|
analisi FATTORIALE E disegni complessi CON FATTORI INCROCIATI
12.10. LETTURA DI UN TABULATO INFORMATICO
Sono riportati due tabulati di calcolatore su esempi già discussi nel capitolo.
ESEMPIO. Si vuole verificare se insetti adulti della stessa specie che vivono in 4 località differenti (A, B, C, D) hanno differenze significative nelle loro dimensioni, considerando pure che dalla primavera all'autunno continuano ad aumentare.
Risposta
General Linear Models Procedure
1) Class Levels Values
STAGIONE 3 autunno estate primaver
LOCALITA 4 a b c d
Number of observations in data set = 24
2) Dependent Variable: INSETTI
Source DF Sum of Squares F Value Pr > F
Model 11 3052.12500000 13.40 0.0001
Error 12 248.50000000
Corrected Total 23 3300.62500000
R-Square C.V. INSETTI Mean
0.924711 6.779353 67.1250000
Source DF Type I SS F Value Pr > F
STAGIONE 2 1870.75000000 45.17 0.0001 LOCALITA 3 1084.12500000 17.45 0.0001 STAGIONE*LOCALITA 6 97.25000000 0.78 0.5995
Source DF Type III SS F Value Pr > F
STAGIONE 2 1870.75000000 45.17 0.0001 LOCALITA 3 1084.12500000 17.45 0.0001 STAGIONE*LOCALITA 6 97.25000000 0.78 0.5995
3) Tukey's Studentized Range (HSD) Test for variable: INSETTI
NOTE: This test controls the type I experimentwise error rate.
Alpha= 0.05 Confidence= 0.95 df= 12 MSE= 20.70833 Critical Value of Studentized Range= 3.773 Minimum Significant Difference= 6.07
Comparisons significant at the 0.05 level are indicated by '***'.
Simultaneous Simultaneous Lower Difference Upper STAGIONE Confidence Between Confidence Comparison Limit Means Limit
autunno - estate 4.555 11.625 16.695 *** autunno - primaver 15.555 21.625 27.695 ***
estate - autunno -16.695 -11.625 -4.555 *** estate - primaver 4.930 11.000 17.070 ***
primaver - autunno -27.695 -21.625 -15.555 *** primaver - estate -17.070 -11.000 -4.930 ***
4) Scheffe's test for variable: INSETTI
NOTE: This test controls the type I experimentwise error rate but generally has a higher type II error rate than Tukey's for all pairwise comparisons.
Alpha= 0.05 Confidence= 0.95 df= 12 MSE= 20.70833 Critical Value of F= 3.88529 Minimum Significant Difference= 6.3426
Comparisons significant at the 0.05 level are indicated by '***'.
Simultaneous Simultaneous Lower Difference Upper STAGIONE Confidence Between Confidence Comparison Limit Means Limit
autunno - estate 4.282 11.625 16.968 *** autunno - primaver 15.282 21.625 27.968 ***
estate - autunno -16.968 -11.625 -4.282 *** estate - primaver 4.657 11.000 17.343 ***
primaver - autunno -27.968 -21.625 -15.282 *** primaver - estate -17.343 -11.000 -4.657 ***
5) Dunnett's T tests for variable: INSETTI
NOTE: This tests controls the type I experimentwise error for comparisons of all treatments against a control.
Alpha= 0.05 Confidence= 0.95 df= 12 MSE= 20.70833 Critical Value of Dunnett's T= 2.502 Minimum Significant Difference= 5.6938
Comparisons significant at the 0.05 level are indicated by '***'.
Simultaneous Simultaneous Lower Difference Upper STAGIONE Confidence Between Confidence Comparison Limit Means Limit
estate - autunno -16.319 -11.625 -4.931 *** primaver - autunno -27.319 -21.625 -15.931 ***
6) Student-Newman-Keuls test for variable: INSETTI
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= 12 MSE= 20.70833
Number of Means 2 3 Critical Range 4.9574623 6.0700016
Means with the same letter are not significantly different.
SNK Grouping Mean N STAGIONE
A 77.875 8 autunno
B 67.250 8 estate
C 56.250 8 primavera
7) Tukey's Studentized Range (HSD) Test for variable: INSETTI
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= 12 MSE= 20.70833 Critical Value of Studentized Range= 3.773 Minimum Significant Difference= 6.07
Means with the same letter are not significantly different.
Tukey Grouping Mean N STAGIONE
A 77.875 8 autunno
B 67.250 8 estate
C 56.250 8 primavera
8) Scheffe's test for variable: INSETTI
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= 12 MSE= 20.70833 Critical Value of F= 3.88529 Minimum Significant Difference= 6.3426
Means with the same letter are not significantly different.
Scheffe Grouping Mean N STAGIONE
A 77.875 8 autunno
B 67.250 8 estate
C 56.250 8 primavera
9) Tukey's Studentized Range (HSD) Test for variable: INSETTI
NOTE: This test controls the type I experimentwise error rate.
Alpha= 0.05 Confidence= 0.95 df= 12 MSE= 20.70833 Critical Value of Studentized Range= 4.199 Minimum Significant Difference= 7.8
Comparisons significant at the 0.05 level are indicated by '***'.
Simultaneous Simultaneous Lower Difference Upper LOCALITA Confidence Between Confidence Comparison Limit Means Limit
c - b -1.800 6.000 13.800 c - a 7.700 15.500 23.300 *** c - d 8.200 16.000 23.800 ***
b - c -13.800 -6.000 1.800 b - a 1.700 9.500 17.300 *** b - d 2.200 11.000 17.800 ***
a - c -23.300 -15.500 -7.700 *** a - b -17.300 -9.500 -1.700 *** a - d -7.300 0.500 8.300
d - c -23.800 -16.000 -8.200 *** d - b -17.800 -11.000 -2.200 *** d - a -8.300 -0.500 7.300
10)
Scheffe's test for variable: INSETTI
NOTE: This test controls the type I experimentwise error rate but generally has a higher type II error rate than Tukey's for all pairwise comparisons.
Alpha= 0.05 Confidence= 0.95 df= 12 MSE= 20.70833 Critical Value of F= 3.49029 Minimum Significant Difference= 8.5017
Comparisons significant at the 0.05 level are indicated by '***'.
Simultaneous Simultaneous Lower Difference Upper LOCALITA Confidence Between Confidence Comparison Limit Means Limit
c - b -2.502 6.000 14.502 c - a 6.998 15.500 24.002 *** c - d 7.498 16.000 24.502 ***
b - c -14.502 -6.000 2.502 b - a 0.998 9.500 18.002 *** b - d 1.498 11.000 18.502 ***
a - c -24.002 -15.500 -6.998 *** a - b -18.002 -9.500 -0.998 *** a - d -8.002 0.500 9.002
d - c -24.502 -16.000 -7.498 *** d - b -18.502 -11.000 -1.498 *** d - a -9.002 -0.500 8.002
11)
Dunnett's T tests for variable: INSETTI
NOTE: This tests controls the type I experimentwise error for comparisons of all treatments against a control.
Alpha= 0.05 Confidence= 0.95 df= 12 MSE= 20.70833 Critical Value of Dunnett's T= 2.683 Minimum Significant Difference= 7.0489
Comparisons significant at the 0.05 level are indicated by '***'.
Simultaneous Simultaneous Lower Difference Upper LOCALITA Confidence Between Confidence Comparison Limit Means Limit
c - a 8.451 15.500 22.549 *** b - a 2.451 9.500 16.549 *** d - a -7.549 -0.500 6.549
12)
Student-Newman-Keuls test for variable: INSETTI
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= 12 MSE= 20.70833
Number of Means 2 3 4 Critical Range 5.7243844 7.0090341 7.8000392
Means with the same letter are not significantly different.
SNK Grouping Mean N LOCALITA
A 76.500 6 c
B 70.500 6 b
C 61.000 6 a C C 60.500 6 d
13) Tukey's Studentized Range (HSD) Test for variable: INSETTI
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= 12 MSE= 20.70833 Critical Value of Studentized Range= 4.199 Minimum Significant Difference= 7.8
Means with the same letter are not significantly different.
Tukey Grouping Mean N LOCALITA
A 76.500 6 c A A 70.500 6 b
B 61.000 6 a B B 60.500 6 d
14) Scheffe's test for variable: INSETTI
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= 12 MSE= 20.70833 Critical Value of F= 3.49029 Minimum Significant Difference= 8.5017
Means with the same letter are not significantly different.
Scheffe Grouping Mean N LOCALITA
A 76.500 6 c A A 70.500 6 b
B 61.000 6 a B B 60.500 6 d
Level of Level of -----------INSETTI----------- STAGIONE LOCALITA N Mean SD
autunno a 2 74.5000000 6.36396103 autunno b 2 78.5000000 4.94974747 autunno c 2 85.0000000 4.24264069 autunno d 2 73.5000000 4.94974747 estate a 2 61.0000000 5.65685425 estate b 2 73.0000000 5.65685425 estate c 2 77.0000000 4.24264069 estate d 2 58.0000000 2.82842712 primaver a 2 47.5000000 3.53553391 primaver b 2 60.0000000 4.24264069 primaver c 2 67.5000000 3.53553391 primaver d 2 50.0000000 2.82842712
| |||||||||||||||||||||||||||||||||||||||||
| 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 | |||||||||||||||||||||||||||||||||||||||||