| Exemple de Kenton |
| The UNIVARIATE Procedure |
| Variable: Caisse (Nombre de caisses de boîtes de céréales) |
| Design de la boîte=1 |
| Moments | |||
| N | 5 | Sum Weights | 5 |
| Mean | 14.6 | Sum Observations | 73 |
| Std Deviation | 2.30217289 | Variance | 5.3 |
| Skewness | -1.0326585 | Kurtosis | 1.12851549 |
| Uncorrected SS | 1087 | Corrected SS | 21.2 |
| Coeff Variation | 15.7683074 | Std Error Mean | 1.02956301 |
| Basic Statistical Measures | |||
| Location | Variability | ||
| Mean | 14.60000 | Std Deviation | 2.30217 |
| Median | 15.00000 | Variance | 5.30000 |
| Mode | . | Range | 6.00000 |
| Interquartile Range | 2.00000 | ||
| Tests for Location: Mu0=0 | ||||
| Test | Statistic | p Value | ||
| Student's t | t | 14.18077 | Pr > |t| | 0.0001 |
| Sign | M | 2.5 | Pr >= |M| | 0.0625 |
| Signed Rank | S | 7.5 | Pr >= |S| | 0.0625 |
| Quantiles (Definition 5) | |
| Quantile | Estimate |
| 100% Max | 17 |
| 99% | 17 |
| 95% | 17 |
| 90% | 17 |
| 75% Q3 | 16 |
| 50% Median | 15 |
| 25% Q1 | 14 |
| 10% | 11 |
| 5% | 11 |
| 1% | 11 |
| 0% Min | 11 |
| Extreme Observations | |||
| Lowest | Highest | ||
| Value | Obs | Value | Obs |
| 11 | 1 | 11 | 1 |
| 14 | 4 | 14 | 4 |
| 15 | 5 | 15 | 5 |
| 16 | 3 | 16 | 3 |
| 17 | 2 | 17 | 2 |
| Exemple de Kenton |
| The UNIVARIATE Procedure |
| Variable: Caisse (Nombre de caisses de boîtes de céréales) |
| Design de la boîte=1 |
Stem Leaf # Boxplot
17 0 1 |
16 0 1 +-----+
15 0 1 *-----*
14 0 1 +--+--+
13 |
12 |
11 0 1 |
----+----+----+----+
Normal Probability Plot
17.5+ +*++
| * ++++
| * +++++
14.5+ * ++++
| ++++
| +++++
11.5+ +++*
+----+----+----+----+----+----+----+----+----+----+
-2 -1 0 +1 +2
|
| Exemple de Kenton |
| The UNIVARIATE Procedure |
| Variable: Caisse (Nombre de caisses de boîtes de céréales) |
| Design de la boîte=2 |
| Moments | |||
| N | 5 | Sum Weights | 5 |
| Mean | 13.4 | Sum Observations | 67 |
| Std Deviation | 3.64691651 | Variance | 13.3 |
| Skewness | 1.06383002 | Kurtosis | 0.20182034 |
| Uncorrected SS | 951 | Corrected SS | 53.2 |
| Coeff Variation | 27.2157948 | Std Error Mean | 1.63095064 |
| Basic Statistical Measures | |||
| Location | Variability | ||
| Mean | 13.40000 | Std Deviation | 3.64692 |
| Median | 12.00000 | Variance | 13.30000 |
| Mode | . | Range | 9.00000 |
| Interquartile Range | 4.00000 | ||
| Tests for Location: Mu0=0 | ||||
| Test | Statistic | p Value | ||
| Student's t | t | 8.216067 | Pr > |t| | 0.0012 |
| Sign | M | 2.5 | Pr >= |M| | 0.0625 |
| Signed Rank | S | 7.5 | Pr >= |S| | 0.0625 |
| Quantiles (Definition 5) | |
| Quantile | Estimate |
| 100% Max | 19 |
| 99% | 19 |
| 95% | 19 |
| 90% | 19 |
| 75% Q3 | 15 |
| 50% Median | 12 |
| 25% Q1 | 11 |
| 10% | 10 |
| 5% | 10 |
| 1% | 10 |
| 0% Min | 10 |
| Extreme Observations | |||
| Lowest | Highest | ||
| Value | Obs | Value | Obs |
| 10 | 2 | 10 | 2 |
| 11 | 5 | 11 | 5 |
| 12 | 1 | 12 | 1 |
| 15 | 3 | 15 | 3 |
| 19 | 4 | 19 | 4 |
| Exemple de Kenton |
| The UNIVARIATE Procedure |
| Variable: Caisse (Nombre de caisses de boîtes de céréales) |
| Design de la boîte=2 |
Stem Leaf # Boxplot
19 0 1 |
18 |
17 |
16 |
15 0 1 +-----+
14 | |
13 | + |
12 0 1 *-----*
11 0 1 +-----+
10 0 1 |
----+----+----+----+
Normal Probability Plot
19.5+ * +++
| +++
| +++
16.5+ ++
| *++
| +++
13.5+ +++
| ++ *
| +*+
10.5+ * +++
+----+----+----+----+----+----+----+----+----+----+
-2 -1 0 +1 +2
|
| Exemple de Kenton |
| The UNIVARIATE Procedure |
| Variable: Caisse (Nombre de caisses de boîtes de céréales) |
| Design de la boîte=3 |
| Moments | |||
| N | 4 | Sum Weights | 4 |
| Mean | 19.5 | Sum Observations | 78 |
| Std Deviation | 2.64575131 | Variance | 7 |
| Skewness | 0.8639188 | Kurtosis | -0.2857143 |
| Uncorrected SS | 1542 | Corrected SS | 21 |
| Coeff Variation | 13.5679554 | Std Error Mean | 1.32287566 |
| Basic Statistical Measures | |||
| Location | Variability | ||
| Mean | 19.50000 | Std Deviation | 2.64575 |
| Median | 19.00000 | Variance | 7.00000 |
| Mode | . | Range | 6.00000 |
| Interquartile Range | 4.00000 | ||
| Tests for Location: Mu0=0 | ||||
| Test | Statistic | p Value | ||
| Student's t | t | 14.74061 | Pr > |t| | 0.0007 |
| Sign | M | 2 | Pr >= |M| | 0.1250 |
| Signed Rank | S | 5 | Pr >= |S| | 0.1250 |
| Quantiles (Definition 5) | |
| Quantile | Estimate |
| 100% Max | 23.0 |
| 99% | 23.0 |
| 95% | 23.0 |
| 90% | 23.0 |
| 75% Q3 | 21.5 |
| 50% Median | 19.0 |
| 25% Q1 | 17.5 |
| 10% | 17.0 |
| 5% | 17.0 |
| 1% | 17.0 |
| 0% Min | 17.0 |
| Extreme Observations | |||
| Lowest | Highest | ||
| Value | Obs | Value | Obs |
| 17 | 4 | 17 | 4 |
| 18 | 3 | 18 | 3 |
| 20 | 2 | 20 | 2 |
| 23 | 1 | 23 | 1 |
| Exemple de Kenton |
| The UNIVARIATE Procedure |
| Variable: Caisse (Nombre de caisses de boîtes de céréales) |
| Design de la boîte=3 |
Stem Leaf # Boxplot
23 0 1 |
22 |
21 +-----+
20 0 1 | |
19 *--+--*
18 0 1 | |
17 0 1 +-----+
----+----+----+----+
Normal Probability Plot
23.5+ * ++++
| ++++
| ++++
20.5+ +*++
| +++
| ++*+
17.5+ *++++
+----+----+----+----+----+----+----+----+----+----+
-2 -1 0 +1 +2
|
| Exemple de Kenton |
| The UNIVARIATE Procedure |
| Variable: Caisse (Nombre de caisses de boîtes de céréales) |
| Design de la boîte=4 |
| Moments | |||
| N | 5 | Sum Weights | 5 |
| Mean | 27.2 | Sum Observations | 136 |
| Std Deviation | 3.96232255 | Variance | 15.7 |
| Skewness | 0.35686462 | Kurtosis | 1.45928841 |
| Uncorrected SS | 3762 | Corrected SS | 62.8 |
| Coeff Variation | 14.5673623 | Std Error Mean | 1.77200451 |
| Basic Statistical Measures | |||
| Location | Variability | ||
| Mean | 27.20000 | Std Deviation | 3.96232 |
| Median | 27.00000 | Variance | 15.70000 |
| Mode | . | Range | 11.00000 |
| Interquartile Range | 2.00000 | ||
| Tests for Location: Mu0=0 | ||||
| Test | Statistic | p Value | ||
| Student's t | t | 15.34985 | Pr > |t| | 0.0001 |
| Sign | M | 2.5 | Pr >= |M| | 0.0625 |
| Signed Rank | S | 7.5 | Pr >= |S| | 0.0625 |
| Quantiles (Definition 5) | |
| Quantile | Estimate |
| 100% Max | 33 |
| 99% | 33 |
| 95% | 33 |
| 90% | 33 |
| 75% Q3 | 28 |
| 50% Median | 27 |
| 25% Q1 | 26 |
| 10% | 22 |
| 5% | 22 |
| 1% | 22 |
| 0% Min | 22 |
| Extreme Observations | |||
| Lowest | Highest | ||
| Value | Obs | Value | Obs |
| 22 | 3 | 22 | 3 |
| 26 | 4 | 26 | 4 |
| 27 | 1 | 27 | 1 |
| 28 | 5 | 28 | 5 |
| 33 | 2 | 33 | 2 |
| Exemple de Kenton |
| The UNIVARIATE Procedure |
| Variable: Caisse (Nombre de caisses de boîtes de céréales) |
| Design de la boîte=4 |
Stem Leaf # Boxplot
32 0 1 0
30
28 0 1 +-----+
26 00 2 *--+--*
24
22 0 1 0
----+----+----+----+
Normal Probability Plot
33+ *+++++
| +++++
| ++*++
| * +++*++
| +++++
23+ +*+++
+----+----+----+----+----+----+----+----+----+----+
-2 -1 0 +1 +2
|
| Exemple de Kenton |
| The UNIVARIATE Procedure |
| Variable: Caisse (Nombre de caisses de boîtes de céréales) |
| Schematic Plots |
|
34 +
|
| 0
|
32 +
|
|
|
30 +
|
|
|
28 + +-----+
| | |
| *--+--*
| | |
26 + +-----+
|
|
|
24 +
|
| |
| |
22 + | 0
| +-----+
| | |
| | |
20 + | |
| | + |
| | *-----*
| | | |
18 + | | |
| | +-----+
| | | |
| | |
16 + +-----+ |
| | | |
| *-----* +-----+
| | + | | |
14 + +-----+ | |
| | | + |
| | | |
| | | |
12 + | *-----*
| | | |
| | +-----+
| |
10 + |
------------+-----------+-----------+-----------+-----------
Design 1 2 3 4
|
| Exemple de Kenton |
| The ANOVA Procedure |
| Class Level Information | ||
| Class | Levels | Values |
| Design | 4 | 1 2 3 4 |
| Number of observations | 19 |
| Exemple de Kenton |
| The ANOVA Procedure |
| Dependent Variable: Caisse Nombre de caisses de boîtes de céréales |
| Source | DF | Sum of Squares | Mean Square | F Value | Pr > F |
| Model | 3 | 588.2210526 | 196.0736842 | 18.59 | <.0001 |
| Error | 15 | 158.2000000 | 10.5466667 | ||
| Corrected Total | 18 | 746.4210526 |
| R-Square | Coeff Var | Root MSE | Caisse Mean |
| 0.788055 | 17.43042 | 3.247563 | 18.63158 |
| Source | DF | Anova SS | Mean Square | F Value | Pr > F |
| Design | 3 | 588.2210526 | 196.0736842 | 18.59 | <.0001 |
| Exemple de Kenton |
| The ANOVA Procedure |
| Tukey's Studentized Range (HSD) Test for Caisse |
|
| Alpha | 0.05 |
| Error Degrees of Freedom | 15 |
| Error Mean Square | 10.54667 |
| Critical Value of Studentized Range | 4.07597 |
| Comparisons significant at the 0.05 level are indicated by ***. |
||||
| Design Comparison |
Difference Between Means |
Simultaneous 95% Confidence Limits |
||
| 4 - 3 | 7.700 | 1.421 | 13.979 | *** |
| 4 - 1 | 12.600 | 6.680 | 18.520 | *** |
| 4 - 2 | 13.800 | 7.880 | 19.720 | *** |
| 3 - 4 | -7.700 | -13.979 | -1.421 | *** |
| 3 - 1 | 4.900 | -1.379 | 11.179 | |
| 3 - 2 | 6.100 | -0.179 | 12.379 | |
| 1 - 4 | -12.600 | -18.520 | -6.680 | *** |
| 1 - 3 | -4.900 | -11.179 | 1.379 | |
| 1 - 2 | 1.200 | -4.720 | 7.120 | |
| 2 - 4 | -13.800 | -19.720 | -7.880 | *** |
| 2 - 3 | -6.100 | -12.379 | 0.179 | |
| 2 - 1 | -1.200 | -7.120 | 4.720 | |
| Exemple de Kenton |
| The ANOVA Procedure |
| Bonferroni (Dunn) t Tests for Caisse |
|
| Alpha | 0.05 |
| Error Degrees of Freedom | 15 |
| Error Mean Square | 10.54667 |
| Critical Value of t | 3.03628 |
| Comparisons significant at the 0.05 level are indicated by ***. |
||||
| Design Comparison |
Difference Between Means |
Simultaneous 95% Confidence Limits |
||
| 4 - 3 | 7.700 | 1.085 | 14.315 | *** |
| 4 - 1 | 12.600 | 6.364 | 18.836 | *** |
| 4 - 2 | 13.800 | 7.564 | 20.036 | *** |
| 3 - 4 | -7.700 | -14.315 | -1.085 | *** |
| 3 - 1 | 4.900 | -1.715 | 11.515 | |
| 3 - 2 | 6.100 | -0.515 | 12.715 | |
| 1 - 4 | -12.600 | -18.836 | -6.364 | *** |
| 1 - 3 | -4.900 | -11.515 | 1.715 | |
| 1 - 2 | 1.200 | -5.036 | 7.436 | |
| 2 - 4 | -13.800 | -20.036 | -7.564 | *** |
| 2 - 3 | -6.100 | -12.715 | 0.515 | |
| 2 - 1 | -1.200 | -7.436 | 5.036 | |
| Exemple de Kenton |
| The ANOVA Procedure |
| Scheffe's Test for Caisse |
|
| Alpha | 0.05 |
| Error Degrees of Freedom | 15 |
| Error Mean Square | 10.54667 |
| Critical Value of F | 3.28738 |
| Comparisons significant at the 0.05 level are indicated by ***. |
||||
| Design Comparison |
Difference Between Means |
Simultaneous 95% Confidence Limits |
||
| 4 - 3 | 7.700 | 0.859 | 14.541 | *** |
| 4 - 1 | 12.600 | 6.150 | 19.050 | *** |
| 4 - 2 | 13.800 | 7.350 | 20.250 | *** |
| 3 - 4 | -7.700 | -14.541 | -0.859 | *** |
| 3 - 1 | 4.900 | -1.941 | 11.741 | |
| 3 - 2 | 6.100 | -0.741 | 12.941 | |
| 1 - 4 | -12.600 | -19.050 | -6.150 | *** |
| 1 - 3 | -4.900 | -11.741 | 1.941 | |
| 1 - 2 | 1.200 | -5.250 | 7.650 | |
| 2 - 4 | -13.800 | -20.250 | -7.350 | *** |
| 2 - 3 | -6.100 | -12.941 | 0.741 | |
| 2 - 1 | -1.200 | -7.650 | 5.250 | |
| Exemple de Kenton |
| The ANOVA Procedure |
| Tukey's Studentized Range (HSD) Test for Caisse |
|
| Alpha | 0.05 |
| Error Degrees of Freedom | 15 |
| Error Mean Square | 10.54667 |
| Critical Value of Studentized Range | 4.07597 |
| Minimum Significant Difference | 6.1019 |
| Harmonic Mean of Cell Sizes | 4.705882 |
|
| Means with the same letter are not significantly different. |
|||
| Tukey Grouping | Mean | N | Design |
| A | 27.200 | 5 | 4 |
| B | 19.500 | 4 | 3 |
| B | |||
| B | 14.600 | 5 | 1 |
| B | |||
| B | 13.400 | 5 | 2 |
| Exemple de Kenton |
| The ANOVA Procedure |
| Bonferroni (Dunn) t Tests for Caisse |
|
| Alpha | 0.05 |
| Error Degrees of Freedom | 15 |
| Error Mean Square | 10.54667 |
| Critical Value of t | 3.03628 |
| Minimum Significant Difference | 6.4283 |
| Harmonic Mean of Cell Sizes | 4.705882 |
|
| Means with the same letter are not significantly different. |
|||
| Bon Grouping | Mean | N | Design |
| A | 27.200 | 5 | 4 |
| B | 19.500 | 4 | 3 |
| B | |||
| B | 14.600 | 5 | 1 |
| B | |||
| B | 13.400 | 5 | 2 |
| Exemple de Kenton |
| The ANOVA Procedure |
| Scheffe's Test for Caisse |
|
| Alpha | 0.05 |
| Error Degrees of Freedom | 15 |
| Error Mean Square | 10.54667 |
| Critical Value of F | 3.28738 |
| Minimum Significant Difference | 6.6487 |
| Harmonic Mean of Cell Sizes | 4.705882 |
|
| Means with the same letter are not significantly different. |
|||
| Scheffe Grouping | Mean | N | Design |
| A | 27.200 | 5 | 4 |
| B | 19.500 | 4 | 3 |
| B | |||
| B | 14.600 | 5 | 1 |
| B | |||
| B | 13.400 | 5 | 2 |
| Exemple de Kenton |
| Variance Components Estimation Procedure |
| Class Level Information | ||
| Class | Levels | Values |
| Design | 4 | 1 2 3 4 |
| Number of observations | 19 |
| Dependent Variable: | Caisse |
| Type 1 Analysis of Variance | ||||
| Source | DF | Sum of Squares | Mean Square | Expected Mean Square |
| Design | 3 | 588.221053 | 196.073684 | Var(Error) + 4.7368 Var(Design) |
| Error | 15 | 158.200000 | 10.546667 | Var(Error) |
| Corrected Total | 18 | 746.421053 | . | . |
| Type 1 Estimates | |
| Variance Component | Estimate |
| Var(Design) | 39.16681 |
| Var(Error) | 10.54667 |
| Exemple de Kenton |
| Variance Components Estimation Procedure |
| Class Level Information | ||
| Class | Levels | Values |
| Design | 4 | 1 2 3 4 |
| Number of observations | 19 |
| Dependent Variable: | Caisse |
| Maximum Likelihood Iterations | |||
| Iteration | Objective | Var(Design) | Var(Error) |
| 0 | 55.5695918881 | 45.9439130908 | 9.5653270642 |
| 1 | 55.1015926483 | 28.3686785127 | 10.4537337097 |
| 2 | 55.0994032935 | 27.4608872617 | 10.5348869803 |
| 3 | 55.0994032761 | 27.4633793537 | 10.5346558795 |
| 4 | 55.0994032761 | 27.4633793537 | 10.5346558795 |
| Convergence criteria met. |
| Maximum Likelihood Estimates | |
| Variance Component | Estimate |
| Var(Design) | 27.46338 |
| Var(Error) | 10.53466 |
| Asymptotic Covariance Matrix of Estimates | ||
| Var(Design) | Var(Error) | |
| Var(Design) | 437.84537 | -2.78271 |
| Var(Error) | -2.78271 | 14.76389 |