A marketing firm was testing a new television.Five volunteers were asked to judge the clarity of the picture from varying viewing distances.  They were told to rate the television on a 8-point scale, “0” Very Bad “7” Excellent, from four distances..  The ratings are below.  Person        9 feet        12 feet      15 feet         18 feet   A          3                4               7             6          P=20 n=5  B          0                3               6             3          P=12 k=4  C          2                1               5             4          P=12 N=20  D          0                1               4             3          P=8 G=60  E           0                1               3             4          P=8 ∑X2=262                T=5         T=10          T=25        T=20              SS=8        SS=9          SS=10     SS=6

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A marketing firm was testing a new television.Five volunteers were asked to judge the clarity of the picture from varying viewing distances.  They were told to rate the television on a 8-point scale, “0” Very Bad “7” Excellent, from four distances..  The ratings are below. 

Person        9 feet        12 feet      15 feet         18 feet  

A          3                4               7             6          P=20 n=5 

B          0                3               6             3          P=12 k=4 

C          2                1               5             4          P=12 N=20 

D          0                1               4             3          P=8 G=60 

E           0                1               3             4          P=8 ∑X2=262 

 

            T=5         T=10          T=25        T=20 

            SS=8        SS=9          SS=10     SS=6 

 

Using the output below and α=.01 two tailed...

What was the obtained value of the omnibus F?_______________________________ 

How many degrees of freedom are used to identify the critical value of the F_______________ 

 

Multivariate Tests
Effect
Value
F
Hypothesis df Error df Sig
factor1 Pillal's Trace
989 136.250
2.000
3.000 .001
Wilks' Lambda
.011 136.250
2.000
3.000 .001
Hotelling's Trace
90.833 136.250°
2.000
3.000 .001
Roy's Largest Root 90.833 136.250
2.000
3.000 .001
Multivariate Tests
Noncent.
Effect
Partial Eta Squared
Parameter
Observed Power
factor1
Pilla's Trace
.989
272.500
1.000
Wilks' Lambda
.989
272.500
1.000
Hotelling's
Trace
.989
272.500
1.000
Roy's Largest
Root
.989
272.500
1.000
Mauchly's Test of Sphericity
Measure: MEASURE 1
Within Subjects
Effect
Approx.
Mauchly's W Chi-Square
df
Sig.
Epsilon
Greenhouse-Geisser
factor1
.000
.533
Mauchly's Test of Sphericity
Measure: MEASURE_1
Within Subjects Effect
Epsilon
Huynh-Feldt
Lower-bound
factor1
.833
333
Tests of Within-Subjects Effects
Measure: MEASURE_1
Type Illi Sum
of Squares
Mean
Square
16.667 25.000
31.250 25.000
Source
df
F
Sig.
Sphericity Assumed
Greenhouse-Geisser
Huynh-Feldt
factor1
50.000
.000
50.000
1.600
.001
50.000
2.500
20.000 25.000
.000
Lower-bound
50.000
1.000
50.000
5.000
.007
Transcribed Image Text:Multivariate Tests Effect Value F Hypothesis df Error df Sig factor1 Pillal's Trace 989 136.250 2.000 3.000 .001 Wilks' Lambda .011 136.250 2.000 3.000 .001 Hotelling's Trace 90.833 136.250° 2.000 3.000 .001 Roy's Largest Root 90.833 136.250 2.000 3.000 .001 Multivariate Tests Noncent. Effect Partial Eta Squared Parameter Observed Power factor1 Pilla's Trace .989 272.500 1.000 Wilks' Lambda .989 272.500 1.000 Hotelling's Trace .989 272.500 1.000 Roy's Largest Root .989 272.500 1.000 Mauchly's Test of Sphericity Measure: MEASURE 1 Within Subjects Effect Approx. Mauchly's W Chi-Square df Sig. Epsilon Greenhouse-Geisser factor1 .000 .533 Mauchly's Test of Sphericity Measure: MEASURE_1 Within Subjects Effect Epsilon Huynh-Feldt Lower-bound factor1 .833 333 Tests of Within-Subjects Effects Measure: MEASURE_1 Type Illi Sum of Squares Mean Square 16.667 25.000 31.250 25.000 Source df F Sig. Sphericity Assumed Greenhouse-Geisser Huynh-Feldt factor1 50.000 .000 50.000 1.600 .001 50.000 2.500 20.000 25.000 .000 Lower-bound 50.000 1.000 50.000 5.000 .007
Error(factor1) Sphericity Assumed
8.000
12
.667
Greenhouse-Geisser
Huynh-Feldt
8.000
6.400
1.250
8.000
10.000
.800
Lower-bound
8.000
4.000
2.000
Tests of Within-Subjects Effects
Measure: MEASURE_1
Partial Eta
Squared
Noncent.
Parameter
Observed
Power
Source
factor1
Sphericity Assumed
862
75.000
1.000
Greenhouse-Geisser
.862
40.000
.997
Huynh-Feldt
.862
62.500
1.000
Lower-bound
862
25.000
.955
Error(factor1)
Sphericity Assumed
Greenhouse-Geisser
Huynh-Feldt
Lower-bound
a. Computed using alpha = .05
Tests of Within-Subjects Contrasts
Measure: MEASURE_1
Type Illi Sum
of Squares
Source
factor1
df Mean Square
F
Sig.
36.000 360.000 .000
3.333 .142
factor1
Linear
36.000 1
Quadratic
5.000
5.000
Cubic
9.000| 1
9.000
22.500 .009
Error(factor1) Linear
400| 4
.100
Quadratic
6.000 4
1.500
Cubic
1.600
4
400
Tests of Within-Subjects Contrasts
Measure: MEASURE_1
Source
factor1
Partial Eta Squared Noncent. Parameter Observed Power
factor1
Linear
.989
360.000
1.000
Quadratic
455
3.333
290
Cubic
849
22.500
.936
Error(factor1) Linear
Quadratic
Cubic
a. Computed using alpha = .05
Tests of Between-Subjects Effects
Measure: MEASURE 1
Transformed Variable: Average
Type III Sum of
Squares
180.000 1
24.000 4
df Mean Square
Partial Eta
Squared
Source
F
Sig.
Intercept
180.000 30.000 |.005
.882
Error
6.000
Tests of Between-Subjects Effects
Measure: MEASURE_1
Transcribed Image Text:Error(factor1) Sphericity Assumed 8.000 12 .667 Greenhouse-Geisser Huynh-Feldt 8.000 6.400 1.250 8.000 10.000 .800 Lower-bound 8.000 4.000 2.000 Tests of Within-Subjects Effects Measure: MEASURE_1 Partial Eta Squared Noncent. Parameter Observed Power Source factor1 Sphericity Assumed 862 75.000 1.000 Greenhouse-Geisser .862 40.000 .997 Huynh-Feldt .862 62.500 1.000 Lower-bound 862 25.000 .955 Error(factor1) Sphericity Assumed Greenhouse-Geisser Huynh-Feldt Lower-bound a. Computed using alpha = .05 Tests of Within-Subjects Contrasts Measure: MEASURE_1 Type Illi Sum of Squares Source factor1 df Mean Square F Sig. 36.000 360.000 .000 3.333 .142 factor1 Linear 36.000 1 Quadratic 5.000 5.000 Cubic 9.000| 1 9.000 22.500 .009 Error(factor1) Linear 400| 4 .100 Quadratic 6.000 4 1.500 Cubic 1.600 4 400 Tests of Within-Subjects Contrasts Measure: MEASURE_1 Source factor1 Partial Eta Squared Noncent. Parameter Observed Power factor1 Linear .989 360.000 1.000 Quadratic 455 3.333 290 Cubic 849 22.500 .936 Error(factor1) Linear Quadratic Cubic a. Computed using alpha = .05 Tests of Between-Subjects Effects Measure: MEASURE 1 Transformed Variable: Average Type III Sum of Squares 180.000 1 24.000 4 df Mean Square Partial Eta Squared Source F Sig. Intercept 180.000 30.000 |.005 .882 Error 6.000 Tests of Between-Subjects Effects Measure: MEASURE_1
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