MS Error ⎜ +
⎜ ni n j ⎟
⎝
⎠
Multiple Comparisons, adjLSD or Bonferroni
t * has df = df Error and 99% or higher confidence for each comparison
Confidence coefficient for each comparison = 1 −
0.05
⎛ k (k − 1) ⎞
⎜
⎟
⎝ 2 ⎠
⎛1
1 ⎞⎟
adjLSD = t * MS Error ⎜ +
⎜ ni n j ⎟
⎝
⎠
Multiple Comparisons, HSD
q * and 95% confidence for the set of comparisons
⎛1
1 ⎞
HSD = q * MS Error ⎜ + ⎟
⎜ ni n j ⎟
⎠
⎝
2