2 levels (1 or 2)
The ANOVA Procedure
Class Level Information
Class Levels Values
PERLEVEL 2 1 2
Number of Observations Read 80
Number of Observations Used 80
1st Dependent Variable (DV) analyzed
The ANOVA Procedure
ANOVA F-test for testing differences in mean DV1 for two IV levels
Dependent Variable: EFFORT
Sum of
Source DF Squares Mean Square F Value Pr > F
Model 1 22.8703938 22.8703938 15.74 0.0002
Error 78 113.3171062 1.4527834
Corrected Total 79 136.1875000
R-Square Coeff Var Root MSE EFFORT Mean
0.167933 28.78363 1.205315 4.187500
Source DF Anova SS Mean Square F Value Pr > F
PERLEVEL 1 22.87039385 22.87039385 15.74 0.0002
2nd DV analyzed
The ANOVA Procedure
ANOVA F-test for testing differences in mean DV2 for two IV levels
Dependent Variable: UND
Sum of
Source DF Squares Mean Square F Value Pr > F
Model 1 9.3002113 9.3002113 3.92 0.0513
Error 78 185.1872887 2.3741960
Corrected Total 79 194.4875000
R-Square Coeff Var Root MSE UND Mean
0.047819 36.36207 1.540843 4.237500
Source DF Anova SS Mean Square F Value Pr > F
PERLEVEL 1 9.30021129 9.30021129 3.92 0.0513
Note: Good strategy is conduct univariate ANOVA F-tests at a small α (e.g., α = .01 or .02)
The ANOVA Procedure
ANOVA F-test for testing differences in mean DV3 for two IV levels
3rd DV analyzed
Dependent Variable: QUALITY
Sum of
Source DF Squares Mean Square F Value Pr > F
Model 1 7.6597701 7.6597701 5.45 0.0221
Error 78 109.5402299 1.4043619
Corrected Total 79 117.2000000
R-Square Coeff Var Root MSE QUALITY Mean
0.065356 28.90385 1.185058 4.100000
Source DF Anova SS Mean Square F Value Pr > F
PERLEVEL 1 7.65977011 7.65977011 5.45 0.0221
4th DV analyzed
The ANOVA Procedure
ANOVA F-test for testing differences in mean DV4 for two IV levels
Dependent Variable: LUCK
Sum of
Source DF Squares Mean Square F Value Pr > F
Model 1 10.5261663 10.5261663 3.64 0.0599
Error 78 225.2738337 2.8881261
Corrected Total 79 235.8000000
R-Square Coeff Var Root MSE LUCK Mean
0.044640 37.35052 1.699449 4.550000
Source DF Anova SS Mean Square F Value Pr > F
PERLEVEL 1 10.52616633 10.52616633 3.64 0.0599
5th DV analyzed
The ANOVA Procedure
ANOVA F-test for testing differences in mean DV3 for two IV levels
Dependent Variable: DIFF
Sum of
Source DF Squares Mean Square F Value Pr > F
Model 1 4.3206981 4.3206981 2.50 0.1180
Error 78 134.8668019 1.7290616
Corrected Total 79 139.1875000
R-Square Coeff Var Root MSE DIFF Mean
0.031042 39.69624 1.314938 3.312500
Source DF Anova SS Mean Square F Value Pr > F
PERLEVEL 1 4.32069811 4.32069811 2.50 0.1180
Multivariate Analysis of Variance
p-values for MANOVA test of Ho: no mean vector differences between the 2 PERLEEVEL groups
MANOVA Test Criteria and Exact F Statistics
for the Hypothesis of No Overall PERLEVEL Effect
H = Anova SSCP Matrix for PERLEVEL E = Error SSCP Matrix
S=1 M=1.5 N=36
Statistic Value F Value Num DF Den DF Pr > F
Wilks' Lambda 0.67500180 7.13 5 74 <.0001
Pillai's Trace 0.32499820 7.13 5 74 <.0001
Hotelling-Lawley Trace 0.48147752 7.13 5 74 <.0001
Roy's Greatest Root 0.48147752 7.13 5 74 <.0001
Levene's Test for Homogeneity of EFFORT Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
PERLEVEL 1 1.0414 1.0414 0.30 0.5832
Error 78 267.5 3.4300
p-value for testing equality of variances in DV for 2 PERLEVEL groups
(Fail to reject Ho implies equality of variances)
Levene's Test for Homogeneity of UND Variance
DV analyzed
Sum of Mean
Source DF Squares Square F Value Pr > F
PERLEVEL 1 12.2948 12.2948 1.51 0.2235
Error 78 636.9 8.1650
Levene's Test for Homogeneity of QUALITY Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
PERLEVEL 1 11.3703 11.3703 3.51 0.0646
Error 78 252.3 3.2350
Levene's Test for Homogeneity of LUCK Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
PERLEVEL 1 8.0512 8.0512 0.63 0.4285
Error 78 991.5 12.7112
Levene's Test for Homogeneity of DIFF Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
PERLEVEL 1 3.4087 3.4087 0.89 0.3477
Error 78 297.9 3.8188
The ANOVA Procedure
1st DV analyzed
Bonferroni (Dunn) t Tests for EFFORT
NOTE: This test controls the Type I experimentwise error rate.
Alpha 0.05
Error Degrees of Freedom 78
Error Mean Square 1.452783
Critical Value of t 1.99085
Minimum Significant Difference 0.5581
Harmonic Mean of Cell Sizes 36.975
NOTE: Cell sizes are not equal.
Means with the same letter are not significantly different.
Ranking of DV means (means with different letters are significantly different)
Bon Grouping Mean N PERLEVEL
A 4.8966 29 2
B 3.7843 51 1
Bonferroni (Dunn) t Tests for UND
NOTE: This test controls the Type I experimentwise error rate.
2nd DV analyzed
Alpha 0.05
Error Degrees of Freedom 78
Error Mean Square 2.374196
Critical Value of t 1.99085
Minimum Significant Difference 0.7134
Harmonic Mean of Cell Sizes 36.975
NOTE: Cell sizes are not equal.
Means with the same letter are not significantly different.
Ranking of DV means (means with the same letter are not significantly different)
Bon Grouping Mean N PERLEVEL
A 4.6897 29 2
A
A 3.9804 51 1
Bonferroni (Dunn) t Tests for QUALITY
3rd DV analyzed
NOTE: This test controls the Type I experimentwise error rate.
Alpha 0.05
Error Degrees of Freedom 78
Error Mean Square 1.404362
Critical Value of t 1.99085
Minimum Significant Difference 0.5487
Harmonic Mean of Cell Sizes 36.975
NOTE: Cell sizes are not equal.
Means with the same letter are not significantly different.
Bon Grouping Mean N PERLEVEL
A 4.3333 51 1
B 3.6897 29 2
4th DV analyzed
Bonferroni (Dunn) t Tests for LUCK
NOTE: This test controls the Type I experimentwise error rate.
Alpha 0.05
Error Degrees of Freedom 78
Error Mean Square 2.888126
Critical Value of t 1.99085
Minimum Significant Difference 0.7869
Harmonic Mean of Cell Sizes 36.975
NOTE: Cell sizes are not equal.
Means with the same letter are not significantly different.
Bon Grouping Mean N PERLEVEL
A 4.8235 51 1
A
A 4.0690 29 2
Bonferroni (Dunn) t Tests for DIFF
5th DV analyzed
NOTE: This test controls the Type I experimentwise error rate.
Alpha 0.05
Error Degrees of Freedom 78
Error Mean Square 1.729062
Critical Value of t 1.99085
Minimum Significant Difference 0.6088
Harmonic Mean of Cell Sizes 36.975
NOTE: Cell sizes are not equal.
Means with the same letter are not significantly different.
Bon Grouping Mean N PERLEVEL
A 3.6207 29 2
A
A 3.1373 51 1
Math81
SAS-Problem2-Results-Key.docx
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