# 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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