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Governments all over the world are faced with numerous challenges while running their countries on a daily basis. The predominant challenges which arise are those which involve statistical methodologies. Official statistics to South Africa’s infrastructure are very important and because of this it is important that an effort is made to reduce the challenges that occur during the development of official statistics. For official statistics to be developed successfully quality standards need to be built into an organisational framework and form a system of architecture (Statistics New Zealand 2009:1). Therefore, this study seeks to develop a statistical methodology that is appropriate and scientifically correct using an automated statistical system for audits in government regulatory authorities. The study makes use of Mathematica to provide guidelines on how to develop and use an automated statistical audit system. A comprehensive literature study was conducted using existing secondary sources. A quantitative research paradigm was adopted for this study, to empirically assess the demographic characteristics of tenants of Social Housing Estates and their perceptions towards the rental units they inhabit. More specifically a descriptive study was undertaken. Furthermore, a sample size was selected by means of convenience sampling for a case study on SHRA to assess the respondent’s biographical information. From this sample, a pilot study was conducted investigating the general perceptions of the respondents regarding the physical conditions and quality of their units. The technical development of an automated statistical audit system was discussed. This process involved the development and use of a questionnaire design tool, statistical analysis and reporting and how Mathematica software served as a platform for developing the system. The findings of this study provide insights on how government regulatory authorities can best utilise automated statistical audits for regulation purposes and achieved this by developing an automated statistical audit system for government regulatory authorities. It is hoped that the findings of this study will provide government regulatory authorities with practical suggestions or solutions regarding the generating of official statistics for regulatory purposes, and that the suggestions for future research will inspire future researchers to further investigate automated statistical audit systems, statistical analysis, automated questionnaire development, and government regulatory authorities individually.

Thesis (MAcc)--Stellenbosch University, 2011. / ENGLISH ABSTRACT: The quality of external audits has increasingly come under the spotlight over the last decade as a result of a number of audit failures. The use of scientifically based statistical sampling as a sampling technique is allowed, but not required by International Standards on Auditing. The science behind this sampling technique can add to the credibility and quality of the audit. Accordingly the main objective of this study was to explore certain key aspects of the use of statistical sampling as a sampling technique in the audits of financial statements done by South African Registered Auditors accredited by the Johannesburg Stock Exchange (JSE). A literature review of the most recent local and international studies related to the key aspects addressed in this study was done. An empirical study was then done by means of a questionnaire that was sent to the JSE-accredited auditing firms for completion. The questionnaire focused on what was allowed by the firms’ audit methodologies regarding the key aspects investigated in this study and not on the actual usage of statistical sampling in audits performed by the firms. The following main conclusions were drawn in respect of the four key aspects that were investigated: 1. In investigating the extent to which statistical sampling is used by auditing firms, it was found that the majority of them was allowed to use the principles of statistical sampling. Upon further investigation it was found that only 38% were explicitly allowed to use it in all three sampling steps (size determination, selection of items and evaluation of results). The evaluation step was identified as the most problematic statistical sampling phase. 2. Two reasons why auditors decided not use statistical sampling as a sampling technique were identified, namely the perceived inefficiency (costliness) of the statistical sampling process, and a lack of understanding, training and experience in the use thereof. 3. In investigating how professional judgement is exercised in the use of statistical sampling, it was found that the audit methodologies of the majority of the auditing firms prescribed the precision and confidence levels to be used, and further that the minority indicated that they were allowed to adjust these levels using their professional judgement. The partner in charge of the audit was identified to be typically responsible for final authorisation of the sampling approach to be followed. 4. It was found that approximately a third of the auditing firms did not use computer software for assistance in using statistical sampling. The majority of the auditing firms did however have a written guide on how to use statistical sampling in practice available as a resource to staff. The value of this study lies in its contribution to the existing body of knowledge in South Africa regarding the use of statistical sampling in auditing. Stakeholders in statistical sampling as an auditing technique that can benefit from this study include Registered Auditors in practice, academics, and, from regulatory, education and training perspectives, the Independent Regulatory Board for Auditors and the South African Institute of Chartered Accountants. / AFRIKAANSE OPSOMMING: Na aanleiding van 'n aantal oudit mislukkings in die afgelope dekade het die kwaliteit van eksterne oudits toenemend onder die soeklig gekom. Die gebruik van wetenskaplik gebaseerde statistiese steekproefneming word deur die International Standards on Auditing toegelaat, maar nie vereis nie, as 'n steekproefnemingstegniek. Die wetenskap agter hierdie steekproefnemingstegniek kan tot die geloofwaardigheid en die kwaliteit van die oudit bydra. Die hoofdoel van hierdie studie was gevolglik om sekere sleutel aspekte van die gebruik van statistiese steekproefneming as 'n steekproefnemingstegniek in die oudits van finansiële state soos gedoen deur Suid-Afrikaanse Geregistreerde Ouditeure geakkrediteer deur die Johannesburgse Effektebeurs (JSE), te verken. 'n Literatuurstudie van die mees onlangse plaaslike en internasionale studies wat verband hou met die sleutel aspekte wat in hierdie studie aangespreek word, is gedoen. 'n Empiriese studie is daarna gedoen met behulp van 'n vraelys wat vir die voltooiing aan die JSE-geakkrediteerde ouditeursfirmas gestuur is. Die vraelys het gefokus op wat toegelaat word deur die firmas se oudit metodologieë ten opsigte van die sleutel aspekte ondersoek in hierdie studie en nie op die werklike gebruik van statistiese steekproefneming in oudits wat deur die firmas uitgevoer word nie. Die volgende hoofgevolgtrekkings is gemaak ten opsigte van die vier sleutel aspekte wat ondersoek is: 1. In die ondersoek na die mate waarin statistiese steekproefneming gebruik word deur ouditeursfirmas, is gevind dat die meerderheid toegelaat was om die beginsels van statistiese steekproefneming te gebruik. By verdere ondersoek is gevind dat slegs 38% uitdruklik toegelaat word om dit te gebruik in al drie steekproefneming stappe (grootte-bepaling, keuse van items en evaluering van resultate). Die evalueringstap is geïdentifiseer as die mees problematiese statistiese steekproefnemings fase. 2. Twee redes waarom ouditeure besluit het om nie statistiese steekproefneming as 'n steekproefnemingstegniek te gebruik nie is geïdentifiseer, naamlik die vermeende ondoeltreffendheid (hoë koste) van die statistiese steekproefnemingsproses, en 'n gebrek aan begrip, opleiding en ondervinding in die gebruik daarvan. 3. Met die ondersoek van die wyse waarop professionele oordeel uitgeoefen word in die gebruik van statistiese steekproefneming, is gevind dat die presisiepeil en vertrouensvlakke wat gebruik word deur die meerderheid van die ouditeursfirmas se oudit metodologieë voorgeskryf word, en verder het die minderheid aangedui dat hulle hierdie vlakke mag aanpas deur hul professionele oordeel te gebruik. Die vennoot in beheer van die oudit is geïdentifiseer as tipies verantwoordelik vir die finale goedkeuring van die steekproefnemingsbenadering wat gevolg word . 4. Daar is gevind dat ongeveer 'n derde van die ouditeursfirmas nie gebruik maak van rekenaarsagteware vir bystand in die gebruik van statistiese steekproefneming nie. Die meerderheid van die ouditeursfirmas het egter 'n geskrewe gids oor hoe om statistiese steekproefneming in die praktyk te gebruik as 'n hulpmiddel aan personeel beskikbaar. Die waarde van hierdie studie lê in sy bydrae tot die bestaande liggaam van kennis in Suid-Afrika met betrekking tot die gebruik van statistiese steekproefneming in ouditkunde. Belanghebbers in statistiese steekproefneming as 'n oudittegniek wat kan baat vind by hierdie studie sluit in Geregistreerde Ouditeure in praktyk, akademici, en, vanuit regulerings-, opvoedings- en opleidingsperspektiewe, die Independent Regulatory Board for Auditors en die Suid-Afrikaanse Instituut van Geoktrooieerde Rekenmeesters.

This research examined the performance of three parametric methods for confidence intervals: the classical, the Bonferroni, and the bootstrap-t method, as applied to estimating the mean of voucher populations in accounting. Usually auditing populations do not follow standard models. The population for accounting audits generally is a nonstandard mixture distribution in which the audit data set contains a large number of zero values and a comparatively small number of nonzero errors. This study assumed a situation in which only overstatement errors exist. The nonzero errors were assumed to be normally, exponentially, and uniformly distributed. Five indicators of performance were used. The classical method was found to be unreliable. The Bonferroni method was conservative for all population conditions. The bootstrap-t method was excellent in terms of reliability, but the lower limit of the confidence intervals produced by this method was unstable for all population conditions. The classical method provided the shortest average width of the confidence intervals among the three methods. This study provided initial evidence as to how the parametric bootstrap-t method performs when applied to the nonstandard distribution of audit populations of line items. Further research should provide a reliable confidence interval for a wider variety of accounting populations.