Multivariate Analysis of Variance - Assignment Example

 MANOVA (F-test).

2nd step:           Randomly selected the sample

                        Normally distributed

                        Homogeneity of variance

                        Equal/similar sample sizes for each level of

                        Orthogonal error

                        Independent variables are categorical variables

                        Dependent variables are continuous

                        there and no gross outliers

                        The model assumes a causal relationship

3rd step:            Research question: “Are there any significant differences in participants' mean ratings by the different judges.”

The hypotheses tested:  H0: There is no difference in the mean rating of participants by the different judges in the different levels.

 H1: There is no difference in the mean rating of participants by the different judges at the different levels.

4th step:           Alpha (level of significance) = .05

5th step:           total = 15 – 8 = 7

dfBT = 8 – 8 = 0

dfWT = 15 – 8= 7

6th step:           Critical F value = 314.659

Multivariate Tests

Effect

Value

F

Hypothesis df

Error df

Sig.

Partial Eta Squared

Consent. Parameter

Observed Power

Country

Pillai's Trace

.883

314.659b

7.000

293.000

.000

.883

2202.613

1.000

Wilks' Lambda

.117

314.659b

7.000

293.000

.000

.883

2202.613

1.000

Hotelling's Trace

7.517

314.659b

7.000

293.000

.000

.883

2202.613

1.000

Roy's Largest Root

7.517

314.659b

7.000

293.000

.000

.883

2202.613

1.000

7th step:          

Tests of Within-Subjects Effects

Measure: MEASURE_1

Source

Type III Sum of Squares

df

Mean Square

F

Sig.

Partial Eta Squared

Consent. Parameter

Observed Power

Country

Sphericity Assumed

289.530

7

41.361

273.452

.000

.478

1914.163

1.000

Greenhouse-Geisser

289.530

3.232

89.585

273.452

.000

.478

883.771

1.000

Huynh-Feldt

289.530

3.271

88.504

273.452

.000

.478

894.568

1.000

Lower-bound

289.530

1.000

289.530

273.452

.000

.478

273.452

1.000

Error(Country)

Sphericity Assumed

316.581

2093

.151

Greenhouse-Geisser

316.581

966.341

.328

Huynh-Feldt

316.581

978.146

.324

Lower-bound

316.581

299.000

1.059

a. Computed using alpha =

F observed = 273.452

8th step:           Fobserved = 273.452< Fcritical = 314.659

9th step:           Fail to reject the null hypothesis, H0.

Results

it can be concluded that there existed a statistically significant difference between the ratings given by the judges whereby, F (8, 393) = 314.659.74, P=.000 < .0005; Wilk's λ = 0.117, partial ε2 = .883 (see table below)

Multivariate Tests

Effect

Value

F

Hypothesis df

Error df

Sig.

Partial Eta Squared

Consent. Parameter

Observed Power

Country

Pillai's Trace

.883

314.659b

7.000

293.000

.000

.883

2202.613

1.000

Wilks' Lambda

.117

314.659b

7.000

293.000

.000

.883

2202.613

1.000

Hotelling's Trace

7.517

314.659b

7.000

293.000

.000

.883

2202.613

1.000

Roy's Largest Root

7.517

314.659b

7.000

293.000

.000

.883

2202.613

1.000

Method

Participants

            the data is a product of the International Pancake-Flipping contest, where eight judges rated the flipping styles of 300 competitors. The number of participants is therefore 300 based on the flipping pancake contest and the respective judge's ratings. The judges are randomly referred to as judge 1 to judge 8. The results are for different levels across different countries across the 300 participants who form the study sample. A power analysis revealed that, for a one-way MANOVA with SMALL effect size (h2 = .883) and an alpha of .05, 300 participants yielded a power of 1.0. 

Design

            M ANOVA was used to determine whether there was a difference between the participant's ratings by the judges across the various levels of participation. The independent variable was the level of participation across the different countries while the dependent variable was the judges ranging from judge one to judge 8 in terms of rating, rated as either high or low.  

Materials

The event organizers submitted consent forms to allow access and usage of the data collected during the event. Given the data was collected during the event, no specific questionnaires or interview schedules were administered

Procedure

The event organizers were served with consent forms to request data access and use for the research. Once accessed the data for different levels were classified according to the judges and rated as either high or low. after classification, the data were entered into the SPSS analysis pack and analyzed.

Results

MANOVA outputs indicated that there was a significant effect of the different judge’s decisions concerning the grading of the participants. This involved determining the way that the dependent variables vary for the independent variable and involves looking at the Tests of Between-Subjects Effects but first variances homogeneity is checked using The Mauchly test. The test is used to assess the validity of the sphericity assumption which underlies repeated evaluation for MANOVA. Notably, wherever the level of significance for Mauchly’s test is given as being < 0.05, then sphericity is assumed. Based on the table shown below, P=.040, which is less than .040, and hence sphericity is not assumed.

It is important to point out that there is a need to employ an alpha correction to account for multiple ANOVAs being implemented, including the Bonferroni correction. As a result, a statistical significance is accepted at P < .025.for further details, see table below: There is a statistically significant effect on both level 1 (F (1, 299) = 368.593; P < .0005; partial ε2 = .552) and level 2 (F (1, 299) = 1015.391; P < .0005; partial ε2 = .773).