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
Factor
k–1
Error
C. Total
R2 
Mean Square
F-Ratio
 ni Yi   Y  
SS Factor
k - 1
MS Factor
MS Error
N–k
 ni  1si2
SS Error
N - k 
N–1
 Yij  Y  
2
2
SSFactor
SSC.Total
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 significant
Confidence interval for the difference in two means
Yi   Y j    LSD
Multiple Comparisons, HSD
q * and 95% confidence for the set of comparisons
1
1 
HSD  q * MS Error  
 ni n j 


Yi   Y j   HSD then the difference in sample means is statistically significant
2