Results and Data Analysis: Analysis of Variance (ANOVA)

Subject: Risk Management
Pages: 17
Words: 5867
Reading time:
28 min
Study level: PhD

Introduction

Analysis of variance (ANOVA) is a statistical method that evaluates the potential differences among a group of means (Urdan 2017). The dependent variable is often at the scale-level, whereas the independent variable is at the nominal-level and may have two or more categories. The purpose of this section is to provide a brief literature review of ANOVA and present the findings of ANOVA testing about whether there is a relationship between respondents’ views on various management issues based on job levels.

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Literature Review

According to Pyrczak (2016), the ANOVA test was developed in 1918 by Ronald Fisher. It is an extension of the t and the z test whose limitation is the inability to tackle nominal level variables with two categories. This test may also be referred to as the Fisher analysis of variance (Rouder et al. 2016). Since its inception, ANOVA has found widespread use among students and researchers. The research design often determines the use of ANOVA. Three ways of ANOVA are possible: one-way ANOVA, two-way ANOVA, and N-way ANOVA (Roberts & Russo 2014).

A one-way ANOVA is applied when there is only one independent variable. For example, one-way ANOVA can be used to examine the math scores of high school students in a school district. On the other hand, a two-way ANOVA is performed when there is a need to compare two independent variables (Curtis et al. 2015). Expanding the initial example provided, a two-way ANOVA can assess the differences in math scores (the dependent variable) by the school (the first independent variable) and gender (the second independent variable). Consequently, it is possible to study the connection between the two independent variables by looking at interactions. Interactions reveal the uneven distribution of variation across all groups of the independent variables. For instance, males may have higher math scores overall compared to females. However, this difference could be greater in private schools than public schools. Another term used to identify two-way ANOVA is factorial ANOVA. Complex studies may compel a researcher to use more than two dependent variables. In this case, an N-way ANOVA is used, where N refers to the number of independent variables (Roberts & Russo 2014). For example, the math scores of high school students can be assessed by the school, gender, ethnicity, and age simultaneously.

Since ANOVA entails comparing means, there is a need to formulate null and alternative hypotheses. The standard null hypothesis for an ANOVA test is that there is no significant difference among groups (Curtis et al. 2015). The alternative hypothesis, conversely, assumes that at least one significant difference exists among the groups.

After formulating the hypotheses, the researcher should test the assumptions of ANOVA. The next step entails computing the F-ratio and the related probability value, which is referred to as the p-value. The null hypothesis is rejected if the p-value linked to the F is smaller than the established level of significance, which could be 0.05 or 0.01. Rejecting the null hypothesis implies that the alternative hypothesis is supported and that the means of all the groups are unequal. Subsequently, the researcher needs to conduct post hoc tests to identify the groups that differ from each other. Post hoc tests are t-tests that analyse mean differences between groups. Several post hoc tests exist, including Dunnet, Scheffe, Bonferroni, and Tukey tests (Kucuk et al. 2016). These tests reduce the chances of type I errors, which is the erroneous rejection of the null hypothesis (Kucuk et al. 2016).

Two main factors are used to determine whether ANOVA is suitable for analysis. The first factor is the level of measurement of the variables. The dependent variable must be a continuous level of measurement, which could be interval or ratio). On the other hand, the independent variables must be categorical, which could be nominal or ordinal. Since ANOVA is a parametric test, it is guided by three assumptions and has some assumptions. The first assumption is that the data are normally distributed. The second assumption of ANOVA is that the variances are homogeneous. This assumption implies that the variance between the groups should be more or less equal. The third assumption of ANOVA is that the observations are independent of each other. Various tests can be used to test these assumptions. For example, Levene’s test or the Brown-Forsythe Test can be used to test the assumption of homogeneity of variance. Similarly, the normality of the distribution can be tested using skewness and kurtosis, histograms, and tests such as the Kolmogorov-Smirnov or Shapiro-Wilk (Roberts & Russo 2014). The study design is useful in determining the assumption of independence. Nevertheless, researchers should be cautious and keep an eye open for irrelevant or confounding variables.

The main strength of ANOVA as a method of data analysis is that it is a robust procedure regarding contraventions of the assumption of normality. Literature published in the 1950s and earlier stated that the F-tests used in ANOVA were not robust following contraventions of the assumption that the populations of the variables follow a normal distribution, especially for unbalanced scenarios and small alpha (α) levels (Field & Wilcox 2017). It was also believed that violating the assumption of equal variances led to drastic type I errors. However, studies conducted by Donaldson in the 1960s revealed that the F-test was conservative despite small divergences from the assumptions of equal variance and normality, which did not affect the overall significance substantially (Field & Wilcox 2017). Additionally, these effects reduce with an increase in the sample size. This realization has increased the popularity of ANOVA as a statistical method of analysis.

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Research Hypotheses

Based on the principles and assumptions of ANOVA as explained in the above sub-section, the researcher formulated the hypotheses indicated in Table 1. The hypotheses were grouped based on the four main factors being investigated. The details of each analysis are explained in the following sections.

Table 1. Table of research hypotheses

Restatement of Research Hypotheses
  1. Causes of Variation Related to the Determinants of Risk Governance Framework
1 H0 1: β1 = 0. There is no statistically significant difference between the respondents’ views on “Determinants of Risk Governance Framework Factors related to Job Levelissues”.
HΑ1: β1 ≠ 0. There is a statistically significant difference between the respondents’ views on “Determinants of Risk Governance Framework Factors related to Job Levelissues”.
  1. Causes of Variation Related to Risk-based Audit and the Success of Projects
2 H0 11: β11 = 0. There is no statistically significant difference between the respondents’ views on “Risk-based Audit and the Success of Projects related to Job Level issues”.
HΑ11: β11 ≠ 0. There is a statistically significant difference between the respondents’ views on “Risk-based Audit and the Success of Projects related to Job Level issues”.
3- Causes of Variation Related to the Impact of Negative Events of Projects Factors
3 H0 12: β12 = 0. There is no statistically significant difference between the respondents’ views on “Impact of Negative Events of Projects Factors related to Job Level issues”.
HΑ 12: β12 ≠ 0. There is a statistically significant difference between the respondents’ views on “Impact of Negative Events of Projects Factors related to Job Level issues”.
4- Causes of Variation Related to Internal Audit Function in Overseeing Risk Management
4 H0 13: β13 = 0. There is no statistically significant difference between the respondents’ views on “Internal Audit function in Overseeing Risk Management related to Job Level issues”.
HΑ 13: β13 ≠ 0. There is a statistically significant difference between the respondents’ views on “Internal Audit Function in Overseeing Risk Management related to Job Level issues”.

Analysis of Variance of Determinants of Risk Governance Framework Factors related to Job Level Issues

Analysis using ANOVA was performed to determine if there were any significant differences between the respondent’s perceptions of determinants of risk governance framework factors. A total of 10 factors were tested, including “Strategy”, “Risk Appraisal and Insight”, “Risk Decision and Process Implementation”, “Risk Management and Governance”, “Review Risk Development and Decision”, “Risk Communication”, “Risk Culture”, “Financial and Technical Capacity”, “Risk Appetite”, and “Risk Ownership” between 3 groups based on their job levels (employee, middle management, and top management). A total of 10 hypotheses were tested (1. H0 1: β1 = 0 or ≠ 0; 2. H0 2: β2 = 0 or ≠ 0; 3. H0 3: β3 = 0 or ≠ 0; H0 4: β4 = 0 or ≠ 0; 5. H0 5: β5 = 0 or ≠ 0; 6. H0 6: β6 = 0 or ≠ 0; H0 7: β7 = 0 or ≠ 0; 8. H0 8: β8 = 0 or ≠ 0; 9. H0 9: β9 = 0 or ≠ 0; 9. H0 10: β10 = 0 or ≠ 0). An ANOVA analysis was conducted to justify the statistical differences of the groups’ responses in each category. The hypothesis test was computed using SPSS software at a significance level of 0.05. The F-statistic and the p-values were observed.

Analysis of Variance of Strategy Related to Job Level

Respondents were asked to respond to 9 items by indicating the likelihood of the existence of those factors in their organization. The results indicated in Table 1 in Appendix A under the column ‘Sig.’ show p-values greater than 0.05 for the 9 factors tested. Therefore, there was no significant difference between respondents’ perceptions of strategy based on job levels. Therefore, the H0 hypothesis was accepted for the causes of variation related to strategy. In this case, there was no need for further tests to determine the difference in specific means between the respondents.

Analysis of Variance of Risk Appraisal and Insight Related to Job Level

Respondents were asked to respond to 10 items by indicating the likelihood of the existence of those factors in their organization. The results indicated in Table 2 in Appendix A under the column ‘Sig.’ show p-values greater than 0.05 for the 10 factors tested. Therefore, there was no significant difference between respondents’ perceptions of risk appraisal and insight based on job levels. Therefore, the H0 hypothesis was accepted for the causes of variation related to risk appraisal and insight. In this case, there was no need for further tests to determine the difference in specific means between the respondents.

Analysis of Variance of Risk Decision and Process Implementation Related to Job Level

Respondents were asked to respond to 4 items by indicating the likelihood of the existence of those factors in their organization. The results indicated in Table 3 in Appendix A under the column ‘Sig.’ show p-values greater than 0.05 for the 4 factors tested. Therefore, there was no significant difference between respondents’ perceptions of risk decision and process implementation based on job levels. Therefore, the H0 hypothesis was accepted for the causes of variation related to risk decision and process implementation. In this case, there was no need for further tests to determine the difference in specific means between the respondents.

Analysis of Variance of Risk Management and Governance Related to Job Level

Respondents were asked to respond to 19 items by indicating the likelihood of the existence of those factors in their organization. The results indicated Table 4 in Appendix A under the column ‘Sig.’ show p-values greater than 0.05 for the 19 factors tested. Therefore, there was no significant difference between respondents’ perceptions of risk management and governance based on job levels. Therefore, the H0 hypothesis was accepted for the causes of variation related to risk management and governance. In this case, there was no need for further tests to determine the difference in specific means between the respondents.

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Analysis of Variance of Review Risk Development and Decision Related to Job Level

Respondents were asked to respond to 10 items by indicating the likelihood of the existence of those factors in their organization. The results indicated Table 5 in Appendix A under the column ‘Sig.’ show p-values greater than 0.05 for the 10 factors tested. Therefore, there was no significant difference between respondents’ perceptions of review risk development and decision based on job levels. Therefore, the H0 hypothesis was accepted for the causes of variation related to review risk development and decision. In this case, there was no need for further tests to determine the difference in specific means between the respondents.

Analysis of Variance of Risk Communication Related to Job Level

Respondents were asked to respond to 12 items by indicating the likelihood of the existence of those factors in their organization. The results indicated Table 6 in Appendix A under the column ‘Sig.’ show p-values greater than 0.05 for the 12 factors tested. Therefore, there was no significant difference between respondents’ perceptions of risk communication based on job levels. Therefore, the H0 hypothesis was accepted for the causes of variation related to risk communication. In this case, there was no need for further tests to determine the difference in specific means between the respondents.

Analysis of Variance of Risk Culture Related to Job Level

Respondents were asked to respond to 8 items by indicating the likelihood of the existence of those factors in their organization. As shown in Table 2, 2 out of 8 factors tested showed significant differences between respondents’ perceptions of risk culture variation based on job levels. Thus the null hypothesis was refuted. To find out the statistical difference between the views of respondents’ about factor RCU5 “existence of a process for risk culture audit”, the results in Table 2 showed that F = 3.636 with a p-value = 0.030. With regard to factor RCU8 “existence of formal training of fraud risk awareness and ethical culture”, the result in Table 2 showed that F = 3.338 with p = 0.040, which was lower than the previous factor. The findings on the remaining 6 factors that were insignificant are included in Table 7 of Appendix A.

Table 2. ANOVA test for risk culture variation factors related to the job level
Sum of Squares df Mean Square F Sig.
RCU5 Between Groups 12.384 2 6.192 3.636 .030
Within Groups 189.055 111 1.703
Total 201.439 113
RCU8 Between Groups 9.727 2 4.864 3.308 .040
Within Groups 163.194 111 1.470
Total 172.921 113

Additional examination of the Tukey HSD post hoc multiple comparison tests with regard to factor RCU5 showed that there was a significant difference in the views of employees and top management (p = 0.023) regarding the existence of a process for risk culture audit in the organization (Table 3). Similarly, the Tukey HSD test showed that there was a significant difference in the views of employees and top management (p = 0.034) regarding the existence of formal training of fraud risk awareness and ethical culture.

Table 3. Post hoc test for factor RCU5 and RCU8

Dependent Variable (I) Job_Level (J) Job_Level Mean Difference (I-J) Std. Error Sig. 95% Confidence Interval
Lower Bound Upper Bound
RCU5 Employee Middle Management .437 .294 .301 -.26 1.14
Top Management .806* .300 .023 .09 1.52
Middle Management Employee -.437 .294 .301 -1.14 .26
Top Management .369 .306 .451 -.36 1.10
Top Management Employee -.806* .300 .023 -1.52 -.09
Middle Management -.369 .306 .451 -1.10 .36
RCU8 Employee Middle Management .443 .273 .241 -.21 1.09
Top Management .705* .279 .034 .04 1.37
Middle Management Employee -.443 .273 .241 -1.09 .21
Top Management .262 .284 .628 -.41 .94
Top Management Employee -.705* .279 .034 -1.37 -.04
Middle Management -.262 .284 .628 -.94 .41
*. The mean difference is significant at the 0.05 level.

Analysis of Variance of Financial and Technical Capacity Related to Job Level

Respondents were asked to respond to 5 items by indicating the likelihood of the existence of those factors in their organization. The results indicated Table 8 in Appendix A under the column ‘Sig.’ show p-values greater than 0.05 for the 5 factors tested. Therefore, there was no significant difference between respondents’ perceptions of financial and technical capacity based on job levels. Therefore, the H0 hypothesis is accepted for the causes of variation related to financial and technical capacity. In this case, there was no need for further tests to determine the difference in specific means between the respondents.

Analysis of Variance of Risk Appetite Related to Job Level

Respondents were asked to respond to 9 items by indicating the likelihood of the existence of those factors in their organization. The results indicated Table 9 in Appendix A under the column ‘Sig.’ show p-values greater than 0.05 for the 9 factors tested. Therefore, there was no significant difference between respondents’ perceptions of risk appetite based on job levels. Therefore, the H0 hypothesis is accepted for the causes of variation related to risk appetite. In this case, there was no need for further tests to determine the difference in specific means between the respondents.

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Analysis of Variance of Ownership Factors Related to Job Level

Respondents were asked to respond to 7 items by indicating the likelihood of the existence of those factors in their organization. An ANOVA test was performed to determine if there were any significant differences between the respondent’s perceptions of ownership factors related to the job level. Table 4 indicated that there was a significant difference between respondents’ perceptions of 1 out of the 7 ownership factors. The difference was significant on factor O7 “existence of a third-party professional service provider for risk management activities” (F = 4.008, p = 0.021). There was no significant difference in the views of respondents on the other 6 factors as indicated in Table 10 of Appendix A. Thus, there was a need to conduct additional tests on this factor to identify where the differences existed in factor O7.

Table 4. ANOVA test for ownership factors related to job level
Sum of Squares df Mean Square F Sig.
O7 Between Groups 13.221 2 6.611 4.008 .021
Within Groups 183.068 111 1.649
Total 196.289 113

Additional examination of the Tukey HSD post hoc multiple comparison tests with regard to factor O7 showed that there was a significant difference in the views of employees and top management (p = 0.015) regarding the likelihood of the existence of a third-party professional service provider for risk management activities in the organization (Table 5).

Table 5. Post hoc test for factor O7

Dependent Variable (I) Job_Level (J) Job_Level Mean Difference (I-J) Std. Error Sig. 95% Confidence Interval
Lower Bound Upper Bound
O7 Employee Middle Management .345 .289 .459 -.34 1.03
Top Management .836* .296 .015 .13 1.54
Middle Management Employee -.345 .289 .459 -1.03 .34
Top Management .490 .301 .238 -.22 1.20
Top Management Employee -.836* .296 .015 -1.54 -.13
Middle Management -.490 .301 .238 -1.20 .22
*. The mean difference is significant at the 0.05 level.

Based on the findings of the analysis, only 3 out of the 93 determinants of “Risk Governance Framework” factors related to job level issues were significant. Therefore, the null hypothesis was rejected, leading to the conclusion that there is at least one statistically significant difference between the respondents’ views on determinants of risk governance framework factors related to job level issues. Significant differences existed in one ownership factor (O7 “existence of third-party professional service provider for risk management activities”) and two risk culture factors. However, the contribution of these factors was minimal.

Analysis of Variance of Risk-Based Audit and the Success of Projects Factors Related to Job Level

An ANOVA test was performed to determine if there were any significant differences between the respondent’s perceptions of risk-based audit and the success of projects related to job level. Causes of variation related to risk-based audit and the success of projects was were examined where the 11th hypothesis was tested (11. H0 11: β11 = 0 or ≠ 0). The hypothesis test was done at a significance level of 0.05. The F-statistic and the p-values were observed.

A total of 28 factors was examined based on 3 job levels (employee, middle management, and top management). Out of these, only 5 were significant: RG1 “the achievement of strategy objectives”, RG2 “delivering projects on time and budget”, RG8 “fewer surprises and crisis in projects”, RG9 “more focus on efficiency of project phases”, and RG14 “better organizational readiness”. Table 6 indicated that there was a significant difference between respondents’ perceptions of RG1 based on job levels even though the difference was not highly significant (F = 3.115, p = 0.048). There was a significant difference between respondents’ perceptions of RG2 based on job levels (F = 4.465, p = 0.014). The respondents’ perceptions of RG8, and RG9 were statistically significant at (F = 3.600, p = 0.031) and (F = 3.455, p = 0.035) respectively. Similarly, there was a significant difference between the respondents’ perceptions of RG14 based on job levels even though the difference was not highly significant (F = 3.090, p = 0.049). There was no significant difference in 23 out of 28 factors as indicated in Table 11 in Appendix A.

Table 6. ANOVA test for risk-based audit and the success of projects factors related to job level
Sum of Squares df Mean Square F Sig.
RG1 Between Groups 5.659 2 2.829 3.115 .048
Within Groups 100.833 111 .908
Total 106.491 113
RG2 Between Groups 7.382 2 3.691 4.465 .014
Within Groups 91.750 111 .827
Total 99.132 113
RG8 Between Groups 6.627 2 3.313 3.600 .031
Within Groups 102.154 111 .920
Total 108.781 113
RG9 Between Groups 6.093 2 3.046 3.455 .035
Within Groups 97.872 111 .882
Total 103.965 113
RG14 Between Groups 5.149 2 2.574 3.090 .049
Within Groups 92.474 111 .833
Total 97.623 113

The statistically significant findings in Table 6 necessitated the performance of post hoc tests to determine the specific groups where significant differences in perceptions occurred. Therefore, Tukey’s HSD post hoc tests were done with regard to factors RG1, RG2, RG8, RG9, and RG14. The findings are summarized in Table 7 where the findings of the column labelled Sig. were used to identify the differences. P-values ˂0.05 were useful in identifying the significant differences. It was noted that:

  • For RG1 “the achievement of strategy objectives”, there was a significant difference in the views of employees and middle management regarding the likelihood of achievement of strategy objectives in helping the organization achieve its goals. However, this difference was not highly significant (p = 0.047). Despite the low significance, this finding indicated that the attainment of objectives influences, though its usefulness may be low compared to other risk-based audit processes.
  • For RG2 “delivering projects on time and budget”, there was a significant difference in the views of employees and middle management (p = 0.013) regarding the likelihood of delivering projects on time and budget in contributing to helping the organization achieve its goals. This difference could be attributed to the fact that employees report directly to middle-level management and the two parties are likely to engage in discussions concerning the meeting of deadlines to deliver timely projects.
  • For RG8 “fewer surprises and crisis in projects”, significant differences in opinions regarding the likelihood of fewer surprises and crisis in projects contributing to the attainment of project objectives were observed between employees and middle management (p = 0.023).
  • For RG9 “more focus on efficiency of project phases”, there was no significant difference on the respondents’ regarding the likelihood of increased focus on the efficiency of projects’ phases on realizing organizational objectives between the 3 job levels.
  • For RG14 “better organizational readiness”, there was a significant difference in the views of employees and middle management (p = 0.013) regarding the likelihood of enhanced organizational readiness in helping an organization achieve its project objectives.

For the other 23 factors, there was no need to conduct post hoc tests because the factors were not significant. Overall, the ANOVA result for “risk-based audit and the success of projects factors” based on job levels indicated that there were statistically significant differences between the respondents’ perceptions of 5 out of 28 factors tested. Therefore, the null hypothesis was rejected.

Table 7. Post hoc test for factors RG1, RG2, RG8, RG9, and RG14

Dependent Variable (I) Job_Level (J) Job_Level Mean Difference (I-J) Std. Error Sig. 95% Confidence Interval
Lower Bound Upper Bound
RG1 Employee Middle Management -.516* .215 .047 -1.03 -.01
Top Management -.378 .219 .202 -.90 .14
Middle Management Employee .516* .215 .047 .01 1.03
Top Management .138 .223 .810 -.39 .67
Top Management Employee .378 .219 .202 -.14 .90
Middle Management -.138 .223 .810 -.67 .39
RG2 Employee Middle Management -.591* .205 .013 -1.08 -.10
Top Management -.426 .209 .108 -.92 .07
Middle Management Employee .591* .205 .013 .10 1.08
Top Management .165 .213 .720 -.34 .67
Top Management Employee .426 .209 .108 -.07 .92
Middle Management -.165 .213 .720 -.67 .34
RG8 Employee Middle Management -.580* .216 .023 -1.09 -.07
Top Management -.287 .221 .398 -.81 .24
Middle Management Employee .580* .216 .023 .07 1.09
Top Management .292 .225 .397 -.24 .83
Top Management Employee .287 .221 .398 -.24 .81
Middle Management -.292 .225 .397 -.83 .24
RG9 Employee Middle Management -.501 .211 .051 -1.00 .00
Top Management -.459 .216 .090 -.97 .05
Middle Management Employee .501 .211 .051 .00 1.00
Top Management .042 .220 .980 -.48 .56
Top Management Employee .459 .216 .090 -.05 .97
Middle Management -.042 .220 .980 -.56 .48
RG14 Employee Middle Management -.499* .206 .044 -.99 -.01
Top Management -.340 .210 .242 -.84 .16
Middle Management Employee .499* .206 .044 .01 .99
Top Management .159 .214 .739 -.35 .67
Top Management Employee .340 .210 .242 -.16 .84
Middle Management -.159 .214 .739 -.67 .35
*. The mean difference is significant at the 0.05 level.

Analysis of Variance of the Impact of Negative Events of Projects Related to Job Level

An ANOVA test was conducted to determine if there were any significant differences between the respondent’s perceptions of the impact of negative events of projects related to the job level. A total of 10 factors was considered based on 3 job levels (employee, middle management, and top management). Causes of variation related to the impact of negative events of projects factors were examined where the 12th hypothesis was tested (12. H0 12: β12 = 0 or ≠ 0). The hypothesis test was done at a significance level of 0.05. The F-statistic and the p-values were observed. Respondents were asked to rate the occurrence of 10 negative events of projects in the organization. These events included “experiencing schedule delays”, “cost overrun”, “lack of control over the projects phases”, “past project failures”, “the failure of governance model to manage key projects”, “the existence of unresolved issues and disputes”, “a lack of independent monitoring of progress”, “a lack of reporting to board and executives”, “failure to achieve the business objectives”, and “a loss of opportunity cost of doing the wrong projects”.

Table 11 in Appendix A indicated that there was no significant difference between respondents’ perceptions of the 10 factors tested based on job levels. The opinions of respondents on the impact of negative events of projects did not differ significantly, which implied that all employees were in agreement regarding the incidence of specific negative events in the organization. This agreement is a good indicator because it implies that all members of the organization are informed about the ongoing at their workplace with regard to the incidence of negative project activities. There was no need for additional post hoc analyses since the results were insignificant. Therefore, there was sufficient evidence to reject the null hypothesis and conclude that there is no statistically significant difference between the respondents’ views on the impact of negative events of projects factors related to job level issues.

Analysis of Variance of Internal Audit Function in Overseeing Risk Management Related to Job Level

An ANOVA test was conducted to determine if there were any significant differences between the respondent’s perceptions of internal audit function in overseeing risk management related to job level. Causes of variation related to internal audit function in overseeing risk management were examined where the 13th hypothesis was tested (13. H0 13: β13 = 0 or ≠ 0). The hypothesis test was done at a significance level of 0.05. The F-statistic and the p-values were observed. Respondents were asked to rate the importance of various audit factors in the management of organisation risk by choosing one out of five options. A total of 11 factors was tested out of which the opinions of the respondents on 6 factors were significant based on 3 job levels (employee, middle management, and top management). These factors were IAF1 “Providing independent assurance on risk management processes”, IAF6 “Providing assurance through written reports covering how key risks are managed”, IAF8 “Participating in setting the organization’s risk appetite”, IAF9 “Developing the organizational policies for its risk management processes”, IAF10 “Developing risk management strategy for board approval”, and IAF11 “Implementation risk responses on management’s behalf”.

Table 9 indicated that there was a significant difference between respondents’ perceptions of IAF1 based on job levels (F = 3.934, p = 0.022). There was a significant difference between respondents’ perceptions of IAF6 based on job levels (F = 4.274, p = 0.016). These differences could be attributed to differences in work experience, educational level, or age. Respondents’ perceptions of IAF8, IAF9, IAF10, and IAF11 were statistically significant at (F = 3.394, p = 0.037), (F = 3.753, p = 0.026), (F = 4.516, p = 0.013), and (F = 5.087, p = 0.008) respectively.

Table 9. ANOVA for audit function in overseeing risk management related to job level

Sum of Squares df Mean Square F Sig.
IAF1 Between Groups 6.598 2 3.299 3.934 .022
Within Groups 93.086 111 .839
Total 99.684 113
IAF6 Between Groups 5.740 2 2.870 4.274 .016
Within Groups 74.541 111 .672
Total 80.281 113
IAF8 Between Groups 11.441 2 5.720 3.394 .037
Within Groups 187.059 111 1.685
Total 198.500 113
IAF9 Between Groups 12.656 2 6.328 3.753 .026
Within Groups 187.134 111 1.686
Total 199.789 113
IAF10 Between Groups 13.493 2 6.747 4.516 .013
Within Groups 165.840 111 1.494
Total 179.333 113
IAF11 Between Groups 16.958 2 8.479 5.087 .008
Within Groups 185.006 111 1.667
Total 201.965 113

Having rejected the null hypothesis, it was necessary to determine where the differences were observed using Tukey’s HSD post hoc tests with regard to Factors IAF1, IAF6, IAF8, IAF9, IAF10, and IAF11. In Table 10, it was noted that:

  • For IAF1 “Providing independent assurance on risk management processes”, there were differences in the respondents’ opinions regarding the importance of providing independent assurance on risk management processes for risk management between top management and middle management (p = 0.020).
  • For IAF6 “Providing assurance through written reports covering how key risks are managed”, there were significant differences (p = 0.012) between the perceptions of top management and employees regarding the regarding the importance of providing assurance through written reports covering how key risks are managed on risk management.
  • For IAF8 “Participating in setting the organization’s risk appetite”, there was a significant difference between the perceptions of middle management and top management regarding the importance of participating in setting the organization’s risk appetite on risk management (p = 0.045). Nevertheless, this difference was not highly significant. However, it indicated that participation in creating an organization’s risk appetite was a useful audit function in risk management.
  • For IAF9 “Developing the organizational policies for its risk management processes”, there was a significant difference in the perceptions of middle and top management regarding the value of developing the organizational policies for its risk management processes in audit functions (p = 0.030).
  • For IAF10 “Developing risk management strategy for board approval”, there was a significant difference between the perceptions of top management and employees on the importance of developing risk management strategy for board approval as an audit function (p = 0.011).
  • For IAF11 “Implementation risk responses on management’s behalf”, there was a significant difference between the perceptions of top management and employees on the importance of implementing risk responses on management’s behalf as an audit function (p = 0.016). A significant difference based on this factor was also noted between middle and top management (p = 0.019). This observation indicated that diverse opinions existed regarding the importance of implementing risk responses in an organization. Therefore, there was a need to conduct additional investigations regarding this factor.

Table 10. Post hoc test – factor IAF1, IAF6, IAF8, IAF9, IAF10, and IAF11

Dependent Variable (I) Job_Level (J) Job_Level Mean Difference (I-J) Std. Error Sig. 95% Confidence Interval
Lower Bound Upper Bound
IAF1 Employee Middle Management .160 .206 .719 -.33 .65
Top Management -.424 .211 .114 -.93 .08
Middle Management Employee -.160 .206 .719 -.65 .33
Top Management -.584* .215 .020 -1.09 -.07
Top Management Employee .424 .211 .114 -.08 .93
Middle Management .584* .215 .020 .07 1.09
IAF6 Employee Middle Management -.227 .185 .437 -.67 .21
Top Management -.551* .189 .012 -1.00 -.10
Middle Management Employee .227 .185 .437 -.21 .67
Top Management -.323 .192 .216 -.78 .13
Top Management Employee .551* .189 .012 .10 1.00
Middle Management .323 .192 .216 -.13 .78
IAF8 Employee Middle Management -.105 .292 .932 -.80 .59
Top Management .630 .299 .093 -.08 1.34
Middle Management Employee .105 .292 .932 -.59 .80
Top Management .735* .304 .045 .01 1.46
Top Management Employee -.630 .299 .093 -1.34 .08
Middle Management -.735* .304 .045 -1.46 -.01
IAF9 Employee Middle Management -.137 .292 .887 -.83 .56
Top Management .646 .299 .082 -.06 1.36
Middle Management Employee .137 .292 .887 -.56 .83
Top Management .783* .304 .030 .06 1.51
Top Management Employee -.646 .299 .082 -1.36 .06
Middle Management -.783* .304 .030 -1.51 -.06
IAF10 Employee Middle Management .237 .275 .666 -.42 .89
Top Management .829* .281 .011 .16 1.50
Middle Management Employee -.237 .275 .666 -.89 .42
Top Management .592 .286 .102 -.09 1.27
Top Management Employee -.829* .281 .011 -1.50 -.16
Middle Management -.592 .286 .102 -1.27 .09
IAF11 Employee Middle Management .004 .291 1.000 -.69 .70
Top Management .838* .297 .016 .13 1.54
Middle Management Employee -.004 .291 1.000 -.70 .69
Top Management .834* .302 .019 .12 1.55
Top Management Employee -.838* .297 .016 -1.54 -.13
Middle Management -.834* .302 .019 -1.55 -.12
*. The mean difference is significant at the 0.05 level.

The insignificant factors are indicated in Table 12 of Appendix A. Since there were significant differences in respondents’ perceptions in 6 out of the 11 factors examined, there was sufficient evidence to reject the null hypothesis and conclude that there is a statistically significant difference between the respondents’ views on audit function in overseeing risk management related to job level issues.

Summary

This chapter presented the data collected using one-way ANOVA to analyse the statistical differences among the groups’ responses. SPSS software and a significance level of 0.05 were used for this analysis. The testing of hypotheses involved calculations at α = 0.05 and observation of the F-statistic and the p-value to determine significant differences. The observed differences were considered significant in cases where p ˂ 0.05. On the other hand, the differences were considered insignificant when p ≥ 0.05. In addition, Tukey’s HSD post hoc tests were used to find the significant differences between the respondents’ perceptions about the factors under investigation. The results showed that there was a statistically significant difference in respondents’ views in 14 out 142 factors. There were statistically significant variations in 3 out of the 4 areas where causes of variation were investigated.

References

Curtis, MJ, Bond, RA, Spina, D, Ahluwalia, A, Alexander, S, Giembycz, MA, Gilchrist, A, Hoyer, D, Insel, PA, Izzo, AA & Lawrence, AJ 2015, ‘Experimental design and analysis and their reporting: new guidance for publication in BJP’, British Journal of Pharmacology, vol. 172, no. 14, pp. 3461-3471.

Field, AP & Wilcox, RR 2017, ‘Robust statistical methods: a primer for clinical psychology and experimental psychopathology researchers’, Behaviour Research and Therapy, vol. 98, pp. 19-38.

Kucuk, U, Eyuboglu, M, Kucuk, HO & Degirmencioglu, G 2016, ‘Importance of using proper post hoc test with ANOVA’, International Journal of Cardiology, vol. 209, p. 346.

Pyrczak, F 2016, Making sense of statistics: a conceptual overview, 6th edn, Routledge, London.

Roberts, M & Russo, R 2014, A student’s guide to analysis of variance, Routledge, London.

Rouder, JN, Engelhardt, CR, McCabe, S & Morey, RD 2016, ‘Model comparison in ANOVA’, Psychonomic Bulletin & Review, vol. 23 no. 6, pp. 1779-1786.

Urdan, T C 2017, Statistics in plain English, 4th edn, Routledge, London.

Appendices

Appendix A

Table 1. Strategy

ANOVA
Sum of Squares df Mean Square F Sig.
S1 Between Groups .253 2 .127 .089 .915
Within Groups 158.168 111 1.425
Total 158.421 113
S2 Between Groups 2.449 2 1.225 .985 .377
Within Groups 138.016 111 1.243
Total 140.465 113
S3 Between Groups 1.142 2 .571 .454 .636
Within Groups 139.489 111 1.257
Total 140.632 113
S4 Between Groups .910 2 .455 .346 .708
Within Groups 145.871 111 1.314
Total 146.781 113
S5 Between Groups 7.729 2 3.864 2.668 .074
Within Groups 160.797 111 1.449
Total 168.526 113
S6 Between Groups .110 2 .055 .040 .961
Within Groups 152.144 111 1.371
Total 152.254 113
S7 Between Groups 3.723 2 1.861 1.374 .257
Within Groups 150.347 111 1.354
Total 154.070 113
S8 Between Groups .401 2 .201 .131 .877
Within Groups 170.064 111 1.532
Total 170.465 113
S9 Between Groups .052 2 .026 .018 .982
Within Groups 158.580 111 1.429
Total 158.632 113

Table 2. Risk appraisal and insight

ANOVA
Sum of Squares df Mean Square F Sig.
RAI1 Between Groups .945 2 .472 .342 .711
Within Groups 153.336 111 1.381
Total 154.281 113
RAI2 Between Groups .716 2 .358 .262 .770
Within Groups 151.810 111 1.368
Total 152.526 113
RAI3 Between Groups .703 2 .351 .275 .760
Within Groups 141.762 111 1.277
Total 142.465 113
RAI4 Between Groups .227 2 .113 .079 .924
Within Groups 159.738 111 1.439
Total 159.965 113
RAI5 Between Groups 1.297 2 .649 .501 .607
Within Groups 143.720 111 1.295
Total 145.018 113
RAI6 Between Groups .418 2 .209 .164 .849
Within Groups 141.862 111 1.278
Total 142.281 113
RAI7 Between Groups .661 2 .330 .224 .800
Within Groups 163.594 111 1.474
Total 164.254 113
RAI8 Between Groups .981 2 .490 .342 .711
Within Groups 159.379 111 1.436
Total 160.360 113
RAI9 Between Groups 1.770 2 .885 .720 .489
Within Groups 136.484 111 1.230
Total 138.254 113
RAI10 Between Groups .039 2 .019 .015 .985
Within Groups 145.479 111 1.311
Total 145.518 113

Table 3. Risk decision and process implementation

ANOVA
Sum of Squares df Mean Square F Sig.
RD1 Between Groups .793 2 .397 .297 .744
Within Groups 148.225 111 1.335
Total 149.018 113
RD2 Between Groups .662 2 .331 .242 .786
Within Groups 151.908 111 1.369
Total 152.570 113
RD3 Between Groups .571 2 .285 .203 .817
Within Groups 155.999 111 1.405
Total 156.570 113
RD4 Between Groups .276 2 .138 .117 .890
Within Groups 131.346 111 1.183
Total 131.623 113

Table 4. Risk management and governance related to job level

ANOVA
Sum of Squares df Mean Square F Sig.
RMG1 Between Groups 2.704 2 1.352 .993 .374
Within Groups 151.155 111 1.362
Total 153.860 113
RMG2 Between Groups .175 2 .087 .070 .933
Within Groups 139.062 111 1.253
Total 139.237 113
RMG3 Between Groups .546 2 .273 .171 .843
Within Groups 177.559 111 1.600
Total 178.105 113
RMG4 Between Groups 1.400 2 .700 .385 .681
Within Groups 201.521 111 1.816
Total 202.921 113
RMG5 Between Groups .102 2 .051 .036 .965
Within Groups 157.521 111 1.419
Total 157.623 113
RMG6 Between Groups .308 2 .154 .107 .899
Within Groups 159.946 111 1.441
Total 160.254 113
RMG7 Between Groups .068 2 .034 .024 .977
Within Groups 158.292 111 1.426
Total 158.360 113
RMG8 Between Groups .312 2 .156 .097 .908
Within Groups 178.469 111 1.608
Total 178.781 113
RMG9 Between Groups 3.437 2 1.719 1.394 .252
Within Groups 136.817 111 1.233
Total 140.254 113
RMG10 Between Groups .114 2 .057 .045 .956
Within Groups 139.825 111 1.260
Total 139.939 113
RMG11 Between Groups .126 2 .063 .046 .956
Within Groups 153.208 111 1.380
Total 153.333 113
RMG12 Between Groups 2.306 2 1.153 1.030 .361
Within Groups 124.299 111 1.120
Total 126.605 113
RMG13 Between Groups .638 2 .319 .219 .804
Within Groups 161.862 111 1.458
Total 162.500 113
RMG14 Between Groups .989 2 .494 .340 .713
Within Groups 161.511 111 1.455
Total 162.500 113
RMG15 Between Groups .422 2 .211 .149 .862
Within Groups 157.368 111 1.418
Total 157.789 113
RMG16 Between Groups 1.156 2 .578 .419 .659
Within Groups 153.265 111 1.381
Total 154.421 113
RMG17 Between Groups .148 2 .074 .052 .950
Within Groups 158.870 111 1.431
Total 159.018 113
RMG18 Between Groups .615 2 .308 .239 .788
Within Groups 142.902 111 1.287
Total 143.518 113
RMG19 Between Groups .828 2 .414 .310 .734
Within Groups 148.199 111 1.335
Total 149.026 113

Table 5. Risk development and decision related to job level

ANOVA
Sum of Squares df Mean Square F Sig.
RRD1 Between Groups .006 2 .003 .002 .998
Within Groups 157.932 111 1.423
Total 157.939 113
RRD2 Between Groups .314 2 .157 .121 .886
Within Groups 143.476 111 1.293
Total 143.789 113
RRD3 Between Groups .967 2 .483 .338 .714
Within Groups 158.656 111 1.429
Total 159.623 113
RRD4 Between Groups .349 2 .175 .122 .885
Within Groups 158.221 111 1.425
Total 158.570 113
RRD5 Between Groups 4.144 2 2.072 1.438 .242
Within Groups 159.961 111 1.441
Total 164.105 113
RRD6 Between Groups 6.264 2 3.132 2.284 .107
Within Groups 152.201 111 1.371
Total 158.465 113
RRD7 Between Groups 1.455 2 .728 .528 .592
Within Groups 153.115 111 1.379
Total 154.570 113
RRD8 Between Groups .618 2 .309 .251 .779
Within Groups 136.899 111 1.233
Total 137.518 113
RRD9 Between Groups .696 2 .348 .270 .764
Within Groups 143.093 111 1.289
Total 143.789 113
RRD10 Between Groups .571 2 .286 .250 .780
Within Groups 127.052 111 1.145
Total 127.623 113

Table 6. Risk communication related to job level

ANOVA
Sum of Squares df Mean Square F Sig.
RC1 Between Groups .276 2 .138 .091 .913
Within Groups 168.294 111 1.516
Total 168.570 113
RC2 Between Groups 1.552 2 .776 .590 .556
Within Groups 146.071 111 1.316
Total 147.623 113
RC3 Between Groups 2.785 2 1.392 1.034 .359
Within Groups 149.470 111 1.347
Total 152.254 113
RC4 Between Groups .532 2 .266 .172 .842
Within Groups 171.573 111 1.546
Total 172.105 113
RC5 Between Groups 1.207 2 .604 .392 .677
Within Groups 170.977 111 1.540
Total 172.184 113
RC6 Between Groups .167 2 .083 .061 .941
Within Groups 150.956 111 1.360
Total 151.123 113
RC7 Between Groups 5.651 2 2.826 2.094 .128
Within Groups 149.787 111 1.349
Total 155.439 113
RC8 Between Groups 2.304 2 1.152 .788 .457
Within Groups 162.301 111 1.462
Total 164.605 113
RC9 Between Groups 7.173 2 3.586 2.224 .113
Within Groups 179.012 111 1.613
Total 186.184 113
RC10 Between Groups 3.836 2 1.918 1.281 .282
Within Groups 166.234 111 1.498
Total 170.070 113
RC11 Between Groups 1.777 2 .888 .590 .556
Within Groups 167.241 111 1.507
Total 169.018 113
RC12 Between Groups .437 2 .218 .152 .859
Within Groups 159.633 111 1.438
Total 160.070 113

Table 7. Risk culture

ANOVA
Sum of Squares df Mean Square F Sig.
RCU1 Between Groups 2.066 2 1.033 .807 .449
Within Groups 142.040 111 1.280
Total 144.105 113
RCU2 Between Groups .859 2 .429 .311 .733
Within Groups 153.106 111 1.379
Total 153.965 113
RCU3 Between Groups 2.077 2 1.039 .767 .467
Within Groups 150.344 111 1.354
Total 152.421 113
RCU4 Between Groups 6.386 2 3.193 2.328 .102
Within Groups 152.219 111 1.371
Total 158.605 113
RCU6 Between Groups 8.504 2 4.252 3.066 .051
Within Groups 153.960 111 1.387
Total 162.465 113
RCU7 Between Groups 1.966 2 .983 .711 .494
Within Groups 153.552 111 1.383
Total 155.518 113

Table 8. Financial and technical capacity

ANOVA
Sum of Squares df Mean Square F Sig.
F1 Between Groups .018 2 .009 .008 .992
Within Groups 127.316 111 1.147
Total 127.333 113
F2 Between Groups 1.550 2 .775 .652 .523
Within Groups 131.897 111 1.188
Total 133.447 113
F3 Between Groups .062 2 .031 .026 .975
Within Groups 132.430 111 1.193
Total 132.491 113
F4 Between Groups 1.151 2 .575 .548 .580
Within Groups 116.507 111 1.050
Total 117.658 113
F5 Between Groups .311 2 .155 .098 .907
Within Groups 175.944 111 1.585
Total 176.254 113

Table 9. Risk appetite

ANOVA
Sum of Squares df Mean Square F Sig.
RA1 Between Groups 1.242 2 .621 .415 .661
Within Groups 165.890 111 1.495
Total 167.132 113
RA2 Between Groups .387 2 .194 .121 .886
Within Groups 177.972 111 1.603
Total 178.360 113
RA3 Between Groups .033 2 .017 .011 .989
Within Groups 162.072 111 1.460
Total 162.105 113
RA4 Between Groups .476 2 .238 .168 .846
Within Groups 157.462 111 1.419
Total 157.939 113
RA5 Between Groups 1.039 2 .520 .383 .682
Within Groups 150.478 111 1.356
Total 151.518 113
RA6 Between Groups 2.246 2 1.123 .822 .442
Within Groups 151.692 111 1.367
Total 153.939 113
RA7 Between Groups .085 2 .042 .031 .969
Within Groups 149.670 111 1.348
Total 149.754 113
RA8 Between Groups .040 2 .020 .014 .986
Within Groups 153.118 111 1.379
Total 153.158 113
RA9 Between Groups 1.734 2 .867 .651 .523
Within Groups 147.783 111 1.331
Total 149.518 113

Table 10. Ownership factors

ANOVA
Sum of Squares df Mean Square F Sig.
O1 Between Groups 1.176 2 .588 .476 .622
Within Groups 137.079 111 1.235
Total 138.254 113
O2 Between Groups .503 2 .252 .205 .815
Within Groups 136.488 111 1.230
Total 136.991 113
O3 Between Groups .197 2 .098 .067 .935
Within Groups 163.040 111 1.469
Total 163.237 113
O4 Between Groups .134 2 .067 .048 .953
Within Groups 156.120 111 1.406
Total 156.254 113
O5 Between Groups .116 2 .058 .043 .958
Within Groups 150.138 111 1.353
Total 150.254 113
O6 Between Groups 1.188 2 .594 .400 .671
Within Groups 164.672 111 1.484
Total 165.860 113

Table 11. Risk based audit process on success of the projects

ANOVA
Sum of Squares df Mean Square F Sig.
RG3 Between Groups .497 2 .249 .255 .775
Within Groups 108.073 111 .974
Total 108.570 113
RG4 Between Groups 2.928 2 1.464 1.173 .313
Within Groups 138.510 111 1.248
Total 141.439 113
RG5 Between Groups 2.618 2 1.309 1.366 .259
Within Groups 106.330 111 .958
Total 108.947 113
RG6 Between Groups .533 2 .266 .224 .800
Within Groups 131.932 111 1.189
Total 132.465 113
RG7 Between Groups 1.640 2 .820 .881 .417
Within Groups 103.308 111 .931
Total 104.947 113
RG10 Between Groups 2.798 2 1.399 1.678 .191
Within Groups 92.535 111 .834
Total 95.333 113
RG11 Between Groups 3.679 2 1.840 1.886 .156
Within Groups 108.259 111 .975
Total 111.939 113
RG12 Between Groups 4.874 2 2.437 2.442 .092
Within Groups 110.784 111 .998
Total 115.658 113
RG13 Between Groups 5.425 2 2.712 2.826 .064
Within Groups 106.540 111 .960
Total 111.965 113
RG15 Between Groups 2.481 2 1.241 1.513 .225
Within Groups 91.036 111 .820
Total 93.518 113
RG16 Between Groups 3.073 2 1.537 1.631 .200
Within Groups 104.585 111 .942
Total 107.658 113
RG17 Between Groups 2.066 2 1.033 1.146 .322
Within Groups 100.040 111 .901
Total 102.105 113
RG18 Between Groups 4.987 2 2.493 2.825 .064
Within Groups 97.960 111 .883
Total 102.947 113
RG19 Between Groups 1.820 2 .910 .837 .436
Within Groups 120.706 111 1.087
Total 122.526 113
RG20 Between Groups 4.181 2 2.090 2.222 .113
Within Groups 104.424 111 .941
Total 108.605 113
RG21 Between Groups 4.796 2 2.398 2.926 .058
Within Groups 90.958 111 .819
Total 95.754 113
RG22 Between Groups .487 2 .244 .266 .767
Within Groups 101.767 111 .917
Total 102.254 113
RG23 Between Groups 2.050 2 1.025 .908 .406
Within Groups 125.284 111 1.129
Total 127.333 113
RG24 Between Groups 1.865 2 .932 .880 .418
Within Groups 117.583 111 1.059
Total 119.447 113
RG25 Between Groups .128 2 .064 .063 .939
Within Groups 112.889 111 1.017
Total 113.018 113
RG26 Between Groups 1.561 2 .781 .896 .411
Within Groups 96.693 111 .871
Total 98.254 113
RG27 Between Groups .527 2 .263 .283 .754
Within Groups 103.228 111 .930
Total 103.754 113
RG28 Between Groups .862 2 .431 .490 .614
Within Groups 97.708 111 .880
Total 98.570 113

Table 12. Impact of negative events of projects

ANOVA
Sum of Squares df Mean Square F Sig.
IN1 Between Groups 3.463 2 1.731 1.531 .221
Within Groups 125.555 111 1.131
Total 129.018 113
IN2 Between Groups 3.294 2 1.647 1.521 .223
Within Groups 120.145 111 1.082
Total 123.439 113
IN3 Between Groups 4.804 2 2.402 1.980 .143
Within Groups 134.635 111 1.213
Total 139.439 113
IN4 Between Groups 2.844 2 1.422 1.083 .342
Within Groups 145.787 111 1.313
Total 148.632 113
IN5 Between Groups 3.751 2 1.876 1.929 .150
Within Groups 107.933 111 .972
Total 111.684 113
IN6 Between Groups 1.451 2 .725 .521 .595
Within Groups 154.514 111 1.392
Total 155.965 113
IN7 Between Groups 5.653 2 2.827 2.446 .091
Within Groups 128.285 111 1.156
Total 133.939 113
IN8 Between Groups 2.415 2 1.208 .849 .431
Within Groups 157.874 111 1.422
Total 160.289 113
IN9 Between Groups 7.153 2 3.576 2.888 .060
Within Groups 137.479 111 1.239
Total 144.632 113
IN10 Between Groups 1.511 2 .756 .574 .565
Within Groups 146.243 111 1.318
Total 147.754 113

Table 13. The role of internal audit function in risk management.

ANOVA
Sum of Squares df Mean Square F Sig.
IAF2 Between Groups 1.957 2 .979 1.098 .337
Within Groups 98.964 111 .892
Total 100.921 113
IAF3 Between Groups 3.379 2 1.690 1.864 .160
Within Groups 100.621 111 .906
Total 104.000 113
IAF4 Between Groups 1.248 2 .624 .829 .439
Within Groups 83.489 111 .752
Total 84.737 113
IAF5 Between Groups 2.530 2 1.265 .875 .420
Within Groups 160.488 111 1.446
Total 163.018 113