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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

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

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

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

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

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

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 ***

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 34.800 10 8

B A 33.733 15 9

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 29.500 6 4

D 22.667 9 1

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

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 29.500 6 4

E 22.667 9 1

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 34.800 10 8

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 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 37.333 6 T

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 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 37.333 6 T

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 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 37.333 6 T

A 36.750 4 D

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 22.000 4 A