A REVIEW ON THE USE OF REGRESSION ANALYSIS IN STUDIES OF AUDIT QUALITY

ABSTRAK Kajian ini bertujuan untuk mereviu bagaimana analisa regresi digunakan dalam suatu fenomena abstrak seperti kualitas audit, suatu konsep yang penting dalam praktik audit (Schroeder et al., 1986) namun belum terdefinisi dengan jelas. Artikel yang direviu dalam kajian ini adalah artikel penelitian yang memasukkan kualitas audit sebagai variabel penelitian, baik sebagai variabel independen maupun dependen. Artikel-artikel tersebut dipilih dengan cara purposif sampling untuk mendapatkan keterwakilan yang seimbang antara artikel jurnal khusus audit dan akuntansi secara umum, serta mewakili jurnal Anglo Saxon dan Anglo American. Artikel yang direviu diterbitkan pada periode 1983-2011 oleh jurnal yang masuk dalam kategori A/A berdasarkan klasifikasi ERA pada tahun 2010. Kajian ini menemukan bahwa sebagian besar artikel-artikel tersebut menggunakan analisa regresi berganda dan menjadikan kualitas audit sebagai variabel dependen serta mengukurnya menggunakan proksi. Kajian ini juga menyoroti ukuran data sampel yang digunakan dan kurangnya pembahasan mengenai asumsi yang digunakan dalam analisa statistik. Kajian ini menyimpulkan bahwa efektivitas dan validitas penggunaan analisa regresi berganda dalam penelitian tidak hanya bergantung pada kemampuan peneliti untuk menggunakannya, namun juga pada kemampuan peneliti untuk mengkomunikasikan hasil penelitiannya kepada pembaca. This study aimed to review how regression analysis has been used in studies of abstract phenomenon, such as audit quality, an importance concept in the auditing practice (Schroeder et al., 1986), yet is not well defined. The articles reviewed were the research articles that include audit quality as research variable, either as dependent or independent variables. The articles were purposefully selected to represent balance combination between audit specific and more general accounting journals and between Anglo Saxon and Anglo American journals. The articles were published between 1983-2011 and from the A/A class journal based on ERA 2010’s classifications. The study found that most of the articles reviewed used multiple regression analysis and treated audit quality as dependent variable and measured it by using a proxy. This study also highlights the size of data sample used and the lack of discussions about the assumptions of the statistical analysis used in most of the articles reviewed. This study concluded that the effectiveness and validity of multiple regressions do not only depends on its application by the researchers but also on how the researchers communicate their findings to the audience. TINJAUAN PENGGUNAAN ANALISA REGRESI DALAM KAJIAN TENTANG KUALITAS AUDIT SEJARAH ARTIKEL: Diterima pertama: Desember 2014 Dinyatakan dapat dimuat : Juni 2015 KATA KUNCI: Kualitas audit, analisa regresi

This study aimed to review how regression analysis has been used in studies of abstract phenomenon, such as audit quality, an importance concept in the auditing practice (Schroeder et al., 1986), yet is not well defined. The articles reviewed were the research articles that include audit quality as research variable, either as dependent or independent variables. The articles were purposefully selected to represent balance combination between audit specific and more general accounting journals and between Anglo Saxon and Anglo American journals. The articles were published between 1983-2011 and from the A/A class journal based on ERA 2010's classifications. The study found that most of the articles reviewed used multiple regression analysis and treated audit quality as dependent variable and measured it by using a proxy. This study also highlights the size of data sample used and the lack of discussions about the assumptions of the statistical analysis used in most of the articles reviewed. This study concluded that the effectiveness and validity of multiple regressions do not only depends on its application by the researchers but also on how the researchers communicate their findings to the audience.

INTRODUCTION
Statistical analysis based on linear regression 1 models, such as multiple regression, has become a major tool for the analysis of a wide range of empirical problems (Western, 1995). The popularity of this tool can be attributed to its easiness to use and understand and, under certain conditions, its ability to give 'best' 2 estimates of population parameters 'efficiently' 3 (Allison, 1999). Additionally, although regression analysis is originally developed for the analysis of measurable observations, it can be used to analyse abstract phenomena as well.
To study how regression analysis has been used in studying an abstract phenomenon, this study reviews research articles on audit quality.
Audit quality is an important concept within the auditing practice because it is the key indicator of auditors' performance and, as such, has been one of the major research topics within the auditing discipline. Yet, despite its importance, no clear definition about audit quality has been developed, even in the auditing standards, and scholars still have different understanding of its meaning, not to mention how to measure audit quality [Schroeder et al., 1986]. The existing audit standards imply only that audit quality is achieved by the issuance of the ''appropriate'' audit report on the client's compliance with generally accepted accounting principles (Francis, 2011).
This study aimed to review the practices of multiple regression analysis used on the audit quality through research articles that using audit quality as a variable. This study will be beneficial for future researchers to be more effectively use multiple regression analysis on audit quality and then effectively communicating their research report.

Theoretical Study.
Regression can simply be defined as statistical relations between variables (Kutner et al., 2004). The variables consist of a single dependent variable 4 and one or more independent variables 5 . If the model involves one independent variable only, the analysis is called simple regression 6 . When the model involves more than one independent variables, the analysis is called multiple regression. Regression can be used for three 1 The word 'regression' is introduced by Sir Francis Galton (1822Galton ( -1911, an English Scientist, in his study of the relationship between heights of fathers and sons (Upton and Cook, 2002) 2 Best refers to the estimators with minimum sampling variation (Bohrnstedt and Carter, 1971). 3 Efficient estimation produces standard errors that are as small as possible (Allison, 1999) 4 Also known as the response variable or outcome variable (Upton and Cook, 2002) 5 Also known as antecedent variables, background variables, predictor variables, explanatory variables, or controlled variables (Upton and Cook, 2002). 6 If the model involve more than one dependent variables, the analysis is called multivariate analysis (Hair et al., 2006). purposes: (1) description, (2) control, and (3) prediction 7 (Kutner et al., 2004).
Like any other statistical technique, regression analysis is developed with several assumptions. The assumptions define the boundaries within which regression analysis will work well. The main assumptions for the multiple regression analysis are (Berry, 1993, p. 12): i. All independent variables (X1, X2, …, Xk) are quantitative or dichotomous, and the dependent variable , Y, is quantitative, continuous, and unbounded. Moreover, all variables are measured without error ii. All independent variables have nonzero variance (i.e., each independent variable has some variation in value) iii. T h e r e i s n o t p e r f e c t multicollinearity (i.e., there is no exact relationship between two or more of the independent variables) iv. At each set values for the k independent variables, (X1j, X2j, …,Xkj), E( j½X1j, X2j,…,Xkj) = 0 (i.e., the mean value of the error term is zero) v. For each Xi, COV(Xij, j) = 0 (i.e., each independent variable is uncorrelated with the error term) vi. At each set of values for the k independent variables, (X1j, X2j, …,Xkj), VAR(εj½X1j, X2j,…,Xkj) = 2 , wher e 2 is a constant (i.e., the conditional variance of the error term is constant); this is known as the assumption of homoscedasticity. vii. For any two observations, (X1j, X2j, …,Xkj) and (X1h, X2h,…,Xkh), COV( j, h) = 0 (i.e., error terms for different observations a r e u n c o r r e l a t e d ) ; t h i s assumptions is known as lack of autocorrelation. viii. At each set of values for the k independent variables, j is normally distributed.
As a set, point i to point vii assumptions are also known as Gauss-Markov Theorem.
In addition to the assumptions, Allison (1999) points out that the robustness of a regression model can be compromised if measurement errors and/or specification errors exist in the model. Specification errors occur when certain variables are mistakenly included or omitted in the model, or when the functional form to represent the variables is incorrect (Bohrnstedt and Carter, 1971). While measurement errors arise due to the assumption in the parametric statistic that the scale used to measure the variables is interval or ratio scale, which is not always the case in empirical problems being studied. 7 Allison (1999) describes that regression can be used in causal analysis, aiming to determine whether a particular independent variable really affects the dependent variable, and to estimate the magnitude of that effect. However, Kutner et al. (2004) argue that the existence of statistical relation between dependent and independent variable(s), no matter how strong it is, does not imply that dependent variable depends causally on independent variable(s). Keith (2006) takes a position that "…we can and do make causal inferences…under certain condiin other cases, such inferences are invalid and misleading…(p.18)".

Sampling
Articles to be reviewed in this study are identified through searching in Business Source Premier database with the key word of audit quality and the publication date between 1983-2011. Only the research articles that include audit quality as research variable, either dependent or independent, are considered in this study. The articles then are purposefully selected to represent balance combination between audit-specific and more general accounting journals and between Anglo-Saxon and Anglo-American journals 8 . The journal where the articles published are A/A* class journals based on ERA 2010's classifications 9 , with the consideration that research articles published in these journals represent benchmark or best practice in the conduct of research within the auditing discipline

Research Questions
The research articles has been analysed using these three major questions: 1) Does it mentions a definition of audit quality? 2) What is the measurement for the audit quality? 3) How the research data being analysed

RESULT AND DISCUSSION
Based on the sampling methods performed, there are 30 articles reviewed from three reputable journals, which are European Accounting Review, Auditing: A Journal of Practice & Theory, and The Accounting Review. The list of the articles and the result can be seen in Appendix 1. The discussion from the results are as follow:

Definition of Audit Quality
This study found out that from 30 research articles reviewed, there were 13 articles did not mention about audit quality definition. While the rest of 17 articles did mention about audit quality definition but with varied definition. These were some definition found in the majority of research articles: 1) An audit that improves the reliability of financial statement information 2) A probability of auditor would discover and report a breach in the client's accounting system 3) Th e magnitude of abs olut e discretionary accruals that influence audit opinion 4) Represents the present (acceptable quality) or absence (unacceptable quality) of audit repot and audit procedures required 5) The probability that auditors will report a known material error 6) The extent to which the audits result in reporting that is in compliance with GAAP 8 Anglo-Saxon and Anglo-American perspectives are generally considered as the major influencer of audit practices in the world 9 http://www.arc.gov.au/era/ 7) The joint probability that auditor will both discover a breach in the clien't accounting system and disclose it.
Based from the observation on that research articles can be concluded that most scholars implied that audit quality can be achieved by a qualified audit report (reporting a breach on the accounting system or GAAP). This conslusion is in line with Francis's (2011) statement that the definition of audit quality in audit standards imply only that audit quality is achieved by the issuance of the ''appropriate'' audit report on the client's compliance with generally accepted accounting principles (Francis, 2011).

Measurement of Audit Quality
The approach used to investigate audit quality varies among journals. In general, multiple regression analysis is the most common method of analysis. Within this method, audit quality is mostly treated as dependent variable and is measured by using a proxy.
The use of a proxy to represent certain variable in the model is a common practice in the regression analysis. Upton and Cook (2002) define a proxy as a measurable variable that is used in place of a variable that cannot be measured. The alternative strategy of using a proxy is to delete the unmeasurable variable from the model (Trenkler and Stahlecker, 1996). In the studies of audit quality this approach is not common because the audit quality is the dependent variable in the model. Furthermore, studies show that, under the criterion of asymptotic bias, using a proxy, even the poor one, is better than dropping the unmeasurable variable (McCallum (1972) and Wickens (1972)). Also, using the scalar valued mean square error (MSE) criterion, Aigner (1974) demonstrates that proxies are preferable in most, but not all, situations. Nonetheless, Maddala (1977) and Frost (1979) recommend the use of reliable proxy only.
In the reviewed research articles, several variables have been used as proxy of audit quality, such as discretionary accruals, auditor size or class, audit fees, and audit report with modified audit opinion, with discretionary accruals become the most commonly used proxy for audit quality. Use of difference proxies to replace the same concept might indicate lack of generally accepted or agreed audit quality measures. Even in the most commonly used proxy, i.e., discretionary accruals, there are still debates about the appropriateness of this variable as proxy of audit quality (Guay et al. 1996) Berry (1993) warns that the use of proxy in regression analysis might result in measurement errors. When proxy is used, researcher can be lured into a false conclusion of valid measurement if there is little error in the measurement of the proxy itself. He further gives example about this issue: "…knowledge that per capita income is measured without any error would not be evidence of the absence of error in the measurement of the concept of level of development when income is used as proxy (p.58)".
Berry advises that researchers must be alert to two possible sources of measurement error when proxy variables are used as indicators: (a) Random or non-random error in the measurement of the true score for the proxy (b) Non-random error resulting from the inability of the true score on the proxy to reflect perfectly the concept being measured.

Data Analysis Technique
The observation on data analysis technique that should be taken as an interest is related to the sample size. Reviews on the studies in the articles found that even though the sample size varies among studies, in several studies the sample size can be as much as more than 10.000 observations/data. Normally, larger sample size is preferable in statistical analysis, however too large samples can also produce incorrect conclusions. Allison (1999) describes that too large sample is like a very sensitive measuring instrument. Because it is very sensitive, large sample will detect any artifactual relationships, such as the sample was not quite random or some bias in the data, along with the true relationships. As such, with very large samples, almost any variable in a regression model is likely to be statistically significant, even if it has no real effect. When a variable has a statistically significant coefficient, researchers tend to say that the coefficient is unlikely to be zero. This evidence can be seen in the studies being reviewed. When the sample is relatively large, some studies shows that the coefficient is statistically significant but the magnitude of this coefficient is relatively low (e.g., Krishnan (2003), Lawrence et al. (2011), Behn et al. (2008) Another common observation is the lack of discussion about the assumptions of the statistical analysis used in the study. For multiple regression analysis, although studies have shown that violation to the assumptions does not impact severely the conclusion reached, providing information about assumptions will help readers understanding and interpreting the findings better. Furthermore, it is seldom for researchers to be able to do research without having to violate some assumptions. As such, by providing further analysis on the assumptions being violated and how this violation affect the interpretation of the findings, researchers have shown his/her mastery on the statistical analysis used.

Guidelines for Future Research
Reviews of research articles on audit quality indicates that the concept of audit quality is definitely still abstract, in terms of the definition and the measurement. The use of various proxies in the studies can be interpreted either positively or negatively. On the positive side, different proxies might indicate the richness of the concept being studied. Yet, on the other hand, too many proxies will prevent the accumulation of knowledge on audit quality, not to mention on the identification of the variables that may affect the audit quality and the relationships among these variables. Having limited proxies are better also as it will minimize the risks of measurement errors. As such, future studies on audit quality should focused more on identifying high quality variables that can be used as generally accepted proxies of audit quality and then focus the research on identifying variables that affect audit quality based on these proxies. Furthermore, using common proxy will facilitate comparisons and comprehensions between studies and accumulation of knowledge about the audit quality.
As observed by Berry, (1993), although most social scientists can recite the formal definitions of the various regression assumptions, many have little appreciation of the substantive meanings of the assumptions. Further, he argues that the use of regression analysis to generate substantive conclusions that are regularly worth believing requires that users consider (a) whether each of the assumptions of regression is likely met in each specific research project at hand and, when some are not met, (b) the implications of these violations. As such, the discussion about how the study has been conducted in the term of the assumptions of the analytical used should be present on any research report to facilitate better interpretation of research findings.
Also, because audit quality is not well defined at this stage, it would be interesting if the researchers in the area approach this topic using various statistical analytical tools. In the last 30 years, statisticians have introduced a number of sophisticated methods. These methods go by such names as logistic regression, Poison regression, structural equation modelling, and survival analysis (Allison, 1999). By using different statistical analysis tools, researcher can approach the subject from different point of view that is necessary to study such abstract concept as audit quality. Perhaps, they can consider using the other paradigm, i.e., interpretivist or critical study approach, in addition to positivist approach that seem to be the major paradigm in the journals being studied. Using different research paradigm will broaden and enrich the understanding about audit quality.

CONCLUSION
The effectiveness and validity of statistical analysis, such multiple regressions, do not depend on the way this tool is applied by researchers only, but also depend on how well researchers communicate their findings to the audience. The researcher might had done the research perfectly, but if they fail to communicate the findings effectively, the readers will not see the benefit and the quality of the research undertaken and, consequently, the research will be impactless.
Referring to communication theory, a communication is considered effective when the sender and the receiver having the same understanding about the message. Similarly, because research study reports/articles represent a communication media between researchers and the readers, the researchers should make sure that they provide as much information as feasible to facilitate readers understanding and interpretation on the research results. a quality audit is one in which an auditor reduces detection risk to a point where ultimate audit risk is at an "appropriately low level. the conditional probability that auditors will report a known material error.

REFERENCES
the likelihood that the auditor would discover the material error (discover assessment) and the conditional probability that the auditor would require the client to correct the error or, if the client refused, would report the error in the audit opinion (disclosure assessment) The joint probability of detecting and reporting material financial statement errors A significant difference in audit quality between Big 6 and non-Big 6 auditors and higher audit quality is associated with Big 6 auditors.
Multiple regressions analysis