L’ANALISI GERARCHICA E

LE COMPONENTI DELLA VARIANZA

14.14   LETTURA DI UN TABULATO INFORMATICO

ESEMPIO su alimentazione, genotipo dei maschi e delle femmine: analisi gerarchica della varianza a 3 fattori

 Livello I Livello II Livello III Livello IV  o  Repliche Nidiata Alimentaz. Maschio Femmina n. di figli Peso di ogni figlio 1 I 1 A 4 20, 22, 24, 22 2 I 1 B 5 22, 25, 21, 26, 22 3 I 2 C 6 27, 22, 24, 28, 21, 28 4 I 2 D 4 38, 36, 35, 38 5 I 2 E 5 31, 32, 35, 38, 32 6 II 3 F 4 29, 32, 30, 28 7 II 3 G 5 33, 39, 40, 31, 32 8 II 3 H 3 28, 27, 25 9 II 4 I 3 26, 27, 28 10 II 4 L 3 31, 32, 33 11 II 5 M 4 28, 32, 30, 26 12 II 5 N 3 33, 26, 43 13 II 6 O 5 27, 27, 26, 28, 30 14 II 6 P 5 35, 28, 28, 35, 30 15 II 6 Q 6 32, 33, 33, 33, 35, 31 16 II 6 R 5 33, 35, 31, 26, 27, 17 III 7 S 5 32, 31, 33, 32, 35 18 III 7 T 6 38, 37, 38, 37, 39, 35 19 III 8 U 5 31, 38, 38, 35, 34 20 III 8 V 5 38, 36, 33, 32, 33 21 III 9 X 6 32, 32, 36, 33, 34, 39 22 III 9 Y 6 31, 32, 32, 30, 33, 30 23 III 9 Z 3 37, 35, 40

General Linear Models Procedure

1)

Class            Levels    Values

ALIMENTAZIONE       3    I II III

MASCHIO             9    1 2 3 4 5 6 7 8 9

FEMMINA            23    A B C D E F G H I L M N O P Q R S T U V X Y Z

Number of observations in data set = 106

2)

Dependent Variable: PESO

Source                  DF    Sum of Squares     F Value      Pr > F

Model                   22     1901.70691824       11.35      0.0001

Error                   83      632.06666667

Corrected Total        105     2533.77358491

R-Square              C.V.               PESO Mean

0.750543          8.805391              31.3396226

Source                  DF         Type I SS     F Value      Pr > F

ALIMENT                  2      660.43723225       43.36      0.0001

MASCHIO                  6      418.19046521        9.15      0.0001

FEMMINA                 14      823.07922078        7.72      0.0001

3)

Student-Newman-Keuls test for variable: PESO

NOTE: This test controls the type I experimentwise error rate

under the complete null hypothesis but not under partial

null hypotheses.

Alpha= 0.05  df= 83  MSE= 7.615261

WARNING: Cell sizes are not equal.

Harmonic Mean of cell sizes= 32.90066

Number of Means         2         3

Critical Range  1.3532596 1.6237331

Means with the same letter are not significantly different.

SNK Grouping              Mean      N  ALIMENTI

A           34.4722     36    III

B           30.6957     46    II

C           27.8750     24    I

4)

Tukey's Studentized Range (HSD) Test for variable: PESO

NOTE: This test controls the type I experimentwise error rate,

but generally has a higher type II error rate than REGWQ.

Alpha= 0.05  df= 83  MSE= 7.615261

Critical Value of Studentized Range= 3.375

Minimum Significant Difference= 1.6237

WARNING: Cell sizes are not equal.

Harmonic Mean of cell sizes= 32.90066

Means with the same letter are not significantly different.

Tukey Grouping              Mean      N  ALIMENT

A           34.4722     36    III

B           30.6957     46    II

C           27.8750     24    I

5)

Scheffe's test for variable: PESO

NOTE: This test controls the type I experimentwise error rate

but generally has a higher type II error rate than REGWF

for all pairwise comparisons

Alpha= 0.05  df= 83  MSE= 7.615261

Critical Value of F= 3.10651

Minimum Significant Difference= 1.6959

WARNING: Cell sizes are not equal.

Harmonic Mean of cell sizes= 32.90066

Means with the same letter are not significantly different.

Scheffe Grouping              Mean      N  ALIMENT

A           34.4722     36    III

B           30.6957     46    II

C           27.8750     24    I

6)

Dunnett's T tests for variable: PESO

NOTE: This tests controls the type I experimentwise error for

comparisons of all treatments against a control.

Alpha= 0.05  Confidence= 0.95  df= 83  MSE= 7.615261

Critical Value of Dunnett's T= 2.695

Comparisons significant at the 0.05 level are indicated by '***'.

Simultaneous            Simultaneous

Lower    Difference     Upper

MASCHIO       Confidence    Between   Confidence

Comparison        Limit       Means       Limit

7 - 1          9.1728     12.5152     15.8575   ***

8 - 1          8.7166     12.1333     15.5501   ***

9 - 1          7.9312     11.0667     14.2021   ***

3 - 1          5.2209      8.5000     11.7791   ***

5 - 1          4.7286      8.4762     12.2238   ***

2 - 1          5.1979      8.3333     11.4688   ***

6 - 1          4.9897      7.9524     10.9151   ***

4 - 1          2.9140      6.8333     10.7526   ***

7)

Student-Newman-Keuls test for variable: PESO

NOTE: This test controls the type I experimentwise error rate

under the complete null hypothesis but not under partial

null hypotheses.

Alpha= 0.05  df= 83  MSE= 7.615261

WARNING: Cell sizes are not equal.

Harmonic Mean of cell sizes= 10.27597

Number of Means         2         3         4         5

Critical Range  2.4214306 2.9053974 3.1919379 3.3950041

Number of Means         6         7         8         9

Critical Range  3.5517011  3.678912 3.7857504  3.877692

Means with the same letter are not significantly different.

SNK Grouping              Mean      N  MASCHIO

A            35.182     11    7

A

A            34.800     10    8

A

B       A            33.733     15    9

B

B       C            31.167     12    3

B       C

B       C            31.143      7    5

B       C

B       C            31.000     15    2

B       C

B       C            30.619     21    6

C

C            29.500      6    4

D            22.667      9    1

8)

Tukey's Studentized Range (HSD) Test for variable: PESO

NOTE: This test controls the type I experimentwise error rate,

but generally has a higher type II error rate than REGWQ.

Alpha= 0.05  df= 83  MSE= 7.615261

Critical Value of Studentized Range= 4.504

Minimum Significant Difference= 3.8777

WARNING: Cell sizes are not equal.

Harmonic Mean of cell sizes= 10.27597

Means with the same letter are not significantly different.

Tukey Grouping              Mean      N  MASCHIO

A            35.182     11    7

A

B       A            34.800     10    8

B       A

B       A   C        33.733     15    9

B           C

B       D   C        31.167     12    3

B       D   C

B       D   C        31.143      7    5

B       D   C

B       D   C        31.000     15    2

D   C

D   C        30.619     21    6

D

D            29.500      6    4

E            22.667      9    1

9)

Scheffe's test for variable: PESO

NOTE: This test controls the type I experimentwise error rate

but generally has a higher type II error rate than REGWF

for all pairwise comparisons

Alpha= 0.05  df= 83  MSE= 7.615261

Critical Value of F= 2.05201

Minimum Significant Difference= 4.9327

WARNING: Cell sizes are not equal.

Harmonic Mean of cell sizes= 10.27597

Means with the same letter are not significantly different.

Scheffe Grouping              Mean      N  MASCHIO

A            35.182     11    7

A

A            34.800     10    8

A

B       A            33.733     15    9

B       A

B       A            31.167     12    3

B       A

B       A            31.143      7    5

B       A

B       A            31.000     15    2

B       A

B       A            30.619     21    6

B

B                    29.500      6    4

C            22.667      9    1

10)

Student-Newman-Keuls test for variable: PESO

NOTE: This test controls the type I experimentwise error rate

under the complete null hypothesis but not under partial

null hypotheses.

Alpha= 0.05  df= 83  MSE= 7.615261

WARNING: Cell sizes are not equal.

Harmonic Mean of cell sizes= 4.339623

Number of Means         2         3         4         5         6

Critical Range  3.7261254  4.470859 4.9117908 5.2242715 5.4653986

Number of Means         7         8         9        10        11

Critical Range  5.6611522 5.8255563 5.9670372 6.0910485 6.2013191

Number of Means        12        13        14        15        16

Critical Range  6.3005091 6.3905809  6.473023 6.5489903 6.6193966

Number of Means        17        18        19        20        21

Critical Range  6.6849769 6.7463311 6.8039548 6.8582624 6.9096034

Number of Means        22        23

Critical Range  6.9582756 7.0045344

Means with the same letter are not significantly different.

SNK Grouping              Mean      N  FEMMINA

A            37.333      3    Z

A

A            37.333      6    T

A

B       A            36.750      4    D

B       A

B       A   C        35.200      5    U

B       A   C

B       A   C        35.000      5    G

B       A   C

B       A   C        34.400      5    V

B       A   C

B       A   C        34.333      6    X

B       A   C

B       A   C        34.000      3    N

B       A   C

B   D   A   C        33.600      5    E

B   D   A   C

E   B   D   A   C        32.833      6    Q

E   B   D   A   C

E   B   D   A   C        32.600      5    S

E   B   D   A   C

E   B   D   A   C        32.000      3    L

E   B   D   A   C

E   B   D   A   C        31.333      6    Y

E   B   D   A   C

E   B   D   A   C        31.200      5    P

E   B   D       C

E   B   D   F   C        30.400      5    R

E       D   F   C

E       D   F   C        29.750      4    F

E       D   F   C

E       D   F   C        29.000      4    M

E       D   F

E   G   D   F            27.600      5    O

E   G       F

E   G       F   H        27.000      3    I

E   G       F   H

E   G       F   H        26.667      3    H

G       F   H

G       F   H        25.000      6    C

G           H

G           H        23.200      5    B

H

H        22.000      4

11)

Tukey's Studentized Range (HSD) Test for variable: PESO

NOTE: This test controls the type I experimentwise error rate,

but generally has a higher type II error rate than REGWQ.

Alpha= 0.05  df= 83  MSE= 7.615261

Critical Value of Studentized Range= 5.288

Minimum Significant Difference= 7.0045

WARNING: Cell sizes are not equal.

Harmonic Mean of cell sizes= 4.339623

Means with the same letter are not significantly different.

Tukey Grouping              Mean      N  FEMMINA

A            37.333      3    Z

A

A            37.333      6    T

A

B       A            36.750      4    D

B       A

B       A   C        35.200      5    U

B       A   C

B       A   C        35.000      5    G

B       A   C

B   D   A   C        34.400      5    V

B   D   A   C

B   D   A   C        34.333      6    X

B   D   A   C

E   B   D   A   C        34.000      3    N

E   B   D   A   C

E   B   D   A   C F      33.600      5    E

E   B   D   A   C F

E   B   D   A   C F      32.833      6    Q

E   B   D   A   C F

E   B   D   A   C F      32.600      5    S

E   B   D   A   C F

E   B   D   A G C F      32.000      3    L

E   B   D   A G C F

E   B   D   A G C F      31.333      6    Y

E   B   D   A G C F

E   B   D   A G C F      31.200      5    P

E   B   D   A G C F

E   B   D   A G C F      30.400      5    R

E   B   D     G C F

E   B   D   H G C F      29.750      4    F

E       D   H G C F

E   I   D   H G C F      29.000      4    M

E   I   D   H G   F

E   I   D   H G   F      27.600      5    O

E   I       H G   F

E   I       H G   F      27.000      3    I

I       H G   F

I       H G   F      26.667      3    H

I       H G

I       H G          25.000      6    C

I       H

I       H            23.200      5    B

I

I                    22.000      4    A

12)

Scheffe's test for variable: PESO

NOTE: This test controls the type I experimentwise error rate

but generally has a higher type II error rate than REGWF

for all pairwise comparisons

Alpha= 0.05  df= 83  MSE= 7.615261

Critical Value of F= 1.67191

Minimum Significant Difference= 11.362

WARNING: Cell sizes are not equal.

Harmonic Mean of cell sizes= 4.339623

Means with the same letter are not significantly different.

Scheffe Grouping              Mean      N  FEMMINA

A            37.333      3    Z

A

A            37.333      6    T

A

A            36.750      4    D

A

B       A            35.200      5    U

B       A

B       A            35.000      5    G

B       A

B       A   C        34.400      5    V

B       A   C

B       A   C        34.333      6    X

B       A   C

B       A   C        34.000      3    N

B       A   C

B       A   C        33.600      5    E

B       A   C

B   D   A   C        32.833      6    Q

B   D   A   C

B   D   A   C        32.600      5    S

B   D   A   C

B   D   A   C        32.000      3    L

B   D   A   C

B   D   A   C        31.333      6    Y

B   D   A   C

B   D   A   C        31.200      5    P

B   D   A   C

B   D   A   C        30.400      5    R

B   D   A   C

B   D   A   C        29.750      4    F

B   D   A   C

B   D   A   C        29.000      4    M

B   D   A   C

B   D   A   C        27.600      5    O

B   D   A   C

B   D   A   C        27.000      3    I

B   D   A   C

B   D   A   C        26.667      3    H

B   D       C

B   D       C        25.000      6    C

D       C

D       C        23.200      5    B

D

D                22.000      4    A

Manuale di Statistica per la Ricerca e la Professione  © Lamberto Soliani   - Dipartimento di Scienze Ambientali, Università di Parma  (apr 05 ed)  ebook version by SixSigmaIn Team  - © 2007