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

This section presents the results of multivariate tests on "factor1" with four different criteria.

| Effect              | Value  | F       | Hypothesis df | Error df | Sig.  |
|---------------------|--------|---------|---------------|----------|-------|
| Pillai'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  |

#### Partial Eta Squared and Power

| Effect              | Partial Eta Squared | Noncent. Parameter | Observed Powerᵃ |
|---------------------|---------------------|--------------------|-----------------|
| Pillai'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

This section tests the assumption of sphericity for within-subjects effects.

**Measure: MEASURE_1**

| Within Subjects Effect | Mauchly's W | Approx. Chi-Square | df | Sig. | Epsilonᵇ | Greenhouse-Geisser |
|------------------------|-------------|--------------------|----|------|----------|--------------------|
| factor1                | .000        |                    | 5  | .    |          | .533               |

**Epsilon Values**

| Within Subjects Effect | Huynh-Feldt | Lower-bound |
|------------------------|-------------|-------------|
| factor1                | .833        | .333        |

### Tests of Within-Subjects Effects

**Measure: MEASURE_1**

This table evaluates the within-subjects effects for
Transcribed Image Text:### Multivariate Tests This section presents the results of multivariate tests on "factor1" with four different criteria. | Effect | Value | F | Hypothesis df | Error df | Sig. | |---------------------|--------|---------|---------------|----------|-------| | Pillai'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 | #### Partial Eta Squared and Power | Effect | Partial Eta Squared | Noncent. Parameter | Observed Powerᵃ | |---------------------|---------------------|--------------------|-----------------| | Pillai'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 This section tests the assumption of sphericity for within-subjects effects. **Measure: MEASURE_1** | Within Subjects Effect | Mauchly's W | Approx. Chi-Square | df | Sig. | Epsilonᵇ | Greenhouse-Geisser | |------------------------|-------------|--------------------|----|------|----------|--------------------| | factor1 | .000 | | 5 | . | | .533 | **Epsilon Values** | Within Subjects Effect | Huynh-Feldt | Lower-bound | |------------------------|-------------|-------------| | factor1 | .833 | .333 | ### Tests of Within-Subjects Effects **Measure: MEASURE_1** This table evaluates the within-subjects effects for
### Analysis of Variance (ANOVA) Output

### Tests of Within-Subjects Effects

**Measure:** MEASURE_1

| Source               | Partial Eta Squared | Noncent. Parameter | Observed Power* |
|----------------------|---------------------|---------------------|-----------------|
| 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            |

*Note: Computed using alpha = .05

### Tests of Within-Subjects Contrasts

**Measure:** MEASURE_1

| Source     | | Type III Sum of Squares | df  | Mean Square | F     | Sig.  |
|------------|---|------------------------|-----|-------------|-------|-------|
| factor1    | Linear    | 36.000                 | 1   | 36.000      | 360.000 | .000  |
|            | Quadratic | 5.000                  | 1   | 5.000       | 3.333   | .142  |
| Error(factor1) | Linear    | .400                   | 4   | .100        |         |       |
|            | Quadratic | 6.000                  | 4   | 1.500       |         |       |

**Within-Subjects Contrasts - Additional Metrics**

| Source             | Partial Eta Squared | Noncent. Parameter | Observed Power* |
|--------------------|---------------------|---------------------|-----------------|
| factor1: Linear    | .989                | 360.000             | 1.000           |
| factor1: Quadratic | .455                | 3.333               | .290            |
| Error(factor1)     | Linear              |                     |                 |
|                    | Quadratic           |                     | .936            |

### Tests of Between-Subjects Effects

**Measure:** MEASURE_1

| Source    | Type III Sum of Squares | df  | Mean Square | F     | Sig.  | Partial Eta Squared |
|-----------|-------------------------|-----|-------------
Transcribed Image Text:### Analysis of Variance (ANOVA) Output ### Tests of Within-Subjects Effects **Measure:** MEASURE_1 | Source | Partial Eta Squared | Noncent. Parameter | Observed Power* | |----------------------|---------------------|---------------------|-----------------| | 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 | *Note: Computed using alpha = .05 ### Tests of Within-Subjects Contrasts **Measure:** MEASURE_1 | Source | | Type III Sum of Squares | df | Mean Square | F | Sig. | |------------|---|------------------------|-----|-------------|-------|-------| | factor1 | Linear | 36.000 | 1 | 36.000 | 360.000 | .000 | | | Quadratic | 5.000 | 1 | 5.000 | 3.333 | .142 | | Error(factor1) | Linear | .400 | 4 | .100 | | | | | Quadratic | 6.000 | 4 | 1.500 | | | **Within-Subjects Contrasts - Additional Metrics** | Source | Partial Eta Squared | Noncent. Parameter | Observed Power* | |--------------------|---------------------|---------------------|-----------------| | factor1: Linear | .989 | 360.000 | 1.000 | | factor1: Quadratic | .455 | 3.333 | .290 | | Error(factor1) | Linear | | | | | Quadratic | | .936 | ### Tests of Between-Subjects Effects **Measure:** MEASURE_1 | Source | Type III Sum of Squares | df | Mean Square | F | Sig. | Partial Eta Squared | |-----------|-------------------------|-----|-------------
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