The levene test of homogeneity

The levene test of homogeneity

 

  1. Introduction

In this assignment, the relationship between the operating revenue of the construction companies in three countries (Denmark, Germany and Ukrain) and the three construction levels (A, B, and C) were investigate. The assignment contained two section. In section one, a one way Anova was conducted to investigate the difference in the mean among the three level of construction industry sector (A= construction of building, B= civil engineering, C=specialized construction) factors. In the second section, the two way analysis of variance ANCOVA was conducted to investigate the mean difference of the operating revenue of construction industry among the three countries and among the construction sectors. In performing the one way analysis of variance (ANOVA) one need one dependent variable which in this assignment was the operating revenue of the construction industry and one independent variable which is a category or factor variable which was the company independence factor.

The assignment had the following variables; dependent variable operating revenue of construction companies, and independent variables are, construction industry sector (A= construction of building, B= civil engineering, C=specialized construction) factor A, and the countries.  The sample used in the assignment was 294. The countries used in the assignment for the data were Denmark, Germany and Ukraine). In the analysis of One way analysis of variance and two way analysis of variance, normality of data is assumed. The other assumption in one way analysis of variance and two way analysis of variance in the equality of variance and the last assumption is the linearity of independence with dependence variance. The data was obtained from the  university database on ORBIS.

 

Results

2 (i) test of one way analysis of variance to determine if there is significant mead difference of the operating revenue among the level of construction industry sector ( A= construction of building, B= civil engineering, C=specialized construction)factors (A, B, C). In this section we shall conduct the test of homogeneity (equality of variance) using the levene test.

The levene test of homogeneity

Hypothesis 1

The null hypothesis: The variance of the residual are equal (homogeneous)

The alternative hypothesis: the variance of the residua are not equal

 

Test of Homogeneity of Variances

OPERATING REVENUEOF THE CONTRUCTION INDUSTRY

Levene Statistic

df1

df2

Sig.

13.305

2

292

.000

From the analysis, the levene statistic was equal to 13.305 with a p- value equal 0.000 which was less than 0.05 significant level. This means that the assumption of homogeneity of the variance among the factors was violated. In the assignment we reject the hypothesis that the homogeneity of variance was not violated.

The test for the main effect

Hypothesis 1

The null hypothesis: The mean operating revenue of the construction companies were no significantly different among the three factor of construction industry sector (A= construction of building, B= civil engineering, C=specialized construction).

The alternative hypothesis: The mean operating revenue of the construction companies were significantly different among the three factor of construction industry sector (A= construction of building, B= civil engineering, C=specialized construction).

From the analysis of the main effect, it can be observed that the f- value was equal to 4.515 with a p-value= 0.012 which was less than 0.05 significant level. This means that there was sufficient evidence to conclude that mean operating revenue of construction companies are significantly difference among the construction industry sector ( A= construction of building, B= civil engineering, C=specialized construction) factor A ( all the three levels of companies independence). At 0.05 significant level, the sample used in the assignment supported the alternative hypothesis that the operating revenue of construction population means are significantly different among the three level of the company independence.

ANOVA

OPERATING REVENUEOF THE CONTRUCTION INDUSTRY

 

Sum of Squares

Df

Mean Square

F

Sig.

Between Groups

741152019065435.900

2

370576009532717.940

4.515

.012

Within Groups

23966264747945324.000

292

82076249136799.060

 

 

Total

24707416767010760.000

294

 

 

 

 

Post hoc analysis

Hypothesis 1

The null hypothesis: There is significant difference in the mean between different construction industry sector (A= construction of building, B= civil engineering, C=specialized construction) factor (A, B, C)

The alternative hypothesis: There is significant difference in the mean between different construction industry sector (A= construction of building, B= civil engineering, C=specialized construction) factor (A, B, C)

 

 

From the analysis of difference in means of the operating revenue between different construction industry sector ( A= construction of building, B= civil engineering, C=specialized construction)s, it can be observed that the difference in mean between level A and Level B means of construction industry sector ( A= construction of building, B= civil engineering, C=specialized construction) factors had a p value of 0.160 which was greater than 0.05 significant level. This means that there is sufficient evidence to conclude that the difference in means operating revenue between level A and Level B means of construction industry sector ( A= construction of building, B= civil engineering, C=specialized construction)s are not significantly different. The analysis indicated that the difference in mean between level A and Level C means of construction industry sector ( A= construction of building, B= civil engineering, C=specialized construction)s had a p value of 0.001 which was less than 0.05 significant level. This means that there is sufficient evidence to conclude that the difference in means operating revenue between level A and Level C means of construction industry sector ( A= construction of building, B= civil engineering, C=specialized construction)s are significantly different. Finally, the analysis indicated that the difference in mean between level B and Level C means of construction industry sector ( A= construction of building, B= civil engineering, C=specialized construction)s had a p value of 0.023 which was less than 0.05 significant level. This means that there is sufficient evidence to conclude that the difference in means operating revenue between level B and Level C means of construction industry sector ( A= construction of building, B= civil engineering, C=specialized construction)s are significantly different

Multiple Comparisons

Dependent Variable: OPERATING REVENUEOF THE CONTRUCTION INDUSTRY

 

(I) FACTOR A

(J) FACTOR A

Mean Difference (I-J)

Std. Error

Sig.

95% Confidence Interval

 

Lower Bound

Upper Bound

LSD

A

B

-1689267.540

1200471.126

.160

-4051940.46

673405.38

C

-5616723.207*

1661303.652

.001

-8886370.49

-2347075.93

B

A

1689267.540

1200471.126

.160

-673405.38

4051940.46

C

-3927455.667*

1716945.959

.023

-7306613.76

-548297.57

C

A

5616723.207*

1661303.652

.001

2347075.93

8886370.49

B

3927455.667*

1716945.959

.023

548297.57

7306613.76

Games-Howell

A

B

-1689267.540

1040438.743

.239

-4152634.33

774099.25

C

-5616723.207

2652031.997

.098

-12054596.23

821149.82

B

A

1689267.540

1040438.743

.239

-774099.25

4152634.33

C

-3927455.667

2791129.139

.345

-10659966.92

2805055.58

C

A

5616723.207

2652031.997

.098

-821149.82

12054596.23

B

3927455.667

2791129.139

.345

-2805055.58

10659966.92

*. The mean difference is significant at the 0.05 level.

 

2 (ii). The two way analysis of variance (ANOVA). In testing that the means operating revenue are significantly different among all categories of factor A (construction industry sector ) and factor B (different countries). The two way analysis of variance allow the test of the interaction effect.

The homogeneity test of variance

Hypothesis 1

The null hypothesis: The variance of the residual are equal (homogeneous)

The alternative hypothesis: the variance of the residual are not equal

Levene's Test of Equality of Error Variancesa

Dependent Variable: OPERATING REVENUEOF THE CONTRUCTION INDUSTRY

F

df1

df2

Sig.

4.831

8

286

.000

Tests the null hypothesis that the error variance of the dependent variable is equal across groups.

a. Design: Intercept + GROUP + FACTOR + GROUP * FACTOR

From the analysis, the levene statistic was equal to 4.831 with a p- value equal 0.000 which was less than 0.05 significant level. This means that the assumption of homogeneity of the variance among the factors was violated. In the assignment we reject the hypothesis that the homogeneity of variance was not violated.

The test for the main effect

Hypothesis 1

The null hypothesis: There is no interaction effect between the construction industry sector ( A= construction of building, B= civil engineering, C=specialized construction)factor and the country factor B

The alternative hypothesis: There is interaction effect between the construction industry sector ( A= construction of building, B= civil engineering, C=specialized construction)factor and the country factor B

From the analysis of the two way ANOVA, it was observed that the interaction effect between the construction industry sector ( A= construction of building, B= civil engineering, C=specialized construction)factor and the country factor B had an F- value of 0.531 with a p- value of 0.731 which was greater than 0.05 significant level. This means that the sample had sufficient evidence that the interaction effect between the construction industry sector ( A= construction of building, B= civil engineering, C=specialized construction)factor and the country factor B were not significant

Hypothesis 2

The null hypothesis: The mean operating revenue of the construction companies were no significantly different among the three factor of construction industry sector (A= construction of building, B= civil engineering, C=specialized construction).

The alternative hypothesis: The mean operating revenue of the construction companies were significantly different among the three factor of construction industry sector (A= construction of building, B= civil engineering, C=specialized construction).

From the analysis of the mean operating revenue among difference levels of construction industry sector , it was observed that the F- value was 4.582 with a p- value = 0.011 which was less than 0.05 significant level. This means that there was sufficient evidence that the mean operating revenue was significantly mean operating revenue difference among different levels of the construction industry sector ( A= construction of building, B= civil engineering, C=specialized construction)factor. At 0.05 significant level the evidence indicate that the sample reject the null hypothesis that mean operating revenue of the construction companies were no significantly different among the three factor of construction industry sector ( A= construction of building, B= civil engineering, C=specialized construction).  

Hypothesis 2

The null hypothesis: The mean operating revenue of the construction companies were no significantly different among the three countries

The alternative hypothesis: The mean operating revenue of the construction companies were significantly different among the three countries.

From the analysis of the mean operating revenue among difference countries, it was observed that the F- value was 0.094 with a p- value = 0.910 which was greater than 0.05 significant level. This means that there was sufficient evidence that the mean operating revenue was significantly mean operating revenue difference among different countries. At 0.05 significant level the evidence indicate that the sample reject the null hypothesis that mean operating revenue of the construction companies were no significantly different among the three counties. 

 

Tests of Between-Subjects Effects

Dependent Variable: OPERATING REVENUEOF THE CONTRUCTION INDUSTRY

Source

Type III Sum of Squares

Df

Mean Square

F

Sig.

Corrected Model

949536563579756.000a

8

118692070447469.500

1.429

.184

Intercept

2601916732160287.000

1

2601916732160287.000

31.322

.000

GROUP

15637334689748.379

2

7818667344874.189

.094

.910

FACTOR

761186306754776.200

2

380593153377388.100

4.582

.011

GROUP * FACTOR

176305375827990.300

4

44076343956997.580

.531

.713

Error

23757880203431020.000

286

83069511200807.770

 

 

Total

26577319294676120.000

295

 

 

 

Corrected Total

24707416767010776.000

294

 

 

 

a. R Squared = .038 (Adjusted R Squared = .012)

 

From the analysis of difference in means of the operating revenue between different construction industry sector ( A= construction of building, B= civil engineering, C=specialized construction)s, it can be observed that the difference in mean between country 1 and country 2 means operating revenue had a p value of 0.776 which was greater than 0.05 significant level. This means that there is sufficient evidence to conclude that the difference in means operating revenue between level A and Level B means of construction industry sector ( A= construction of building, B= civil engineering, C=specialized construction)s are not significantly different. The analysis indicated that the difference in mean between country 1 and country 3 means of operating revenue had a p value of 0.900 which was greater than 0.05 significant level. This means that there is no sufficient evidence to conclude that the difference in means operating revenue between country 1 and country 2 means are significantly different. Finally, the analysis indicated that the difference in mean between country 2 and country 3 means operating revenue had a p value of 0.671 which was less than 0.05 significant level. This means that there is sufficient evidence to conclude that the difference in means operating revenue between country 2 and country 3 means operating revenue are significantly different

Pairwise Comparisons

Dependent Variable: OPERATING REVENUEOF THE CONTRUCTION INDUSTRY

(I) FACTOR B

(J) FACTOR B

Mean Difference (I-J)

Std. Error

Sig.a

95% Confidence Interval for Differencea

Lower Bound

Upper Bound

COUNTRY 1

COUNTRY 2

-433700.113

1522611.959

.776

-3430646.963

2563246.736

COUNTRY 3

188631.458

1493941.494

.900

-2751883.508

3129146.425

COUNTRY 2

COUNTRY 1

433700.113

1522611.959

.776

-2563246.736

3430646.963

COUNTRY 3

622331.572

1461586.681

.671

-2254499.634

3499162.777

COUNTRY 3

COUNTRY 1

-188631.458

1493941.494

.900

-3129146.425

2751883.508

COUNTRY 2

-622331.572

1461586.681

.671

-3499162.777

2254499.634

Based on estimated marginal means

a. Adjustment for multiple comparisons: Least Significant Difference (equivalent to no adjustments).

 

Hypothesis 1

The null hypothesis: There is significant difference in the mean between different construction industry sector (A= construction of building, B= civil engineering, C=specialized construction) factor (A, B, C)

The alternative hypothesis: There is significant difference in the mean between different construction industry sector (A= construction of building, B= civil engineering, C=specialized construction) factor (A, B, C)

 

From the analysis of difference in means of the operating revenue between different construction industry sector ( A= construction of building, B= civil engineering, C=specialized construction)s, it can be observed that the difference in mean between level A and Level B means of construction industry sector ( A= construction of building, B= civil engineering, C=specialized construction)factors had a p value of 0.543 which was greater than 0.05 significant level. This means that there is sufficient evidence to conclude that the difference in means operating revenue between level A and Level B means of construction industry sector ( A= construction of building, B= civil engineering, C=specialized construction)s are not significantly different. The analysis indicated that the difference in mean between level A and Level C& D means of construction industry sector ( A= construction of building, B= civil engineering, C=specialized construction)s had a p value of 0.003 which was less than 0.05 significant level. This means that there is sufficient evidence to conclude that the difference in means operating revenue between level A and Level C means of construction industry sector ( A= construction of building, B= civil engineering, C=specialized construction)s are significantly different. Finally, the analysis indicated that the difference in mean between level B and Level C& D means of construction industry sector ( A= construction of building, B= civil engineering, C=specialized construction)s had a p value of 0.013 which was less than 0.05 significant level. This means that there is sufficient evidence to conclude that the difference in means operating revenue between level B and Level C means of construction industry sector ( A= construction of building, B= civil engineering, C=specialized construction)s are significantly different

Pairwise Comparisons

Dependent Variable: OPERATING REVENUEOF THE CONTRUCTION INDUSTRY

(I) FACTOR A

(J) FACTOR A

Mean Difference (I-J)

Std. Error

Sig.b

95% Confidence Interval for Differenceb

Lower Bound

Upper Bound

A

B

-704203.833

1156679.046

.543

-2980887.397

1572479.731

C

-4836478.948*

1608464.474

.003

-8002408.722

-1670549.173

B

A

704203.833

1156679.046

.543

-1572479.731

2980887.397

C

-4132275.115*

1661739.936

.013

-7403066.623

-861483.607

C

A

4836478.948*

1608464.474

.003

1670549.173

8002408.722

B

4132275.115*

1661739.936

.013

861483.607

7403066.623

Based on estimated marginal means

*. The mean difference is significant at the .05 level.

b. Adjustment for multiple comparisons: Least Significant Difference (equivalent to no adjustments).

 

 

 

 

 

 

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