# Statistical Assessment: Correlation Analysis

## Introduction and Literature Review

Correlation analysis is a statistical assessment technique employed when studying the strength of an association between two continuous variables (Pollock 2015). Correlation analysis determines possible links between variables. However, it does not identify the cause-effect aspect of the connection because it does not consider other variables that may have affected the outcomes (Gelman et al. 2014). The correlation between two variables implies that a change in one variable leads to a systematic change in the other over time. A positive correlation occurs if the value of one variable increases as the value of the second rises. Conversely, a negative correlation happens when the value of one variable decreases as the value of the second reduces.

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Correlation coefficients, which range from +1 to -1, are used to quantify the strength of the association (Johnson 2017). Coefficient values that are close to +1 indicate strong positive associations, whereas those close to -1 indicate negative relations. A correlation coefficient of 0 indicates that no association exists between variables. The purpose of this chapter is to examine the strength of the relationship between risk governance determinants and the effectiveness of public projects.

## Analysis

Ten determinants were investigated in the research each of which contained 2 to 3 clusters based on factor analysis. Spearman’s correlation was performed for all the variables at two levels of significance (0.01 and 0.05). The findings of the analyses are reported in the following sections.

## Project Success

### Association between Strategy (S) and Project Success (RG)

There are two latent clusters for strategy construct: SG1 and SG2. Table 1 shows the correlation values for these relationships. The largest positive correlation at 0.01 significance level is 0.537 with a significance of 0.0. This correlation is between the SG1 “risk alignment process” of the strategy cluster and RG4 “issuance of consolidated reports of disparate risk at board level” of RG. The lowest positive correlation at 0.01 significance level is 0.254. This correlation is between SG2 of the strategy cluster and RG11 of RG. SG2 is “risk oversight practices”, whereas RG11 is “capability to take on critical risks in order to get greater reward”.

Table 1. Association between strategy (S) and project success (RG)

 Strategy SG1 SG2 Project Success RG1 .500** .417** RG2 .496** .371** RG3 .497** .323** RG4 .537** .374** RG5 .504** .356** RG6 .473** .305** RG7 .487** .359** RG8 .474** .317** RG9 .451** .293** RG10 .425** .290** RG11 .455** .254** RG12 .447** .365** RG13 .442** .300** RG14 .429** .329** RG15 .481** .384** RG16 .491** .359** RG17 .527** .414** RG18 .361** .331** RG19 .487** .376** RG20 .480** .394** RG21 .427** .353** RG22 .495** .426** RG23 .523** .337** RG24 .454** .369** RG25 .465** .392** RG26 .397** .315** RG27 .476** .313** RG28 .505** .399**

### Association between Risk Appraisal and Insight (RAI) and Project Success (RG)

There are two latent clusters for the “risk appraisal and insight” (RAI) construct RAIG1 and RAIG2. Table 2 shows the correlation values for these relationships. The largest positive correlation at 0.01 significance level is 0.605. This correlation is between RAIG1 “risk guidelines” of RAI cluster and RG17 “early identification and understanding of internal and external issues pertaining to projects” of RG. The lowest positive correlation at 0.01 significance level is 0.264. This correlation is between RAIG2 “risk assessment process” and RG11 “capability to take on critical risks in order to get a greater reward”.

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Table 2. Association between risk appraisal and insight (RAI) and project success

 Risk Appraisal and Insight RAIG1 RAIG2 Project Success RG1 .562** .445** RG2 .563** .447** RG3 .571** .375** RG4 .581** .440** RG5 .520** .396** RG6 .475** .356** RG7 .504** .399** RG8 .513** .340** RG9 .495** .343** RG10 .477** .332** RG11 .445** .264** RG12 .493** .344** RG13 .474** .389** RG14 .489** .394** RG15 .520** .383** RG16 .536** .436** RG17 .605** .447** RG18 .488** .380** RG19 .538** .412** RG20 .585** .442** RG21 .525** .414** RG22 .558** .424** RG23 .573** .444** RG24 .537** .412** RG25 .563** .413** RG26 .457** .379** RG27 .494** .334** RG28 .504** .402**

### Association between Risk Management and Governance (RMGG) and Project Success (RG)

There are two latent clusters for the “risk management and governance” (RMGG) construct RMGG1 and RMGG2. Table 3 shows the correlation values for these relationships. The largest positive correlation at 0.01 significance level is 0.657. This correlation is between RMGG1 “risk governance” and RG20 “adoption of risk-based audit has enabled optimal utilization of financial resources” of RG. The lowest positive correlation at 0.01 significance level is 0.350. This correlation is between RMGG2 “risk control” of RMGG cluster and RG26 “risk-based audit helps to identify the risk appetite adequately” of RG.

Table 3. Association between risk management and governance (RMGG) and project success

 Risk Management and Governance RMGG1 RMGG2 Project Success RG1 .579** .471** RG2 .548** .412** RG3 .606** .474** RG4 .615** .491** RG5 .596** .450** RG6 .548** .447** RG7 .576** .425** RG8 .518** .431** RG9 .538** .445** RG10 .521** .430** RG11 .479** .410** RG12 .565** .465** RG13 .561** .433** RG14 .517** .404** RG15 .577** .475** RG16 .598** .469** RG17 .610** .453** RG18 .524** .362** RG19 .569** .433** RG20 .657** .518** RG21 .543** .390** RG22 .596** .452** RG23 .620** .501** RG24 .597** .451** RG25 .617** .476** RG26 .496** .350** RG27 .531** .395** RG28 .534** .417**

### Association between Review Risk Development and Decision (RRD) and Project Success (RG)

There are three latent clusters for the “review risk development and decision” (RRD) construct RDG1, RDG2, and RDG3. There are 84 possible correlations as indicated in Table 4. The largest positive correlation at 0.01 significance level is 0.571. This correlation is between RDG2 “effectiveness assurance” of RRD cluster and RG20 “adoption of risk-based audit has enabled optimal utilization of financial resources” of RG. The lowest positive correlation at 0.01 significance level is 0.294. This correlation is between RDG1 “monitoring guidelines” of RRD cluster and RG26 “risk-based audit helps to identify the risk appetite adequately” of RG.

Table 4. Association between review risk development and decision and project success

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 Review Risk Development and Decision RDG1 RDG2 RDG3 Project Success RG1 .393** .515** .483** RG2 .414** .426** .425** RG3 .445** .510** .488** RG4 .419** .490** .471** RG5 .463** .470** .474** RG6 .435** .447** .418** RG7 .388** .473** .454** RG8 .417** .427** .445** RG9 .399** .414** .421** RG10 .324** .458** .444** RG11 .362** .379** .360** RG12 .349** .454** .440** RG13 .384** .480** .434** RG14 .370** .407** .428** RG15 .376** .482** .466** RG16 .386** .517** .467** RG17 .448** .502** .503** RG18 .353** .455** .459** RG19 .386** .476** .461** RG20 .405** .571** .507** RG21 .420** .524** .428** RG22 .468** .513** .472** RG23 .494** .534** .515** RG24 .392** .493** .457** RG25 .423** .534** .516** RG26 .294** .418** .379** RG27 .389** .445** .417** RG28 .366** .473** .436**

### Association between Risk Communication (RCG) and Project Success (RG)

There are three latent clusters for the “risk communication” (RCG) construct: RCG1, RCG2, and RCG3. The 84 possible correlations are possible as indicated in Table 5. The largest positive correlation at 0.01 significance level is 0.580 with a significance of 0.0. This correlation is between RCG2 “risk documentation” of RCG cluster and RG25 “ability to identify the emerging risks associated with strategic plans” of RG. The lowest positive correlation at 0.01 significance level is 0.350. This correlation is between RCG1 “risk communication” of RCG cluster and RG21 “risk-based audit has increased the accountability” of RG.

Table 5. Association between risk communication (RCG) and project success

 Risk Communication RCG1 RCG2 RCG3 Project Success RG1 .444** .496** .451** RG2 .430** .515** .512** RG3 .454** .538** .546** RG4 .401** .573** .561** RG5 .445** .548** .541** RG6 .462** .456** .564** RG7 .404** .528** .438** RG8 .384** .476** .497** RG9 .416** .477** .488** RG10 .370** .513** .438** RG11 .389** .414** .493** RG12 .415** .508** .453** RG13 .370** .507** .496** RG14 .365** .480** .464** RG15 .433** .541** .481** RG16 .441** .558** .514** RG17 .449** .571** .537** RG18 .370** .533** .429** RG19 .398** .525** .512** RG20 .425** .564** .469** RG21 .350** .539** .430** RG22 .486** .563** .533** RG23 .424** .574** .559** RG24 .411** .513** .511** RG25 .505** .580** .535** RG26 .332** .456** .390** RG27 .374** .448** .480** RG28 .320** .498** .422**

### Association between Risk Culture (RCU) and Project Success (RG)

There are two latent clusters for the “risk culture” (RCU) construct: RCUG1 and RCUG2. Table 6 shows the correlation values for the 56 possible relationships. The largest positive correlation at 0.01 significance level is 0.445. This correlation is between RCUG2 “risk culture awareness” of RCU cluster and RG25 “ability to identify the emerging risks associated with strategic plans” of RG. The lowest positive correlation at 0.01 significance level is 0.242. This correlation is between RCUG1 “risk culture development” of RCU cluster and RG18 “increased likelihood of delivering projects on scope, on time, and on budget”.

Table 6. Association between risk culture (RCU) and project success

 RCUG1 RCUG2 Project Success RG1 .332** .444** RG2 .328** .363** RG3 .413** .433** RG4 .340** .316** RG5 .352** .397** RG6 .404** .386** RG7 .327** .402** RG8 .281** .338** RG9 .319** .364** RG10 .284** .346** RG11 .357** .355** RG12 .276** .378** RG13 .266** .349** RG14 .307** .334** RG15 .311** .413** RG16 .340** .411** RG17 .355** .360** RG18 .242** .272** RG19 .355** .338** RG20 .313** .378** RG21 .257** .285** RG22 .418** .439** RG23 .341** .358** RG24 .318** .374** RG25 .395** .445** RG26 .270** .320** RG27 .350** .402** RG28 .296** .366**

### Association between Risk Appetite (RAG) and Project Success (RG)

The “risk appetite” (RAG) construct has two latent clusters: RAG1 and RAG2. Table 7 shows the 56 possible correlation values for these relationships. The largest positive correlation at 0.01 significance level is 0.608. This correlation is between RAG1 “risk appetite” of RAG cluster and RG3 “improvement of understanding of key risks and their wider implications” of RG. The lowest positive correlation at 0.01 significance level is 0.379. This correlation is between RAG2 “risk appetite alignment process” of RAG cluster and RG28 “fewer operational surprises”.

Table 7. Association between risk appetite and project success

 Risk Appetite RAG1 RAG2 Project Success RG1 .531** .452** RG2 .490** .411** RG3 .608** .518** RG4 .549** .534** RG5 .568** .499** RG6 .563** .507** RG7 .551** .511** RG8 .511** .467** RG9 .506** .431** RG10 .495** .436** RG11 .474** .459** RG12 .528** .475** RG13 .567** .450** RG14 .506** .483** RG15 .518** .460** RG16 .507** .459** RG17 .581** .520** RG18 .458** .407** RG19 .505** .468** RG20 .558** .493** RG21 .456** .440** RG22 .531** .510** RG23 .556** .523** RG24 .571** .513** RG25 .594** .570** RG26 .540** .535** RG27 .467** .484** RG28 .431** .379**

### Association between Project success (RGP) and Project Success (RG)

The “project success” (RGP) construct has three latent clusters: RGP1, RGP2, and RGP3. Table 8 shows the correlation values for these relationships. The largest positive correlation at 0.01 significance level is 0.929. This correlation is between RGP3 “effective project risk management” of RG cluster and RG4 “issuance of consolidated reports of disparate risk at board level” of RG. The lowest positive correlation at 0.01 significance level is 0.665. This correlation is between RGP1 “efficient project delivery” of RGP cluster and RG26 “risk-based audit helps to identify the risk appetite adequately” of RG.

Table 8. Association between project success and project success

 Project Success RGP1 RGP2 RGP3 Project Success RG1 .812** .745** .700** RG2 .796** .752** .840** RG3 .797** .805** .866** RG4 .787** .824** .929** RG5 .793** .813** .907** RG6 .792** .773** .922** RG7 .802** .826** .817** RG8 .903** .760** .831** RG9 .890** .761** .818** RG10 .847** .747** .735** RG11 .839** .739** .794** RG12 .881** .762** .737** RG13 .869** .758** .768** RG14 .878** .757** .820** RG15 .862** .805** .732** RG16 .878** .793** .774** RG17 .811** .824** .804** RG18 .808** .774** .703** RG19 .820** .766** .772** RG20 .800** .843** .727** RG21 .687** .868** .747** RG22 .813** .904** .823** RG23 .825** .840** .912** RG24 .810** .907** .850** RG25 .815** .915** .809** RG26 .665** .820** .670** RG27 .785** .870** .819** RG28 .737** .747** .666**

### Association between the Occurrence of Negative Events of Projects and Project Success (RG)

The two latent clusters for the “occurrence of negative events of projects” (IN) constructs are INP1 and INP2. Table 9 shows the correlation values for these relationships. The largest positive correlation at 0.01 significance level is 0.246. This correlation is between the INP2 “project failure” of IN cluster and RG1 “the achievement of strategic objectives” of RG. The lowest positive correlation at 0.05 significance level is 0.185. This correlation is between INP2 “project failure” of IN cluster and RG15 “increased project control to maximize efficiency” of RG. The highest negative correlation is -0.196, which is between the INP1 “governance failure” cluster of IN and RG18 “increased likelihood of delivering projects on scope, on time, and on budget” of RG. The lowest negative correlation is -0.184, which is between the INP1 cluster of IN and RG17 “early identification and understanding of internal and external issues pertaining to projects”.

Table 9. Association between the occurrence of negative events of projects and project success

 Occurrence of Negative Events of Projects INP1 INP2 Project Success RG1 .246** RG2 RG3 .190* RG4 .187* RG5 RG6 RG7 RG8 RG9 .193* RG10 RG11 .191* RG12 RG13 .210* RG14 .231* RG15 .185* RG16 RG17 -.184* RG18 -.196* RG19 RG20 RG21 .223* RG22 RG23 RG24 .196* RG25 RG26 .211* RG27 RG28 .205*

### Association between Internal Audit Function (IAF) and Project Success

The three latent clusters for the “internal audit function” (IAF) construct are IAFR1, IAFR2, and IAFR3. Table 10 shows the 84 possible correlation values for these relationships. The largest positive correlation at 0.01 significance level is 0.588. This correlation is between IAFR1 “role of internal audit” of IAF cluster and RG13 “reassurance of adequate implementation of risk management processes” of RG. The lowest positive correlation at 0.01 significance level is 0.186 with a significance of 0.0. This correlation is between IAFR2 “auditing of risk governance function” of IAF cluster and RG2 “delivering projects on time and budget” of RG.

Table 10. Association between internal audit function (IAF) and project success

 Internal Audit Function IAFR1 IAFR2 IAFR3 Project Success RG1 .517** .461** RG2 .524** .186* .399** RG3 .559** .236* .409** RG4 .523** .431** RG5 .511** .202* .485** RG6 .449** .410** RG7 .524** .462** RG8 .501** .433** RG9 .512** .439** RG10 .450** .367** RG11 .459** .443** RG12 .517** .414** RG13 .588** .469** RG14 .531** .447** RG15 .510** .419** RG16 .525** .477** RG17 .469** .456** RG18 .498** .191* .435** RG19 .478** .407** RG20 .546** .468** RG21 .521** .486** RG22 .532** .201* .503** RG23 .521** .492** RG24 .548** .476** RG25 .530** .208* .477** RG26 .461** .399** RG27 .504** .192* .518** RG28 .501** .447**

## The Occurrence of Negative Events of Projects

### Association between Strategy (S) and the Occurrence of Negative Events of Projects (IN)

Table 11 shows the correlation values for the relationship between the two latent clusters of “strategy” and IN. The largest negative correlation at 0.01 significance level is -0.261. This correlation is between the SG1 “risk alignment process” of strategy and IN8’s “lack of reporting to board and executives” of IN. The smallest negative correlation at the 0.01 level of significance is -0.188. This correlation is between SG1 “risk alignment process” and IN9 “our organization is experiencing failure to achieve the business objectives”.

Table 11. Association between strategy (S) and the occurrence of negative events of projects (IN)

 SG1 SG2 IN1 IN2 IN3 IN4 IN5 IN6 IN7 IN8 -.261** IN9 -.188*

### Association between Risk Appraisal and Insight (RAI) and the Occurrence of Negative Events of Projects (IN)

Table 12 shows the correlation values for the relationship between the two latent clusters of “risk appraisal and insight” and IN. The largest negative correlation at 0.01 significance level is -0.254. This correlation is between RAIG1 “risk alignment process” and IN8 “lack of reporting to board and executives” of IN. The smallest negative correlation at 0.01 level of significance is -0.194. This correlation is between SG1 “risk alignment process” and IN9 “our organization is experiencing failure to achieve the business objectives”.

Table 12: Association between risk appraisal and insight (RAI) and the occurrence of negative events of projects (IN)

 RAIG1 RAIG2 IN1 IN2 IN3 IN4 IN5 IN6 IN7 IN8 -.254** -.215* IN9 -.194*

### Association between Risk Management Governance (RMG) and the Occurrence of Negative Events of Projects (IN)

Table 13 shows the correlation values for the relationship between the two latent clusters of RMG and IN. The largest negative correlation at 0.01 significance level is -0.285. This correlation is between RMGG2 “risk control” of RMG and IN8 “lack of reporting to board and executives” of IN. The smallest negative correlation at 0.05 level of significance is -0.190. This correlation is between RMGG1 “risk governance” and IN5 “governance model fails to manage key projects”.

Table 13. Association between risk management governance (RMG) and the occurrence of negative events of projects (IN)

 RMGG1 RMGG2 IN1 IN2 IN3 IN4 IN5 -.190* IN6 IN7 -.243** IN8 -.282** -.285** IN9 -.227*

### Association between Review Risk Development and Decision (RDG) and the Occurrence of Negative Events of Projects (IN)

Table 14 shows the correlation values for the relationship between the three latent clusters of RDG and IN. The largest negative correlation at 0.01 significance level is -0.257. This correlation is between RMDG2 “effectiveness assurance” of RDG and IN8 “lack of reporting to board and executives” of IN. The smallest negative correlation at 0.01 level of significance is -0.226. This correlation is between RDG3 “monitoring of risk exposure” and IN8 “lack of reporting to board and executives”.

Table 14. Association between review risk development and decision (RDG) and the occurrence of negative events of projects (IN)

 RDG1 RDG2 RDG3 IN1 IN2 IN3 IN4 IN5 -.205* IN6 IN7 -.225* IN8 -.257** -.226* IN9

### Association between Risk Communication (RCG) and the Occurrence of Negative Events of Projects (IN)

Table 15 shows the correlation coefficients for the relationship between the three latent clusters of RCG and IN. The largest negative correlation at 0.01 significance level is -0.281, which is between RCG1 “risk communication” of RDG and IN6 “existence of unresolved issues and disputes” of IN. The smallest negative correlation at 0.05 level of significance is -0.197. This correlation is between RCG3 “risk coordination” and IN6.

Table 15. Association between risk communication (RCG) and the occurrence of negative events of projects (IN)

 RCG1 RCG2 RCG3 IN1 IN2 IN3 IN4 IN5 IN6 -.281** -.197* IN7 IN8 -.210* -.217* -.240* IN9 -.207*

### Association between Risk Culture (RCU) and the Occurrence of Negative Events of Projects (IN)

Table 16 shows the correlation values for the relationship between the two latent clusters of RCU and IN. The only negative correlation at 0.01 significance level is -0.210. This correlation is between RCUG1 “risk culture development” of RCUG and IN6 “existence of unresolved issues and disputes” of IN.

Table 16. Association between risk culture (RCU) and the occurrence of negative events of projects (IN)

 RCUG1 RCUG2 IN1 IN2 IN3 IN4 IN5 IN6 -.210* IN7 IN8 IN9

### Association between Risk Appetite (RAG) and the Occurrence of Negative Events of Projects (IN)

Table 17 shows the correlation values for the relationship between the two latent clusters of RAG and IN. The only negative correlation at 0.05 significance level is -0.196. This correlation is between RAG1 “risk appetite” of RAG and IN8 “lack of reporting to board and executives” of IN.

Table 17. Association between risk appetite (RAG) and the occurrence of negative events of projects (IN)

 RAG1 RAG2 IN1 IN2 IN3 IN4 IN5 IN6 IN7 IN8 -.196* IN9

### Association between Project Success (RGP) and the Occurrence of Negative Events of Projects (IN)

Table 18 shows the correlation values for the relationship between the three latent clusters of RGP and IN. The highest positive correlation at 0.01 significance level is 0.311. This correlation is between RGP1 “efficient project delivery” of RGP and IN1 “our organization is experiencing schedule delays” of IN. The smallest positive correlation at 0.05 significance level is 0.192. This correlation is between RGP2 “efficient risk monitoring” of RGP and IN4 “our organization experienced projects failure in the past” of IN. The smallest negative correlation at 0.05 significance level is -0.200, which is between RGP2 “efficient risk monitoring” and IN7 “lack of independent monitoring of progress”. The largest negative correlation at 0.05 level of significance is -0.210, which is between RGP3 “effective project risk management” and IN7.

Table 18. Association between project success (RGP) and the occurrence of negative events of projects (IN)

 RGP1 RGP2 RGP3 IN1 .208* .193* .194* IN2 .311** .286** .262** IN3 -.204* IN4 .192* IN5 IN6 IN7 -.200* -.210* IN8 IN9

### Association between Occurrence of Negative Events of Projects (INP) and the Occurrence of Negative Events of Projects (IN)

Table 19 shows the correlation values for the relationship between the two latent clusters of INP and IN. The highest positive correlation at 0.01 significance level is 0.917. This correlation is between INP1 “governance failure” and IN7 “lack of independent monitoring of progress” of IN. The smallest positive correlation at 0.01 significance level is 0.413, which is between INP1 “governance failure” and IN2 “our organization is experiencing cost overrun” of IN.

Table 19. Association between occurrence of negative events of projects (INP) and the occurrence of negative events of projects (IN)

 INP1 INP2 IN1 .434** .787** IN2 .413** .840** IN3 .839** .511** IN4 .524** .790** IN5 .852** .612** IN6 .556** .861** IN7 .917** .547** IN8 .842** .643** IN9 .860** .534**

### Association between Internal Audit Function (IAF) and the Occurrence of Negative Events of Projects (IN)

Table 19 shows the correlation values for the relationship between the three latent clusters of IAF and IN. The highest positive correlation at 0.01 significance level is 0.359, which is between IAFR1 “role of internal audit” and IN2 “our organization is experiencing cost overrun” of IN. The smallest positive correlation at 0.05 significance is 0.186, which is between IAFR1 and IN4 “our organization experienced projects failure in the past” of IN. The largest negative correlation is -0.277, which is between IAFR3 “provision of audit reports” and IN7 “lack of independent monitoring of progress”. The smallest negative correlation at 0.05 level of significance is -0.192, which is between IAFR3 and IN5 “governance model fails to manage key projects”.

Table 20. Association between internal audit function (IAF) and the occurrence of negative events of projects (IN)

 IAFR1 IAFR2 IAFR3 IN1 .211* IN2 .359** .206* IN3 IN4 .186* IN5 -.192* IN6 .202* IN7 -.199* -.277** IN8 .209* IN9

## Summary

Correlation analysis has revealed the existence of relationships between risk governance determinants and the effectiveness of public projects. There were more positive relationships between risk governance determinants and project effectiveness than between risk governance determinants and negative events.

## References

Gelman, A, Carlin, JB, Stern, HS, Dunson, DB, Vehtari, A & Rubin, DB 2014, Bayesian data analysis, 3rd ed, CRC Press, Boca Raton, FL.

Johnson, DL 2017, Statistical tools for the comprehensive practice of industrial hygiene and environmental health sciences, 1st edn, John Wiley & Sons, Hoboken, NJ.

Pollock, PH 2015, A Stata® companion to political analysis, 1st edn, CQ Press, California, CA.

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