Summary statistics
| Variable | Label | N | Mean | Std Dev |
|---|---|---|---|---|
|
sales1
sales2
sales3
|
Sales at Price 1
Sales at Price 2
Sales at Price 3
|
8
8
8
|
55.438
53.600
51.338
|
5.441
6.131
6.374
|
The MEANS Procedure
| Variable | Label | N | Mean | Std Dev |
|---|---|---|---|---|
|
sales1
sales2
sales3
|
Sales at Price 1
Sales at Price 2
Sales at Price 3
|
8
8
8
|
55.438
53.600
51.338
|
5.441
6.131
6.374
|
The REG Procedure
Model: MODEL1
Dependent Variable: d12
| Number of Observations Read | 8 |
|---|---|
| Number of Observations Used | 8 |
| Analysis of Variance | |||||
|---|---|---|---|---|---|
| Source | DF | Sum of Squares |
Mean Square |
F Value | Pr > F |
| Model | 0 | 0 | . | . | . |
| Error | 7 | 8.21875 | 1.17411 | ||
| Corrected Total | 7 | 8.21875 | |||
| Root MSE | 1.08356 | R-Square | 0.0000 |
|---|---|---|---|
| Dependent Mean | 1.83750 | Adj R-Sq | 0.0000 |
| Coeff Var | 58.96937 |
| Parameter Estimates | |||||
|---|---|---|---|---|---|
| Variable | DF | Parameter Estimate |
Standard Error |
t Value | Pr > |t| |
| Intercept | 1 | 1.83750 | 0.38310 | 4.80 | 0.0020 |
The REG Procedure
Model: MODEL1
Dependent Variable: d13
| Number of Observations Read | 8 |
|---|---|
| Number of Observations Used | 8 |
| Analysis of Variance | |||||
|---|---|---|---|---|---|
| Source | DF | Sum of Squares |
Mean Square |
F Value | Pr > F |
| Model | 0 | 0 | . | . | . |
| Error | 7 | 14.80000 | 2.11429 | ||
| Corrected Total | 7 | 14.80000 | |||
| Root MSE | 1.45406 | R-Square | 0.0000 |
|---|---|---|---|
| Dependent Mean | 4.10000 | Adj R-Sq | 0.0000 |
| Coeff Var | 35.46484 |
| Parameter Estimates | |||||
|---|---|---|---|---|---|
| Variable | DF | Parameter Estimate |
Standard Error |
t Value | Pr > |t| |
| Intercept | 1 | 4.10000 | 0.51409 | 7.98 | <.0001 |
The REG Procedure
Model: MODEL1
Multivariate Test: Price
| Multivariate Statistics and Exact F Statistics | |||||
|---|---|---|---|---|---|
| S=1 M=0 N=2 | |||||
| Statistic | Value | F Value | Num DF | Den DF | Pr > F |
| Wilks' Lambda | 0.09185282 | 29.66 | 2 | 6 | 0.0008 |
| Pillai's Trace | 0.90814718 | 29.66 | 2 | 6 | 0.0008 |
| Hotelling-Lawley Trace | 9.88698145 | 29.66 | 2 | 6 | 0.0008 |
| Roy's Greatest Root | 9.88698145 | 29.66 | 2 | 6 | 0.0008 |
The REG Procedure
Model: MODEL1
Multivariate Test: Price
| Multivariate Statistics and Exact F Statistics | |||||
|---|---|---|---|---|---|
| S=1 M=0 N=2 | |||||
| Statistic | Value | F Value | Num DF | Den DF | Pr > F |
| Wilks' Lambda | 0.09185282 | 29.66 | 2 | 6 | 0.0008 |
| Pillai's Trace | 0.90814718 | 29.66 | 2 | 6 | 0.0008 |
| Hotelling-Lawley Trace | 9.88698145 | 29.66 | 2 | 6 | 0.0008 |
| Roy's Greatest Root | 9.88698145 | 29.66 | 2 | 6 | 0.0008 |
The GLM Procedure
| Number of Observations Read | 8 |
|---|---|
| Number of Observations Used | 8 |
The GLM Procedure
Dependent Variable: sales1 Sales at Price 1
| Source | DF | Sum of Squares | Mean Square | F Value | Pr > F |
|---|---|---|---|---|---|
| Model | 1 | 24586.53125 | 24586.53125 | 830.39 | <.0001 |
| Error | 7 | 207.25875 | 29.60839 | ||
| Uncorrected Total | 8 | 24793.79000 |
| R-Square | Coeff Var | Root MSE | sales1 Mean |
|---|---|---|---|
| 0.000000 | 9.815305 | 5.441359 | 55.43750 |
| Source | DF | Type I SS | Mean Square | F Value | Pr > F |
|---|---|---|---|---|---|
| Intercept | 1 | 24586.53125 | 24586.53125 | 830.39 | <.0001 |
| Source | DF | Type III SS | Mean Square | F Value | Pr > F |
|---|---|---|---|---|---|
| Intercept | 1 | 24586.53125 | 24586.53125 | 830.39 | <.0001 |
| Parameter | Estimate | Standard Error |
t Value | Pr > |t| |
|---|---|---|---|---|
| Intercept | 55.43750000 | 1.92381109 | 28.82 | <.0001 |
The GLM Procedure
Dependent Variable: sales2 Sales at Price 2
| Source | DF | Sum of Squares | Mean Square | F Value | Pr > F |
|---|---|---|---|---|---|
| Model | 1 | 22983.68000 | 22983.68000 | 611.45 | <.0001 |
| Error | 7 | 263.12000 | 37.58857 | ||
| Uncorrected Total | 8 | 23246.80000 |
| R-Square | Coeff Var | Root MSE | sales2 Mean |
|---|---|---|---|
| 0.000000 | 11.43834 | 6.130952 | 53.60000 |
| Source | DF | Type I SS | Mean Square | F Value | Pr > F |
|---|---|---|---|---|---|
| Intercept | 1 | 22983.68000 | 22983.68000 | 611.45 | <.0001 |
| Source | DF | Type III SS | Mean Square | F Value | Pr > F |
|---|---|---|---|---|---|
| Intercept | 1 | 22983.68000 | 22983.68000 | 611.45 | <.0001 |
| Parameter | Estimate | Standard Error |
t Value | Pr > |t| |
|---|---|---|---|---|
| Intercept | 53.60000000 | 2.16761884 | 24.73 | <.0001 |
The GLM Procedure
Dependent Variable: sales3 Sales at Price 3
| Source | DF | Sum of Squares | Mean Square | F Value | Pr > F |
|---|---|---|---|---|---|
| Model | 1 | 21084.31125 | 21084.31125 | 518.99 | <.0001 |
| Error | 7 | 284.37875 | 40.62554 | ||
| Uncorrected Total | 8 | 21368.69000 |
| R-Square | Coeff Var | Root MSE | sales3 Mean |
|---|---|---|---|
| 0.000000 | 12.41552 | 6.373816 | 51.33750 |
| Source | DF | Type I SS | Mean Square | F Value | Pr > F |
|---|---|---|---|---|---|
| Intercept | 1 | 21084.31125 | 21084.31125 | 518.99 | <.0001 |
| Source | DF | Type III SS | Mean Square | F Value | Pr > F |
|---|---|---|---|---|---|
| Intercept | 1 | 21084.31125 | 21084.31125 | 518.99 | <.0001 |
| Parameter | Estimate | Standard Error |
t Value | Pr > |t| |
|---|---|---|---|---|
| Intercept | 51.33750000 | 2.25348441 | 22.78 | <.0001 |
The GLM Procedure
Repeated Measures Analysis of Variance
| Repeated Measures Level Information | |||
|---|---|---|---|
| Dependent Variable | sales1 | sales2 | sales3 |
| Level of price | 1 | 2 | 3 |
| MANOVA Test Criteria and Exact F Statistics for the Hypothesis of no price Effect H = Type III SSCP Matrix for price E = Error SSCP Matrix S=1 M=0 N=2 |
|||||
|---|---|---|---|---|---|
| Statistic | Value | F Value | Num DF | Den DF | Pr > F |
| Wilks' Lambda | 0.09185282 | 29.66 | 2 | 6 | 0.0008 |
| Pillai's Trace | 0.90814718 | 29.66 | 2 | 6 | 0.0008 |
| Hotelling-Lawley Trace | 9.88698145 | 29.66 | 2 | 6 | 0.0008 |
| Roy's Greatest Root | 9.88698145 | 29.66 | 2 | 6 | 0.0008 |
The GLM Procedure
Repeated Measures Analysis of Variance
Univariate Tests of Hypotheses for Within Subject Effects
| Source | DF | Type III SS | Mean Square | F Value | Pr > F | Adj Pr > F | |
|---|---|---|---|---|---|---|---|
| G - G | H - F | ||||||
| price | 2 | 67.48083333 | 33.74041667 | 49.35 | <.0001 | <.0001 | <.0001 |
| Error(price) | 14 | 9.57250000 | 0.68375000 | ||||
| Greenhouse-Geisser Epsilon | 0.7568 |
|---|---|
| Huynh-Feldt Epsilon | 0.9213 |
The GLM Procedure
Repeated Measures Analysis of Variance
Analysis of Variance of Contrast Variables
price_N represents the contrast between the nth level of price and the last
Contrast Variable: price_1
| Source | DF | Type III SS | Mean Square | F Value | Pr > F |
|---|---|---|---|---|---|
| Mean | 1 | 134.4800000 | 134.4800000 | 63.61 | <.0001 |
| Error | 7 | 14.8000000 | 2.1142857 |
Contrast Variable: price_2
| Source | DF | Type III SS | Mean Square | F Value | Pr > F |
|---|---|---|---|---|---|
| Mean | 1 | 40.95125000 | 40.95125000 | 50.30 | 0.0002 |
| Error | 7 | 5.69875000 | 0.81410714 |
The GLM Procedure
Repeated Measures Analysis of Variance
Means of Within Subjects Effects
| Level of price |
N | Mean | Std Dev |
|---|---|---|---|
| 1 | 8 | 55.43750000 | 5.44135947 |
| 2 | 8 | 53.60000000 | 6.13095192 |
| 3 | 8 | 51.33750000 | 6.37381642 |
The MEANS Procedure
| Variable | Mean | t Value | Pr > |t| |
|---|---|---|---|
|
d12
d13
d23
|
1.838
4.100
2.263
|
4.80
7.98
7.09
|
0.0020
<.0001
0.0002
|