Lab 5

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# Lab 5 - PowerPoint PPT Presentation

Lab 5. Post-hoc Tests &amp; Planned Comparisons. Hand Calculations . Hays, page 398, has step by step instructions for computing a one-way ANOVA by hand. Very helpful. Post-hoc Tests with GLM. PROC GLM; CLASS categorical_variable; MODEL dv=iv;

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### Lab 5

Post-hoc Tests &

Planned Comparisons

Hand Calculations
• Hays, page 398, has step by step instructions for computing a one-way ANOVA by hand. Very helpful.
Post-hoc Tests with GLM

PROC GLM;

CLASS categorical_variable;

MODEL dv=iv;

MEANS categorical_variable /TUKEY SCHEFFE BON;

1 2 3

6 11 14

9 1517

8 12 18

10 11 20

5 13 15

Math test scores for three different grades, 1st, 2nd, and 3rd.

Post Hoc Example – test scores
Data d1;

Cards;

1 6

1 9

1 8

1 10

1 5

2 11

2 15

2 12

2 11

2 13

3 14

3 17

3 18

3 20

3 15

;

Proc print;

PROC GLM;

Run;

Program Editor
Output

Class Level Information

Class Levels Values

Number of observations 15

Output (Cont.)

Dependent Variable: test

Sum of Source DF Squares Mean Square F Value Pr > F

Model 2 211.733 105.86667 24.81 <.0001

Error 12 51.200 4.26667

Corrected Total 14 262.9333

R-Square Coeff Var Root MSE Mean

0.805274 16.83906 2.065591 12.26667

Source Table Notes
• Total Sum of Squares (“Corrected Total”) = Within SS (“Error”) + Between SS (“Model”); 211.733 + 51.2 = 262.93
• Mean Square = SSb/dfb, 211.733/2 = 105.87
• F-value = MSb/MSw = 105.87/4.27 = 24.81
Source Table notes (cont.)
• R-square = SSbetween/SStotal = 211.73/262.93 = .805
• Power, Hays, Table XII, Appendix F
Planned comparisons
• Want to know if students’ math scores improved in grade 3 from the previous two years. (.25 .25 -.5)
Tukey Results

Tukey's Studentized Range (HSD) Test

NOTE: This test controls the Type I experimentwise error rate, but it generally has a higher Type II error rate than REGWQ.

Alpha 0.05

Error Degrees of Freedom 12

Error Mean Square 4.266667

Critical Value of Studentized Range 3.77278

Minimum Significant Difference 3.4851

Means with the same letter are not significantly different.

Dependent Variable:

Grouping Mean N dv

A 16.800 5 3

B 12.400 5 2

C 7.600 5 1

Scheffe Results

Scheffe's Test for test

NOTE: This test controls the Type I experimentwise error rate.

Alpha 0.05

Error Degrees of Freedom 12

Error Mean Square 4.266667

Critical Value of F 3.88529

Minimum Significant Difference 3.6417

Means with the same letter are not significantly different.

Dependent Variable:

Grouping Mean N dv

A 16.800 5 3

B 12.400 5 2

C 7.600 5 1

Bonferroni Test

Bonferroni (Dunn) t Tests for test

NOTE: This test controls the Type I experimentwise error rate, but it generally has a higher Type

II error rate than REGWQ.

Alpha 0.05

Error Degrees of Freedom 12

Error Mean Square 4.266667

Critical Value of t 2.77947

Minimum Significant Difference 3.6311

Means with the same letter are not significantly different.

A 16.800 5 3

B 12.400 5 2

C 7.600 5 1

Proc Means results

The GLM Procedure

Level of

Dependent Variable: dv N Mean Std Dev

1 5 7.6000 2.07364

2 5 12.4000 1.67332

3 5 16.8000 2.38747

Second Tukey Example

Tukey's Studentized Range (HSD) Test for dv

NOTE: This test controls the Type I experimentwise error rate, but it generally has a higher Type II error rate than REGWQ.

Alpha 0.05

Error Degrees of Freedom 12

Error Mean Square 5.833333

Critical Value of Studentized Range 3.77278

Minimum Significant Difference 4.0751

Means with the same letter are not significantly different.

Tukey Grouping Mean N group

A 13.000 5 3

B 6.600 5 2

B

B 5.800 5 1

Second Scheffe example

Scheffe's Test for dv

NOTE: This test controls the Type I experimentwise error rate.

Alpha 0.05

Error Degrees of Freedom 12

Error Mean Square 5.833333

Critical Value of F 3.88529

Minimum Significant Difference 4.2581

Means with the same letter are not significantly different.

Scheffe Grouping Mean N group

A 13.000 5 3

B 6.600 5 2

B

B 5.800 5 1

In-Class Example