Main results and main conclusions see at the end.

 

General Linear Model

Notes
Output Created 06-MAY-2005 18:36:09
Comments
Input Filter <none>
Weight <none>
Split File <none>
N of Rows in Working Data File 22
Missing Value Handling Definition of Missing User-defined missing values are treated as missing.
Cases Used Statistics are based on all cases with valid data for all variables in the model.
Syntax GLM
sinus11 wawe11 knot11 hump11 hsknot11 ashump11 sinus17 wawe17 knot17 hump17
hsknot17 ashump17 sinus23 wawe23 knot23 hump23 hsknot23 ashump23
/WSFACTOR = linewid 3 Polynomial distorti 6 Polynomial
/METHOD = SSTYPE(3)
/SAVE = PRED
/PLOT = PROFILE( distorti*linewid )
/EMMEANS = TABLES(OVERALL)
/PRINT = DESCRIPTIVE
/CRITERIA = ALPHA(.05)
/WSDESIGN = linewid distorti linewid*distorti .

 

Within-Subjects Factors
Measure: MEASURE_1
LINEWID DISTORTI Dependent Variable
1 1 SINUS11
2 WAVE11
3 KNOT11
4 HUMP11
5 HSKNOT11
6 ASHUMP11
2 1 SINUS17
2 WAVE17
3 KNOT17
4 HUMP17
5 HSKNOT17
6 ASHUMP17
3 1 SINUS23
2 WAVE23
3 KNOT23
4 HUMP23
5 HSKNOT23
6 ASHUMP23

Descriptive Statistics

Mean Std. Deviation N
SINUS11 3,45 1,371 22
WAVE11 3,68 1,937 22
KNOT11 3,82 1,868 22
HUMP11 5,86 4,754 22
HSKNOT11 7,45 6,375 22
ASHUMP11 4,41 1,919 22
SINUS17 3,64 1,590 22
WAVE17 3,86 2,031 22
KNOT17 4,09 1,411 22
HUMP17 5,77 3,624 22
HSKNOT17 7,59 3,924 22
ASHUMP17 5,59 2,856 22
SINUS23 4,05 1,618 22
WAVE23 3,41 1,436 22
KNOT23 4,41 1,501 22
HUMP23 4,59 1,790 22
HSKNOT23 7,32 4,581 22
ASHUMP23 5,05 2,681 22

Multivariate Tests(b)
Effect Value F Hypothesis df Error df Sig.
LINEWID Pillai's Trace ,111 1,254(a) 2,000 20,000 ,307
Wilks' Lambda ,889 1,254(a) 2,000 20,000 ,307
Hotelling's Trace ,125 1,254(a) 2,000 20,000 ,307
Roy's Largest Root ,125 1,254(a) 2,000 20,000 ,307
DISTORTI Pillai's Trace ,717 8,614(a) 5,000 17,000 ,000
Wilks' Lambda ,283 8,614(a) 5,000 17,000 ,000
Hotelling's Trace 2,534 8,614(a) 5,000 17,000 ,000
Roy's Largest Root 2,534 8,614(a) 5,000 17,000 ,000
LINEWID * DISTORTI Pillai's Trace ,476 1,088(a) 10,000 12,000 ,438
Wilks' Lambda ,524 1,088(a) 10,000 12,000 ,438
Hotelling's Trace ,907 1,088(a) 10,000 12,000 ,438
Roy's Largest Root ,907 1,088(a) 10,000 12,000 ,438
a Exact statistic
b Design: Intercept
Within Subjects Design: LINEWID+DISTORTI+LINEWID*DISTORTI





Mauchly's Test of Sphericity(b)
Measure: MEASURE_1

Mauchly's W Approx. Chi-Square df Sig. Epsilon(a)
Within Subjects Effect Greenhouse-Geisser Huynh-Feldt Lower-bound
LINEWID ,734 6,196 2 ,045 ,790 ,843 ,500
DISTORTI ,008 93,422 14 ,000 ,317 ,338 ,200
LINEWID * DISTORTI ,002 112,000 54 ,000 ,438 ,568 ,100
Tests the null hypothesis that the error covariance matrix of the orthonormalized transformed dependent variables is proportional to an identity matrix.
a May be used to adjust the degrees of freedom for the averaged tests of significance. Corrected tests are displayed in the Tests of Within-Subjects Effects table.
b Design: Intercept
Within Subjects Design: LINEWID+DISTORTI+LINEWID*DISTORTI

Tests of Within-Subjects Effects
Measure: MEASURE_1
Source Type III Sum of Squares df Mean Square F Sig.
LINEWID Sphericity Assumed 7,914 2 3,957 ,649 ,528
Greenhouse-Geisser 7,914 1,579 5,011 ,649 ,494
Huynh-Feldt 7,914 1,686 4,694 ,649 ,503
Lower-bound 7,914 1,000 7,914 ,649 ,429
Error(LINEWID) Sphericity Assumed 255,975 42 6,095

Greenhouse-Geisser 255,975 33,165 7,718

Huynh-Feldt 255,975 35,407 7,230

Lower-bound 255,975 21,000 12,189

DISTORTI Sphericity Assumed 686,255 5 137,251 15,708 ,000
Greenhouse-Geisser 686,255 1,584 433,229 15,708 ,000
Huynh-Feldt 686,255 1,692 405,623 15,708 ,000
Lower-bound 686,255 1,000 686,255 15,708 ,001
Error(DISTORTI) Sphericity Assumed 917,467 105 8,738

Greenhouse-Geisser 917,467 33,265 27,581

Huynh-Feldt 917,467 35,529 25,823

Lower-bound 917,467 21,000 43,689

LINEWID * DISTORTI Sphericity Assumed 40,662 10 4,066 1,163 ,317
Greenhouse-Geisser 40,662 4,382 9,278 1,163 ,333
Huynh-Feldt 40,662 5,682 7,157 1,163 ,331
Lower-bound 40,662 1,000 40,662 1,163 ,293
Error(LINEWID*DISTORTI) Sphericity Assumed 734,116 210 3,496

Greenhouse-Geisser 734,116 92,031 7,977

Huynh-Feldt 734,116 119,313 6,153

Lower-bound 734,116 21,000 34,958


Tests of Within-Subjects Contrasts
Measure: MEASURE_1
Source LINEWID DISTORTI Type III Sum of Squares df Mean Square F Sig.
LINEWID Linear
3,409E-02 1 3,409E-02 ,004 ,952
Quadratic
7,880 1 7,880 2,616 ,121
Error(LINEWID) Linear
192,716 21 9,177

Quadratic
63,259 21 3,012

DISTORTI
Linear 348,563 1 348,563 30,787 ,000
Quadratic 24,030 1 24,030 3,383 ,080
Cubic 235,037 1 235,037 13,606 ,001
Order 4 72,884 1 72,884 13,688 ,001
Order 5 5,741 1 5,741 2,153 ,157
Error(DISTORTI)
Linear 237,756 21 11,322

Quadratic 149,156 21 7,103

Cubic 362,754 21 17,274

Order 4 111,819 21 5,325

Order 5 55,983 21 2,666

LINEWID * DISTORTI Linear Linear ,237 1 ,237 ,072 ,791
Quadratic 11,260 1 11,260 4,067 ,057
Cubic 2,766 1 2,766 ,530 ,475
Order 4 ,468 1 ,468 ,161 ,693
Order 5 16,214 1 16,214 6,216 ,021
Quadratic Linear 5,479 1 5,479 1,782 ,196
Quadratic ,225 1 ,225 ,096 ,760
Cubic ,947 1 ,947 ,237 ,632
Order 4 2,706E-02 1 2,706E-02 ,006 ,938
Order 5 3,040 1 3,040 ,695 ,414
Error(LINEWID*DISTORTI) Linear Linear 69,142 21 3,292

Quadratic 58,133 21 2,768

Cubic 109,618 21 5,220

Order 4 61,140 21 2,911

Order 5 54,775 21 2,608

Quadratic Linear 64,581 21 3,075

Quadratic 49,517 21 2,358

Cubic 84,007 21 4,000

Order 4 91,342 21 4,350

Order 5 91,863 21 4,374


Tests of Between-Subjects Effects
Measure: MEASURE_1
Transformed Variable: Average
Source Type III Sum of Squares df Mean Square F Sig.
Intercept 9474,669 1 9474,669 137,604 ,000
Error 1445,942 21 68,854



 

 

Profile Plots

Distorti * linewid

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

LINEWID = Width of lines in grid 

1 11 pixels
2 17 pixels
3 23 pixels

 

DISTORTI = Distrotion types

1 SINUS Sinus
2 WAVE Wave
3 KNOT Knot
4 HUMP Hump
5 HSKNOT Half sided knot
6 ASHUMP Asymmetrical hump

 

 

 

 

 

 

RESULTS AND CONCLUSIONS

 

MAIN RESULTS:

(1) the average of  distortion tolerance of  the ’Half sided kont’ is significantly higher than every other averages;

(2) the line width has no significant effect.

 

MAIN CONCLUSIONS: 

(1)  the main cause of the Hermann grid illusion is the straightness of the black-white edges; (Only the Half sided knot includes straight edges!)

(2) the line width plays no significant role.

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Budapest,  May 02, 2005.,

revised: May 07. 2005

 

János GEIER