Question

A research study was conducted to examine the impact of eating a high protein breakfast on adolescents' performance during a physical education physical fitness test. The students were randomly selected and half received a high protein breakfast and half a low protein breakfast. All of the adolescents, both male and female, were given a fitness test with high scores representing better performance. Test scores are recorded below.

Group	High Protein	Low Protein
Males	9 8 8 10 7 8	7 6 5 5 4 5
Females	5 3 3 4 3 4	3 2 2 1 2 1

Compute Levene’s Test of Equality of Error Variances and ANOVA Source Table.

1. Is the main effect for Protein Level significant? – 5 points.

2. Is the main effect for Gender significant? – 5 points.

3. Graph the interaction of Protein Level and Gender – (10 points).

4. Write one paragraph summarizing the results and explaining the findings. – (10 points).

Answer 1

MINITAB used

Compute Levene’s Test of Equality of Error Variances and ANOVA Source Table.

Test for Equal Variances: score versus Gender, Protein

Method

Null hypothesis	All variances are equal
Alternative hypothesis	At least one variance is different
Significance level	α = 0.05

95% Bonferroni Confidence Intervals for Standard Deviations

Gender	Protein	N	StDev	CI
Females	High	6	0.81650	(0.242534, 4.70907)
Females	Low	6	0.75277	(0.278666, 3.48371)
Males	High	6	1.03280	(0.237909, 7.68096)
Males	Low	6	1.03280	(0.237909, 7.68096)

Individual confidence level = 98.75%

Tests

Method	Test Statistic	P-Value
Multiple comparisons	—	0.941
Levene	0.09	0.963

Calculated Levene Test Statistic =0.09, P=0.963which is > 0.05 level of significance. Ho is not rejected.

Equality of Error Variances assumption is not violated.

General Linear Model: score versus Gender, Protein

Method

Factor coding

(-1, 0, +1)

Factor Information

Factor	Type	Levels	Values
Gender	Fixed	2	Females, Males
Protein	Fixed	2	High, Low

Analysis of Variance

Source	DF	Adj SS	Adj MS	F-Value	P-Value
Gender	1	100.042	100.042	118.86	0.000
Protein	1	35.042	35.042	41.63	0.000
Gender*Protein	1	2.042	2.042	2.43	0.135
Error	20	16.833	0.842
Total	23	153.958

Model Summary

S	R-sq	R-sq(adj)	R-sq(pred)
0.917424	89.07%	87.43%	84.26%

1. Is the main effect for Protein Level significant? – 5 points.

Calculated F=41.63, P=0.000 which is < 0.05 level of significance. The main effect for Protein Level is significant.

2. Is the main effect for Gender significant? – 5 points.

Calculated F=118.86, P=0.000 which is < 0.05 level of significance. The main effect for Gender is significant.

3. Graph the interaction of Protein Level and Gender – (10 points).

Since the lines are parallel, interaction is not significant.

4. Write one paragraph summarizing the results and explaining the findings. – (10 points).

A research study was conducted to examine the impact of eating a high protein breakfast on adolescents' performance during a physical education physical fitness test. The main effect for Protein Level is significant, F=41.63, P=0.000. The main effect for Gender is significant, F=118.86, P=0.000. The interaction effect is not significant, F=2.43, P=0.135.