Things to know and formulas for Exam 1
• 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 Assumption
s2p =
(n1 −1)s21 +(n2 −1)s22
n1 +n2 −2
df = n1 + n2 − 2
with
Y1−Y2 ±
∗
t s2p
t=
1
1
+
n1 n2
Y1−Y2
s2p
1
n1
+
1
n2
Analysis of Variance, 1-Factor
Source
Model
Error
df
k–1
N–k
Sums of Squares
k
Mean Square
F
ni(Y i − Y )2
SSM odel /dfM odel
M SModel
M SError
(ni − 1)s2i
SSError /dfError
i=1
k
i=1
Total
N–1
(Yij − Y )2
1
Multiple Comparisons, LSD
t∗ has df = dfError and 95% confidence for each comparison.
√
1
1
∗
LSD = t MSError +
ni ni Multiple Comparisons, adjLSD or Bonferroni
t∗ has df = dfError and 99% or higher confidence for each comparison.
√
1
1
∗
adjLSD = t MSError +
ni ni Factorial Crossing - Multifactor ANOVA
Factor A: a levels, Factor B: b levels, n replicates per treatment combination.
Source
df
Sums of Squares
Mean Square
F
Factor A
a–1
M SA
M SError
Factor B
b–1
M SB
M SError
M SAB
M SError
AB Interaction (a-1)(b-1)
Model
ab–1
k
i=1
Error
ab(n-1)
Total
abn–1
n(Y i − Y )2
(n − 1)s2ij
(Yij − Y )2
2
SSM odel /dfM odel
SSError /dfError
M SModel
M SError