1. Experimental Statistics - Week 4 (Lab)
Chapter 8: Inferences about More Than 2 Population Central Values

2. The CAR data set as SAS needs to see it:   A A A A B B B C C C C D D D D E E E

3. SAS file for CAR data Case 1: Data within SAS FILE : DATA one;
DATA one;
INPUT gas$ octane;
DATALINES; A A . E ;
PROC GLM;
CLASS gas;
MODEL octane=gas;
TITLE 'Gasoline Example - Completely Randomized Design';
MEANS gas;
RUN;
PROC MEANS mean var;
class gas;

4. The SAS Output for CAR data:
Gasoline Example - Completely Randomized Design
General Linear Models Procedure
Dependent Variable: OCTANE
Sum of Mean
Source DF Squares Square F Value Pr > F
Model
Error
Corrected Total
R-Square C.V Root MSE OCTANE Mean   
Source DF Type I SS Mean Square F Value Pr > F
GAS
Textbook Format for ANOVA Table Output - car data
Source SS df MS F p-value
Between
  samples
Within
Totals

5. Problem 1. Descriptive Statistics for CAR Data
The MEANS Procedure
Analysis Variable : octane
Mean Std Dev Minimum Maximum
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6. Problem 3. Descriptive Statistics by Gasoline  
gas=A
  The MEANS Procedure
  Analysis Variable : octane
  Mean Std Dev Minimum Maximum
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   gas=B
   gas=C
Mean Std Dev Minimum Maximum
  gas=D
Analysis Variable : octane
gas=E

8. Question 1: Which gasolines are different?
Question 2: Why didn’t we just do t-tests to compare all combinations of gasolines?
i.e. compare
A vs B
A vs C
D vs E

9. Probability of finding at least 2 of k means significantly different using multiple t-tests at the a = .05 level when all means are actually equal.
k Prob.

10. Fisher’s Least Significant Difference (LSD)
Protected LSD: Preceded by an F-test for overall significance.
Only use the LSD if F is significant. X
Unprotected: Not preceded by an F-test (like individual t-tests).

11. Gasoline Example - Completely Randomized Design -- All 5 Gasolines
The GLM Procedure
Dependent Variable: octane
Sum of
Source DF Squares Mean Square F Value Pr > F
Model
Error
Corrected Total
R-Square Coeff Var Root MSE octane Mean
Source DF Type I SS Mean Square F Value Pr > F
gas

14. PROC GLM; (or ANOVA)
CLASS gas;
MODEL octane=gas;
TITLE 'Gasoline Example - Completely Randomized Design';
MEANS gas/lsd;
RUN;

15. Gasoline Example - Completely Randomized Design
The GLM Procedure
t Tests (LSD) for octane
NOTE: This test controls the Type I comparisonwise error rate, not the
experimentwise error rate.
Alpha
Error Degrees of Freedom
Error Mean Square
Critical Value of t
Least Significant Difference
Means with the same letter are not significantly different.
t Grouping Mean N gas
A E
B D B
C B C
C B
C B B C
C A

16. Bonferroni Multiple Comparisons (BSD)
Number of Pairwise Comparisons

18. PROC GLM;
CLASS gas;
MODEL octane=gas;
TITLE 'Gasoline Example - Completely Randomized Design';
MEANS gas/bon;
RUN;

19. Gasoline Example - Completely Randomized Design
The GLM Procedure
Bonferroni (Dunn) t Tests for octane
NOTE: This test controls the Type I experimentwise error rate, but it generally has a higher Type II error rate than REGWQ.   
Alpha
Error Degrees of Freedom
Error Mean Square
Critical Value of t
Minimum Significant Difference
Means with the same letter are not significantly different.
  Bon Grouping Mean N gas
A E A
B A D B
B C
B B
B A