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 Condition
s2p =
(n1 −1)s21 +(n2 −1)s22
n1 +n2 −2
with
v
u
∗u
t ts2p
Y1−Y2 ±
t=
s
df = n1 + n2 − 2
1
1
+
n1 n2
Y1−Y2
s2p
1
n1
+
1
n2
!
Analysis of Variance, 1-Factor with k levels
Source
Model
df
k–1
Sums of Squares
k
X
i=1
Error
N–k
ni(Y i+ − Y ++)2 SSM odel /dfM odel
k
X
(ni − 1)s2i
i=1
C. Total N–1
Mean Square
XX
(Yij − Y ++)2
1
SSError /dfError
F
M SM odel
M SError
Multiple Comparisons, LSD
t∗ has df = dfError and 95% confidence for each comparison.
v
u
√
u1
1
∗
LSD = t M SError t +
ni nj
Multiple Comparisons, adjLSD or Bonferroni
t∗ has df = dfError and 99% or higher confidence for each comparison.
0.05
Confidence coefficient for each comparison = 1 − k(k−1)
( 2 )
v
u
√
u1
1
∗
adjLSD = t M SError t +
ni nj
Factorial Crossing - Multifactor ANOVA
Factor A: a levels, Factor B: b levels, n replicates per treatment combination.
Source
df
Factor A
a–1
Factor B
b–1
AB Interaction (a-1)(b-1)
Model
ab–1
Error
ab(n-1)
C. Total
abn–1
Sums of Squares
X
X
bn(Y i++ − Y +++)2
an(Y +j+ − Y +++)2
subtraction
XX
Mean Square
F
SSA
a−1
M SA
M SError
SSB
b−1
M SB
M SError
SSAB
(a−1)(b−1)
M SAB
M SError
n(Y ij+ − Y +++)2 SSM odel /dfM odel
XX
XXX
(n − 1)s2ij
(Yijk − Y +++)2
2
SSError /dfError
M SM odel
M SError