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The importance of quantitatively assessing the spatial patterns of geodiversity, and their intrinsic relationship with biodiversity and the ecosystem services provided to society, has been signalized by several authors, due to the relevance of this information in territorial management, the planning of environmental and conservation strategies. Within geodiversity method assessments, the grid system is the most widely used GIS spatial approach to calculate a geodiversity index. Preferred for its simplicity, it implies the fundamental decision of choosing the scale of the analysis, defined by the selection of cell size, determinant for the accuracy and correctness of the final maps. Although this topic has been occasionally approached by some authors within geodiversity assessments, there is no formal procedure for cell size selection. This is a key issue, and, in the scope of the present work, an empirical procedure to select optimal cell size(s) was tested on the national scale in Portugal, in lithology and geomorphology datasets. The quantitative method based on geodiversity indices was applied, using richness, diversity and evenness indices, in a hexagonal analytical grid, through eight cell dimensions. Several descriptive statistical parameters were analyzed, with particular emphasis on dispersion statistical measures. Optimal cell size corresponded to the minimum cell size, once dispersion values were significatively reduced or stabilized, and distributions from evenness and diversity indices were closer to symmetry, which provided more accurate results and higher spatial differentiation, although the final decision should always consider the main purposes of the analysis.

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PurposeThe purpose of this paper is to examine whether the voluntary implementation of an internal audit department (IAD) by municipalities has any influence on external auditors' opinions.Design/methodology/approachThis study population comprises the 308 Portuguese municipalities, from which the authors extracted a sample of 179. Financial and audit reports were collected from the period under analysis (2014–2017). The sample was then divided into two groups: municipalities that had voluntarily implemented an IAD and those that had not. Internal audit departments were characterized according to their robustness – whether they were more or less robust. First, a descriptive statistical analysis of the dataset was performed to analyze the representativeness of the sample and to extract insights. To address the research questions, ordinal random effect regression models were considered.FindingsContrary to the authors' expectations, the voluntary implementation of an IAD had no influence on the audit report type. However, when the authors refined the approach to include the robustness of the IAD, it became clear that this variable does influence the report issued by the external auditor.Originality/valueThis paper contributes to the current literature by determining the effects of the robustness of IADs on municipality audit reports. As far as the authors know, this paper is novel. Since auditing plays an important role in the transparency of public financial statements and in promoting equity, this study shows that a robust IAD is an advantage in the pursuit of these goals.