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 
 1
1 
  
 n1 n2 
Y1  Y2   t * s p
Analysis of Variance, 1-Factor with k levels
Source
df
Sums of Squares
Factor
k–1
Error
C. Total
R2 
SS Factor
SS C.Total
Mean Square
F-Ratio
 ni Yi   Y 
S SFactor
k - 1
MS Factor
MS Error
N–k
 ni  1si2
S SError
N - k 
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 
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Yi   Y j   LSD then the difference in sample means is statistically significan t
Confidence interval for the difference in two means
Yi   Y j    LSD
Analysis of Residuals
To check for equality of standard deviations, plot residuals versus treatments and
compute the standard deviation of the residuals for each treatment.
To check for normality, look at the distribution of residuals.
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