Analysis of Covariance (Term Paper Sample)

Analysis of Covariance, ANCOVA (GLM 2)
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University title
Before performing ANOVA and ANCOVA tests, I carried out tests for normality of this data.
Tests of Normality


Drink

Kolmogorov-Smirnova

Shapiro-Wilk



Statistic

df

Sig.

Statistic

df

Sig.

How Well Does The Person Feel?

Water

.300

5

.161

.833

5

.146


Lucozade

.246

5

.200*

.956

5

.777


Cola

.473

5

.001

.552

5

.000

How Drunk was the Person the Night Before

Water

.198

5

.200*

.957

5

.787


Lucozade

.243

5

.200*

.894

5

.377


Cola

.367

5

.026

.684

5

.006

The Shapiro-Wilk test indicate that all variables come from an approximately normal population since the p-value for all the variables is less than 0.05. Therefore, we can run the ANOVA and ANCOVA tests.
The Relationship between Drink and how well they felt without the covariate
Levene's Test of Equality of Error Variancesa


F

df1

df2

Sig.

1.244

2

12

.323

The lavene’s test indicate that the variations in the variances are not significantly different because the significance value is greater than 0.05. Therefore the assumption of Homoscedasticity (Martin, & Bridgmon, 2012). 
Tests of Between-Subjects Effects


Source

Type III Sum of Squares

df

Mean Square

F

Sig.

Corrected Model

2.133a

2

1.067

.821

.463

Intercept

459.267

1

459.267

353.282

.000

drink

2.133

2

1.067

.821

.463

Error

15.600

12

1.300



Total

477.000

15




Corrected Total

17.733

14




a. R Squared = .120 (Adjusted R Squared = -.026)

Univariate Tests


Sum of Squares

df

Mean Square

F

Sig.

Contrast

2.133

2

1.067

.821

.463

Error

15.600

12

1.300



The variation of how well an individual feels accounted for by this model is 2.133 units. The variable Drink accounts for 2.133 units in the variation of the dependent variable while the variation of wellness of an individual that is not explained is 15.6 units.
General Linear Modeling/ANCOVA with the Covariate
Levene's Test of Equality of Error Variancesa


F

df1

df2

Sig.

.220

2

12

.806

Levene’s test is used to test for equality of error variances of k samples. In this case the significance value for the Levene’s test is 0.806 which is greater than 0.05 implies that the variability of the variances is not significantly different. Thus the assumption of constant variance for the error is obeyed (Kerr, Hall & Kozub, 2013). 
The ANOVA table with the covariate included, from the significance levels it is evident that the covariate predicts the dependent variable significantly since the significance levels all less than 0.05. Therefore, how well person feel after waking up dehydrated is influenced by drinking Lucozade. The amount of variation of how well a person feels accounted by this model is 13.32 units (correlated model), How drunk the person was the previous night accounts for 11.178 units while, the variable drink accounts for 3.464 units. The unexplained amount of variation of how well persons feel has been reduced to 4.413 units from 15.6)
Tests of Between-Subjects Effects

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