Results: classicalgrapefruit.sas

Grapefruit Data

Classical mixed model repeated measures

The GLM Procedure

The GLM Procedure

Data

Class Levels

Class Level Information
Class Levels Values
price 3 1 2 3
store 8 1 2 3 4 5 6 7 8

Number of Observations

Number of Observations Read 24
Number of Observations Used 24

Grapefruit Data

Classical mixed model repeated measures

The GLM Procedure

Dependent Variable: sales

Analysis of Variance

sales

Overall ANOVA

Source DF Sum of Squares Mean Square F Value Pr > F
Model 9 812.6658333 90.2962037 132.06 <.0001
Error 14 9.5725000 0.6837500    
Corrected Total 23 822.2383333      

Fit Statistics

R-Square Coeff Var Root MSE sales Mean
0.988358 1.546797 0.826892 53.45833

Type I Model ANOVA

Source DF Type I SS Mean Square F Value Pr > F
price 2 67.4808333 33.7404167 49.35 <.0001
store 7 745.1850000 106.4550000 155.69 <.0001

Type III Model ANOVA

Source DF Type III SS Mean Square F Value Pr > F
price 2 67.4808333 33.7404167 49.35 <.0001
store 7 745.1850000 106.4550000 155.69 <.0001

Interaction Plot

Interaction Plot for sales by price

Grapefruit Data

Classical mixed model repeated measures

The GLM Procedure

Means

price

sales

Distribution of sales by price

Distribution of sales by price

Means

Level of
price		 N sales
Mean Std Dev
1 8 55.4375000 5.44135947
2 8 53.6000000 6.13095192
3 8 51.3375000 6.37381642

Grapefruit Data

Classical mixed model repeated measures

The GLM Procedure

Random Effects Analysis

Model Expected Mean Squares

Source Type III Expected Mean Square
price Var(Error) + Q(price)
store Var(Error) + 3 Var(store)

Grapefruit Data

Classical mixed model repeated measures

The GLM Procedure

Tests of Hypotheses for Mixed Model Analysis of Variance

Dependent Variable: sales

sales

Type III Model ANOVA

Source DF Type III SS Mean Square F Value Pr > F
price 2 67.480833 33.740417 49.35 <.0001
store 7 745.185000 106.455000 155.69 <.0001
Error: MS(Error) 14 9.572500 0.683750    

Grapefruit Data

Matched t-tests: 0.05/3 = 0.0167

The MEANS Procedure

The MEANS Procedure

Summary statistics

Variable N Mean Std Dev t Value Pr > |t|
One_vs_Two
One_vs_Three
Two_vs_Three
8
8
8
1.8375000
4.1000000
2.2625000
1.0835622
1.4540584
0.9022789
4.80
7.98
7.09
0.0020
<.0001
0.0002