© The Author(s), Published by EDP Sciences, 2026

1 Introduction

Rapid urbanization has increased the need to evaluate environmental quality and human well-being in cities [1]. Consequently, research in urban planning, architecture, and environmental engineering seeks methodologies that integrate physical attributes with subjective experience [2]. Within this context, the soundscape approach has emerged as a standardized framework for assessing acoustic environments, moving beyond traditional analyses based solely on sound pressure level (SPL). Recent work on urban acoustic environments likewise indicates that sound pressure level indices alone may overlook relevant temporal, spectral, and source-related structures, motivating multimetric characterizations that complement SPL with additional acoustic indicators [3].

By integrating perceptual and contextual dimensions, the soundscape approach provides a comprehensive understanding of human interaction with acoustic environments [4–7]. Environmental sound is recognized as a key element of the multisensory experience of a place, influencing how people affectively and cognitively evaluate urban spaces [8]. Consequently, this perspective has led to the development of standardized perceptual assessment tools that translate subjective acoustic experience into structured data.

The ISO 12913 series [9–11] formalizes the soundscape paradigm, emphasizing that soundscape is the acoustic environment as perceived or experienced and/or understood by a person or people, in context, and that context comprises the interrelationships between person, activity, and place, in space and time, which may influence auditory sensation, interpretation, and responses to the acoustic environment [4, 12–14]. The ISO 12913 series provides an internationally accepted framework for soundscape research: Part 1 [9] defines the concept and model, Part 2 [10] details in situ data collection and reporting, and Part 3 [11] guides data analysis. In practical implementations of ISO-guided soundscape assessments, researchers must still make specific design choices regarding questionnaire structure and response formats (e.g., bipolar adjective pairs versus single-attribute items, and ordinal versus metric response options). Such choices can systematically influence how perceptual data are summarized and interpreted in subsequent analyses. However, the extent to which these design decisions affect distributional outcomes and circumplex-based representations has not been consistently quantified in applied soundscape studies. This study therefore addresses these methodological issues, particularly regarding response-scale conversion and questionnaire configuration.

Among the most widely adopted instruments for perceptual soundscape assessment is the Perceived Affective Quality (PAQ) questionnaire, composed of bipolar adjective pairs (e.g., Calm – Chaotic, Monotonous – Vibrant) [10, 15, 16]. These instruments are essential in soundscape research because they provide standardized methods for collecting perceptual data, which may inform evidence-based planning and policymaking in environmental acoustics and urban design [17–20].

Despite the availability of standardized PAQ formats in ISO/TS 12913-2, the comparative effects of these methodological options have not yet been systematically quantified. Specifically, how do different response scale formats and questionnaire configurations influence statistical outcomes, distributional properties, and circumplex-based representations? Understanding these effects is essential for researchers to make informed methodological choices aligned with their analytical objectives. In particular, the distinction between metric and ordinal scales, especially when applied to bipolar semantic configurations, has received limited attention in the soundscape literature [21–24]. However, the choice of scale format may substantially affect not only the sensitivity and resolution of responses, but also the cognitive effort required from participants, the clarity of item interpretation, and the consistency of affective judgments [15, 24–27].

The existing literature on noise annoyance [28, 29], particularly from the International Commission on Biological Effects of Noise (ICBEN), describes two widely used response formats: a five-point ordinal scale with verbal labels, and a 0–10 point numeric rating scale adapted for different languages. Brink et al. [30] converted both the 5-point ordinal and 11-point numeric rating scales to a 0–100 metric, mapping verbal categories to 6, 25, 52, 79, and 95. This conversion underestimated annoyance at the lower end (0 vs. 6) and overestimated it at the upper end (100 vs. 95). Nevertheless, the authors endorsed the ICBEN conversion, as no alternative method offered clear advantages at the extremes. Similarly, Zhang et al. [31] compared a 0–100 linear scale with a 0–10 category scale containing five verbal anchors in laboratory listening tests and found that perceived annoyance results were largely independent of scale type.

From a statistical standpoint, metric scales (interval or ratio) yield numerical values with consistent intervals, making them compatible with a broad range of statistical analyses, including parametric techniques when distributional assumptions are sufficiently met. Such scales enable powerful and detailed modeling across many contexts. Ordinal scales, in contrast, represent ordered categories without defined distances between them. They can simplify the response process and reduce interpretative ambiguity, but they restrict the analyst to ordinal-specific or nonparametric methods, limiting the scope and complexity of statistical models that can be applied [32].

Moreover, when semantic polarity is introduced through bipolar adjective pairs, the interaction between scale format and item configuration becomes even more critical. It remains unclear whether certain scale types facilitate or hinder expressing perceptual contrasts, particularly when respondents are asked to make nuanced affective distinctions [33, 34].

While ISO/TS 12913-2 [10] provides standardized options for scale response formats and questionnaire configurations, the comparative effects of selecting among these options on downstream analytical outcomes have not yet been systematically quantified in applied soundscape studies, which limits the empirical basis for recommending specific format-configuration combinations in different research contexts. This concern is consistent with broader observations in soundscape research, where data-collection tools and protocols vary substantially across studies, particularly with respect to the use of questionnaires and semantic scales in different empirical designs [16]. Moreover, survey methodology has repeatedly shown that response scale format and question construction can alter response behavior and, consequently, statistical results and conclusions, underscoring the importance of empirically testing these design decisions rather than assuming equivalence [24]. Addressing this gap, the present study experimentally compares two methods for converting ordinal responses into a continuous metric scale (Snell’s conversion [35] and fixed-value mapping [30]) as well as two PAQ questionnaire configurations (four bipolar PAQs versus eight single-attribute PAQs [24, 25]). Their influence on both statistical results and spatial representations within the ISO/TS 12913-3 [11] soundscape evaluation framework is investigated.

Building on this comparative and experimental approach, the study aims to evaluate the effectiveness, sensitivity, and interpretative clarity of different PAQ response formats in soundscape questionnaires. By integrating statistical metrics with circumplex graph analyses, this research provides methodological guidance for optimizing the design of perceptual instruments in soundscape studies. Circumplex representations were constructed following ISO/TS 12913-3 coordinate transformations [11], applied at the individual response level as recommended by Mitchell et al. [36], with visualizations based on mean values of the resulting continuous ISOPleasant and ISOEventful coordinates. Ultimately, it contributes to the development of robust and interpretable data collection tools that deepen the understanding of subjective dimensions of acoustic environments and support evidence-based practices in environmental acoustics and urban perception research.

2 Research questions and hypotheses

This study addresses two primary research questions:

Based on prior research on scale format effects and the theoretical foundations of the ISO/TS 12913-3 circumplex model, this study advances the following hypotheses:

3 material and methods

The methodological design combined in situ perceptual data collection in selected urban areas with psychometric analysis², enabling an investigation of how response scale format (metric versus ordinal) and semantic configurations influence participants’ affective judgments. The adopted analytical workflow followed a sequence of procedures designed to ensure the reliability, comparability, and interpretability of the data.

This study was approved by the Research Ethics Committee (CEP) of the University of São Paulo (CAEE 80357224.1.0000.5390 and 63954322.4.0000.5390).

3.1 Study context and site selection

To explore how different response scale formats influence the perceptual evaluation of soundscapes, this study was conducted across five indoor and outdoor environments on the University of São Paulo (USP) campus. Located in the western zone of São Paulo city, Brazil, the campus includes extensive green infrastructure and a mix of natural and built elements that create varied acoustic conditions. Spatial distribution and site characteristics (P1–P5) are shown in Figure 1.

Figure 1. Spatial distribution and visual characterization of the five selected locations.

Outdoor sites (P1 and P4) are open green areas with ground-level vegetation, scattered trees, and nearby buildings. Both are adjacent to roads with regular vehicular traffic, introducing dynamic acoustic layers despite predominantly vegetated surroundings. Indoor sites included a large entrance hall (P2), a semi-open transitional area connecting indoor and outdoor spaces (P3), and a classroom (P5). These locations differ in spatial configuration, materiality, and enclosure, all factors that can shape the acoustic experience and users’ perceptions.

Site selection followed the principle of environmental heterogeneity. Including spaces with distinct physical, visual, and acoustic characteristics created diverse perceptual contexts for testing response behavior under different real-world urban conditions. This diversity ensured that comparisons between metric and ordinal response formats captured the representative perceptual variability of real soundscapes.

3.2 Questionnaire design and semantic structure

The experimental study followed method A from ISO/TS 12913-2 [10] for in situ soundscape evaluation. All questionnaire versions were based on the ISO soundscape circumplex model, which operationalizes perceptual assessment through semantic differential items. The PAQ attributes (Pleasant – Annoying, Eventful – Uneventful, Vibrant – Monotonous, and Calm – Chaotic) were used either as four bipolar adjective pairs or as eight single attributes. The response scale formats used across questionnaire configuration are summarized in Figure 2.

Figure 2. Response scales used across questionnaire configurations: (1) eight single-attributes PAQ metric scale; (2) eight single-attributes PAQ ordinal scale; and (3) four bipolar adjective pairs (PAQ) metric scale.

Four questionnaire versions were developed by combining two response scale formats (1) and two PAQ questionnaire configurations (2):

• (1)

  Five-category ordinal scale Likert-type and continuous metric scale (0–100).

• (2)

  Eight single-attribute PAQs and four bipolar adjective pairs.

The field experiment was conducted on September 23 and October 14, 2024, corresponding to two application sessions in which all questionnaire versions were administered under comparable environmental conditions. Four groups were involved, as detailed below. On each application day, 126 students participated and were divided into two groups, each assigned to one questionnaire version. Six responses from Groups 3 and 4 were subsequently excluded due to incomplete or inconsistent data.

• Group 1 (G1): n = 71, eight single attributes, ordinal response scale. For analytical purposes, this group was later subdivided into G1_S, with responses converted using Snell’s method, and G1_i, with responses converted using fixed-value mapping (see Sect. 3.4.1).

• Group 2 (G2): n = 55, eight single-attribute PAQs, metric response scale.

• Group 3 (G3): n = 61, eight single-attribute PAQs, metric response scale.

• Group 4 (G4): n = 59, four bipolar adjective pairs, metric response scale.

Data were collected in situ using participants’ smartphones through KoboToolbox online platform [37]. All participants received standardized written and verbal instructions to ensure a consistent understanding of the response procedure and provided written informed consent in accordance with the approved ethical procedures.

Finally, to evaluate methodological effects, the dataset was organized into predefined comparison sets (detailed in Sect. 3.4.2) that examined how response scale conversion and PAQ questionnaire configuration influenced perceptual judgments, as summarized in Table 1.

Taken together, these comparisons offer a comprehensive framework for assessing the sensitivity of PAQ instruments to changes in questionnaire design, contributing to a deeper understanding of how perceptual judgments are shaped by instrument structure in soundscape research.

3.3 Data collection and sample characteristics

Data collection was conducted across four distinct application groups (G1 to G4), each corresponding to a distinct questionnaire version as defined in Section 3.2. This design ensured experimental control and enabled direct systematic comparisons between response scale formats and PAQ questionnaire configurations.

Participants were undergraduate students enrolled in the Environmental Comfort course at the Faculty of Architecture, Urbanism, and Design at the University of São Paulo (FAU-USP). This context provided access to individuals with foundational knowledge of environmental quality, supporting informed and contextually grounded soundscape evaluations.

Participation was voluntary (convenience sampling) and followed inclusion criteria requiring individuals to be at least 18 years old and reporting no hearing impairments. All participants were aged between 18 and 25 years. The sample encompassed individuals with diverse personal and perceptual backgrounds, consistent with the subjective nature of soundscape assessment. Such heterogeneity is methodologically relevant, as individual sensitivities and spatial interpretations inherently shape perceptual judgments within the ISO 12913 framework.

Although group sizes varied, all samples were adequate to support the psychometric and comparative analyses applied, as shown in Table 1. Table 2 summarizes the demographic characteristics of the analyzed groups.

3.4 Statistical procedures and comparative analysis

All statistical analyses were carried out using R (v. 4.5.0) [38] and JASP (v. 0.19.3.0) [39], while visual representations were generated with Soundscapy, a Python toolbox developed by Mitchell et al. [36] for perceptual-acoustic soundscape analysis. Following ISO/TS 12913-3 recommendations [11], median values are reported as the primary measure of central tendency for ordinal and ordinal-derived data, given that ordinal scales represent ordered categories without defined intervals. Mean values are additionally reported to provide supplementary distributional context and to facilitate comparison with metric-scale data. Standard deviation, skewness, and kurtosis are also reported to characterize distributional variability, asymmetry, and concentration. This approach ensures that statistical analyses respect the measurement properties of each scale format while enabling comprehensive characterization of response distributions.

3.4.1 Response scale transformation

Given the dual nature of the response formats, ordinal and metric, the first analytical step involved converting ordinal data into continuous values to enable cross-format comparisons under consistent methodological assumptions. Two conversion strategies were applied in parallel.

The first strategy employed Snell’s method [35, 40–42]. Because the questionnaire version used for comparison employed a native 0–100 scale, this conversion was selected to enable direct cross-format comparisons within a common numerical range. Accordingly, a monotonic transformation was prioritized to preserve category ordering while avoiding ad hoc assumptions of equal spacing between ordinal categories. Snell’s procedure estimates latent category thresholds from ordinal data using the inverse logit function³, and each ordinal response is then assigned a continuous latent score corresponding to the midpoint between adjacent thresholds. The resulting latent scores were then linearly rescaled to the 0–100 interval for numerical alignment with the metric format.

The second strategy consisted of assigning fixed numerical values to ordinal categories, following established practices in perceptual research [43, 44]. In this approach, response options were mapped as follows: 0 (strongly disagree), 25 (disagree), 50 (neither agree, nor disagree), 75 (agree), and 100 (strongly agree). This conventional mapping provided a pragmatic basis for cross-format comparisons, while maintaining interpretative clarity for respondents and analytical consistency for researchers.

For the four bipolar PAQ attributes Pleasant – Annoying, Eventful – Uneventful, Vibrant – Monotonous, and Calm – Chaotic, a complementary conversion procedure was applied to ensure analytical symmetry and comparability across PAQs. Participants rated each pair using a unidirectional 0–100 bipolar scale. The original score was retained for the left-hand term (e.g., Pleasant), while its complement to 100 was assigned to the opposite pole (e.g., Annoying). Thus, a rating of 20 on the Pleasant – Annoying scale was interpreted as 20 for Pleasant and 80 for Annoying.

This procedure produced eight complementary variables from the four bipolar adjective pairs, enhancing interpretability and enabling direct comparison across PAQ questionnaire configurations and scale formats.

3.4.2 Group comparisons

After the conversion procedures, the four comparisons listed on Table 1 were conducted.

Comparisons A1 and A2 contrasted Group 1, whose ordinal responses were converted using either Snell’s method or fixed-value mapping, with Group 2, which employed a native metric scale (0–100) under the same questionnaire configuration. Comparisons B1 through B4 examined Groups 3 and 4, both using metric formats but differing in PAQ configurations (eight single attributes vs. four bipolar adjective pairs).

Because the converted outcomes displayed non-normal distributions, between-group differences were assessed using the Mann–Whitney U (Wilcoxon rank-sum) test [45, 46]. The test is computed from the pooled ranking of all observations and the sum of ranks within each group, with U being a one-to-one transformation of the rank-sum statistic [46]. In this framework, the “ranked means” commonly reported in software outputs correspond to the mean rank, defined as the rank sum divided by the group sample size, and provide a descriptive indication of which group tends to occupy higher positions in the pooled ordering [46]. Importantly, the Mann–Whitney test should be interpreted as assessing whether one group tends to yield systematically higher values than the other, that is, whether the samples are consistent with coming from the same distribution, rather than as a general test of equal medians [46, 47]. A median-based interpretation is only justified under a location-shift scenario in which the two population distributions have similar shapes; otherwise, statistically significant results may also reflect differences in spread or distributional shape [47–49].

Standard assumptions for application in the present design, including independent samples and outcomes measured on an ordinal or continuous scale, were verified before analysis [50].

3.4.3 Kernel-density circumplex analysis

To complement the statistical analyses, two-dimensional perceptual soundscape circumplex graphs were generated for each group, representing the dimensions of Eventfulness (E) and Pleasantness (P) according to the ISO/TS 12913-3 framework [11]. The graphs were constructed using Soundscapy [36] and were based on participants’ metric-scale responses. Kernel density estimation employed Scott’s rule for automatic bandwidth selection, as implemented in Soundscapy’s default configuration, ensuring data-driven smoothing consistent with the sample sizes in each group.

Dimensional values were calculated using the standardized equations (Eqs. (1) and (2)) normalized from −1 to +1. The equations remain applicable to bipolar scales, as each response inherently represents the perceptual distance between opposite poles.

$$\begin{array}{cc}\hfill P& =(p-a)+cos{45}^{°}·(ca-ch)+cos{45}^{°}·(v-m)\hfill \end{array}$$(1)

$$\begin{array}{cc}\hfill E& =(e-u)+cos{45}^{°}·(ch-ca)+cos{45}^{°}·(v-m)\hfill \end{array}$$(2)

where: p is pleasant, a is annoying, ca is calm, ch is chaotic, v is vibrant, m is monotonous, e is eventful, and u is uneventful.

As a final step, the statistical and spatial results were jointly examined to assess how different analytical configurations influence PAQ data interpretation and to identify context-specific recommendations for applying these methods in urban soundscape research.

4 Results

4.1 Statistical analysis

This section presents the statistical outcomes from the comparative analyses evaluating how response scale format (Comparisons A) and PAQ questionnaire configuration (Comparisons B) affect PAQ ratings. Between-group differences are assessed using non-parametric significance tests, adopting the conventional significance level (α = 0.05, two-sided), and exact p-values are reported to ensure transparency and support interpretation. To contextualize inferential results, Tables 3 to 8 also report descriptive statistics for each PAQ: mean (M) and median (Mdn) as complementary indicators of central tendency, standard deviation (SD) as a measure of dispersion, skewness (g₁) to quantify distribution asymmetry, and kurtosis (g₂) to characterize distribution concentration and tail behavior. Reporting these descriptors jointly is particularly relevant given the ordinal origins and non-normal distribution patterns associated with the transformed datasets, allowing statistical significance to be interpreted alongside shifts in location, spread, and distributional shape.

4.1.1 Comparisons A

Comparisons A evaluated whether the response scale format, namely an ordinal scale converted to a continuous metric or a native metric scale, significantly affected PAQ ratings.

Comparison A1 (Tab. 3) contrasted an ordinal scale converted using Snell’s method (G1_S) with a native metric (0–100) scale (G2). Under the Snell conversion, the PAQs Vibrant, Pleasant, and Chaotic exhibited the greatest divergence, indicating redistribution of responses along the scale range. For the remaining attributes, no statistically significant differences were observed (all p-values > 0.05), suggesting that, within the limits of the sample size and test sensitivity, ratings were not distinguishable between the two scale formats.

Mann–Whitney U tests revealed statistically significant differences for Vibrant (U = 1146.00, p-value =0.003), Pleasant (U = 2379.50, p-value < 0.001), and Chaotic (U = 1127.00, p-value =0.002). Table 3 presents the Mann–Whitney U results and the descriptive statistics (M, Mdn, SD, g₁, and g₂) for all PAQs in Comparison A1, reporting values as G1_S|G2.

Specifically, for Vibrant, the Snell-converted format (G1_S) tended to yield lower values than the metric format, as reflected in median values (10.80 vs. 20.75), and a smaller standard deviation (SD = 17.29 vs. 23.38). Conversely, Pleasant tended toward higher values in G1_S (medians of 91.38 vs. 76.50) with lower dispersion (SD = 12.89 vs. 18.73). For Chaotic, G2 tended to produce higher ratings, with medians of 17.50 vs. 9.46, with comparable dispersion (SD = 17.43 vs. 19.75).

Differences in kurtosis were also observed among these significant PAQs, for example, Pleasant exhibited a more peaked distribution in G1_S (1.14) than G2 (0.12), suggesting reduced response variability under the Snell conversion. Skewness values also shifted under Snell’s conversion, for instance Pleasant became more negatively skewed in G1_S than in G2 (−1.40 vs. −0.73), indicating stronger concentration toward higher ratings.

In Comparison A2 (Tab. 4), which contrasted the fixed-value mapping (0, 25, 50, 75, 100), G1_i, with the native metric scale, G2, no statistically significant differences were identified for any PAQ (all p-values > 0.05). Descriptive measures appeared similar across formats. For instance, Calm had the same median in both formats (75.00), and Pleasant medians were close (75.00 vs. 76.50).

To quantify the magnitude of differences between response formats, the rank-biserial correlation (r _{r b} ) was employed as an effect size measure for the Mann–Whitney U test. It is computed as r _{r b}  = 2U/(n ₁ × n ₂)−1, where U is the Mann–Whitney statistic and n ₁ and n ₂ are the sample sizes of the two groups under comparison. The resulting values range from −1 to +1, where 0 indicates no difference between distributions and values approaching ±1 reflect near-complete separation between groups. Following conventional benchmarks, effect sizes were classified as small (|r _{r b} |≥0.1), medium (|r _{r b} |≥0.3), and large (|r _{r b} |≥0.5). The sign of r _{r b} is informative regarding the direction of differences: positive values indicate that n ₂ tends to produce higher ratings for a given attribute, while negative values indicate the opposite.

Effect sizes for Comparisons A were generally small to negligible for both conversion methods, with the exception of Vibrant (r _{r b}  = 0.413) and Chaotic (r _{r b}  = 0.423) in Comparison A1, both classified as medium, consistent with the statistically significant differences identified by the Mann–Whitney U tests. In Comparison A2, all r _{r b} values remained below 0.27, confirming the distributional proximity between fixed-value mapping and the native metric scale across all PAQ attributes.

4.1.2 Comparisons B

Comparisons B1 to B4 assessed whether questionnaire configuration influenced ratings when both response formats were metric. Four bipolar adjective pairs (G4) were contrasted with eight single-attribute PAQs (G3) across four locations (P2–P5).

At the second location, P2 (Comparison B1, Tab. 5), Mann–Whitney U tests indicated statistically significant differences for Eventful (U = 2127.50, p-value =0.033), Pleasant (U = 1203.00, p-value =0.004), Calm (U = 1074.50, p-value < 0.001), Uneventful (U = 1027.50, p-value < 0.001), and Monotonous (U = 555.00, p-value < 0.001).

Specifically, the four bipolar adjective pairs configuration tended to yield higher ratings for Pleasant, as reflected in median values (66.00 vs. 50.00), Calm (56.00 vs. 42.00), Uneventful (40.00 vs. 24.00), and Monotonous (53.00 vs. 24.00), whereas Eventful tended toward higher values in the eight single-attribute PAQs (71.00 vs. 60.00). Differences in kurtosis also reflected these distributional contrasts, for example Eventful (1.00 in G3 vs. −0.90 in G4) and Uneventful (0.80 in G3 vs. −0.90 in G4).

At Comparison B2 (Tab. 6), Mann–Whitney U tests identified statistically significant configuration effects for Uneventful (U = 1264.00, p-value =0.004) and Monotonous (U = 498.50, p-value < 0.001). Consistent with these differences, the four bipolar adjective-pair format (G4) tended to produce higher ratings for both attributes (Uneventful median: 68.00 vs. 50.00; Monotonous median: 68.00 vs. 27.00), indicating stronger positioning along these perceptual dimensions under the bipolar configuration. Dispersion generally decreased in G4 for most PAQs, with only minor exceptions (e.g., Chaotic), suggesting a shift toward more consistent response patterns. Complementarily, distributional shape metrics indicated a greater concentration of high-end evaluations in G4, as reflected by more negative skewness in selected attributes (e.g., Pleasant: −1.40 vs. −0.70), reinforcing the tendency for responses to cluster toward higher ratings under the bipolar format at this location.

For Comparison B3 (Tab. 7), Mann–Whitney U tests revealed statistically significant differences for Pleasant (U = 1392.50, p-value =0.033), Uneventful (U = 1198.00, p-value =0.002), and Monotonous (U = 680.00, p-value < 0.001). Consistent with previous comparisons, median values were higher in the four bipolar adjective pairs (G4) for all three attributes: Pleasant (78.00 vs. 73.00), Uneventful (61.00 vs. 38.00), and Monotonous (65.00 vs. 33.00). Dispersion values were slightly lower in G4 for all PAQs, suggesting more stable response distributions under this configuration.

At the final location, P5 (Comparison B4, Tab. 8), Mann–Whitney U tests revealed statistically significant differences for Calm (U = 1411.00, p-value =0.022), Uneventful (U = 1188.00, p-value < 0.001), Monotonous (U = 813.50, p-value < 0.001), and Annoying (U = 1275.50, p-value =0.003). The four bipolar adjective pairs configuration (G4) tended to produce higher ratings for Calm (85.00 vs. 80.00), Uneventful (84.00 vs. 73.00), Monotonous (85.00 vs. 59.00), and Annoying (28.00 vs. 18.00). Kurtosis values suggested more peaked distributions in G4 for some attributes, for example, Calm (2.90 vs. 0.40), Uneventful (1.20 vs. −0.40), and Monotonous (2.60 vs. −0.90).

Across all locations, Uneventful and Monotonous most consistently exhibited significant differences between questionnaire configurations, whereas Vibrant and Chaotic showed no significant variation under any location.

Effect sizes for Comparisons B reveal a consistent pattern across all four locations. For these comparisons, n₁ corresponds to G3 (eight single-attribute PAQs) and n₂ to G4 (four bipolar adjective pairs), such that positive r_rb values indicate that G4 tends to produce higher ratings for a given attribute, while negative values indicate the opposite. Monotonous exhibited the largest effect sizes across all locations (B1: r_rb = 0.692; B2: r_rb = 0.723; B3: r_rb = 0.622; B4: r_rb = 0.548), all classified as large, reflecting the strong and consistent tendency of the bipolar format to concentrate responses toward higher ratings along this dimension. Uneventful showed medium effects across all locations (B1: r_rb = 0.429; B2: r_rb = 0.298; B3: r_rb = 0.334; B4: r_rb = 0.340), while the remaining attributes showed small to negligible effects, with localized exceptions for Calm, Pleasant, and Annoying at specific locations. In particular, Eventful presented negative r_rb values across all four locations (B1: r_rb = −0.182; B2: r_rb = −0.082; B3: r_rb = −0.098; B4: r_rb = −0.218), indicating that the eight single-attribute configuration consistently captured higher eventfulness ratings regardless of location. This ordering confirms that the bipolar four-adjective pair configuration most strongly differentiates from the eight single-attribute format along the Eventfulness–Uneventfulness perceptual axis.

4.2 Two-dimensional perceptual soundscape representations

Two-dimensional perceptual soundscape graphs were constructed in accordance with ISO/TS 12913-3, plotting participant responses along the Pleasantness (x-axis) and Eventfulness (y-axis) dimensions. Kernel Density Estimation (KDE) contours represent areas of higher response concentration, while the four quadrants correspond to the perceptual categories defined by the standard: Vibrant (upper-right), Calm (lower-right), Monotonous (lower-left), and Chaotic (upper-left).

Figure 3. Soundscape circumplex graphs: Snell conversion (G1_S), fixed-value mapping (G1_i), and data collected in metric scale (G2) for Point P1 (open green area).

4.2.1 Comparisons A

Figure 3 shows the graphs for comparisons A. For Group 1, two conversion methods were applied to the original ordinal PAQ scale: Snell conversion (G1_S) and fixed-value mapping (G1_i). The KDE distribution for G1_S shows response density concentrated within the Calm quadrant, with a moderate spread towards Monotonous and Vibrant, and minimal density in Chaotic. The centroid position lies in the positive Pleasantness region and negative Eventfulness region, indicating that judgments remained predominantly Calm.

Under the fixed-value mapping (Fig. 3, G1_i), responses display greater dispersion along the Eventfulness axis, extending into the Vibrant quadrant while maintaining maximum density in Calm.

In Group 2, which uses the native metric scale, KDE contours are more evenly distributed between Calm and Vibrant, with the peak density shifted upward on the Eventfulness axis compared with both G1_S and G1_i. Figure 3 (G2) shows that the Monotonous and Chaotic quadrants remain sparsely populated, indicating low frequency of negative Pleasantness ratings across all formats.

4.2.2 Comparisons B

When comparing Groups 3 and 4, distinct distribution patterns were observed across the four locations.

Figure 4, corresponding to Location 2, shows that both configurations concentrated responses in the Vibrant quadrant. G3_1 exhibited a broader spread extending into the Calm and Chaotic regions, whereas G4_1 formed a more compact cluster with its centroid positioned higher on the Eventfulness axis. Figure 5, corresponding to Location 3, show responses shifted predominantly toward the Calm quadrant. G3_2 displayed a dense, centrally located cluster between Pleasant and Calm, while G4_2 displayed a cluster between Calm and Uneventful.

Figure 4. Soundscape circumplex graphs for Point 2 (P2): G3_1 (eight single-attribute PAQs) and G4_1 (four bipolar adjective pairs) at point P2 (entrance hall).

Figure 5. Soundscape circumplex graphs for Point 3 (P3): G3_2 (eight single-attribute PAQs) and G4_2 (four bipolar adjective pairs) at point P3 (transitional area).

Locations 4 and 5 (Figs. 6 and 7) also exhibited predominantly calm perceptual profiles.

Figure 6. Soundscape circumplex graphs for Point 4 (P4): G3_3 (eight single-attribute PAQs) and G4_3 (four bipolar adjective pairs) at point P (open green area).

Figure 7. Soundscape circumplex graphs for Point 5 (P5): G3_4 (eight single-attribute PAQs) and G4_4 (four bipolar adjective pairs) at point P5 (classroom).

In Location 4, G3_3 spanned the Calm and Vibrant quadrant, presenting an elongated contour along the Pleasantness axis while G4_3 maintained a compact, high-density cluster centered in Calm, positioned between Pleasant and Uneventful.

At Location 5, both groups concentrated strongly in the Calm quadrant, near the transition towards Uneventful. G3_4 displayed a secondary density peak extending toward Monotonous, whereas G4_4 retained a single, well-defined contour. In both cases, the Chaotic quadrant was nearly absent, indicating a consistent perception of positively valanced and low-eventfulness soundscapes.

5 Discussion

This study employed a comparative design to evaluate how different conversion methods (Snell vs. fixed-value mapping) and distinct PAQ questionnaire configurations (four bipolar adjective pairs vs. eight single attributes) affect data interpretation. By integrating inferential statistics, descriptive parameters, and perceptual representations in accordance with ISO/TS 12913-3 [11], the approach provides empirical evidence of the methodological consequences associated with these analytical choices.

5.1 Effects of the response scale transformation – Comparison A

The conversion of ordinal responses into a metric format produced distinct outcomes depending on the method applied. Using Snell’s conversion (G1_S), Mann–Whitney U tests indicated statistically significant differences for the attributes Vibrant, Pleasant, and Chaotic. Descriptive statistics revealed systematic redistributions in median, skewness, and kurtosis, indicating changes in central tendency, distributional shape, and concentration. For instance, Pleasant presented a higher median, reduced variability, and increased kurtosis under Snell’s conversion, resulting in more compact KDE contours in the Calm quadrant compared with the metric scale. Conversely, Vibrant and Chaotic showed lower central tendency values, consistent with reduced density in high-Eventfulness areas of the ISO/TS 12913-3 [11] graphical representation.

The mechanism underlying these variations derives from Snell’s empirical cumulative probability-based adjustment, which repositions category thresholds according to the observed distribution, approximating them on a continuous latent scale, thereby mitigating distortions introduced by arbitrary fixed-interval mappings [35, 40–42]. However, because Snell’s transformation estimates item-specific thresholds from the observed response distribution, it can affect some PAQs more than others. This effect tends to be stronger when responses occupy a restricted portion of the circumplex (e.g., concentrated in Calm with sparse ratings in Chaotic), where asymmetric or truncated distributions amplify item-dependent rescaling. As a result, downstream comparisons and models that are sensitive to distributional shape or relative positioning may be influenced by these attribute-specific redistributions.

In contrast, the fixed-interval mapping (0, 25, 50, 75, 100) applied in Comparison A2 did not produce statistically significant differences compared to the metric scale across any PAQ. Descriptive values were closely aligned between G1_i and G2, and their KDE contours exhibited extensive overlap, with only minor variations along the Eventfulness axis. This pattern indicates that fixed-value mapping effectively preserves rank order and imposes an interval-like structure without substantially altering distributional properties, a point also noted by Menold [34] in relation to scale polarity and granularity. Nevertheless, as no perceptual recalibration occurs, subtle compressions or expansions may remain undetected.

In summary, Comparisons A show that Snell’s conversion modified the response distribution in an attribute-dependent manner, whereas fixed-value mapping produced outcomes more closely aligned with the native metric scale (0–100) (Fig. 8). For statistical procedures sensitive to distributional shape, such as parametric regressions under their required assumptions or percentile-based analyses, these discrepancies can be consequential and should be documented.

Figure 8. Comparative soundscape circumplex graphs between Group 2 (metric scale), in blue, and Group 1 conversed using Snell’s method (left) or fixed-value (right), both in orange, for Point P1 (open green area).

5.2 Effects of questionnaire structure – Comparison B

When both groups used exclusively numeric responses (G3 and G4), observed differences stemmed mainly from the PAQ questionnaire configuration. Across Comparisons B1 to B4 and all four locations (P2 to P5), Monotonous and Uneventful most frequently showed statistically significant differences, whereas no statistically significant differences were detected for Vibrant and Chaotic. In the circumplex graphs, the configuration with four bipolar adjective pairs (G4) consistently produced more compact density clusters in the Calm quadrant, whereas the eight single-attribute PAQs (G3) exhibited KDE contours extending toward Vibrant and Chaotic (Fig. 9).

Figure 9. Comparative soundscape circumplex graphs for Group 3 (eight single-attributes), in blue, and Group 4 (four bipolar adjective pairs), in orange, across the four locations (P2 to P5).

At Location 2, both groups occupied the positive Pleasantness axis, but G3_1 extended further into Vibrant and Chaotic, while G4_1 remained concentrated near Calm, showing lower Eventfulness. Median values followed this pattern, with higher Eventful scores in G3 and higher Calm and Pleasant scores in G4.

At Location 3, distributions shifted toward Calm: G3_2 formed a density centroid, whereas G4_2 extended slightly toward Monotonous. Statistically significant differences occurred for Uneventful and Monotonous, consistent with the reduced spread observed in G4.

At Location 4, both covered Calm and part of Vibrant, although G3_3 presented an elongated contour along the Pleasantness axis, while G4_3 remained compact near the Calm–Vibrant interface. Statistically significant differences were found for Pleasant, Uneventful, and Monotonous, aligning with the stronger concentration observed in G4.

For Location 5, both groups clustered in the Calm quadrant. G3_4 exhibited a secondary density peak toward Monotonous, whereas G4_4 maintained a single, sharply defined centroid. Descriptive kurtosis was higher in G4 for Calm and Monotonous, reflecting more peaked response distributions.

Across all locations, from the highly Eventful P2 to the Uneventful P5, these outcomes show that the reduced bipolar configuration concentrates responses and limits semantic overlap. This tendency is consistent with findings from standardized environmental noise questionnaires such as those developed by ICBEN [30]. In contrast, the expanded eight-attribute configuration captures a broader perceptual range, enhancing spatial granularity but introducing greater response variability.

5.3 Convergence between statistical and perceptual analyses

A key strength of this dataset lies in the convergence between inferential outcomes and perceptual representations. Attributes showing significant Mann–Whitney U tests differences were consistently associated with perceptual shifts in KDE graphs, including centroid relocation, contour deformation, and density redistribution across quadrants.

In Comparison A1, attribute-specific redistributions under Snells transformation were clearly visible through contour compression or expansion, whereas in Comparison A2, statistical similarity was reflected by nearly overlapping KDE profiles.

Across the comparisons B1–B4, attributes with high statistical sensitivity (Monotonous, Uneventful) also showed broader tails in the eight single-attribute configuration (G3) and higher kurtosis with tighter clustering in the configuration with four bipolar adjective pairs (G4). This alignment between numerical and perceptual evidence reinforces the reliability of the findings, as the observed patterns emerge consistently across independent analytical dimensions. The inclusion of skewness and kurtosis metrics further clarified when perceptual evaluations were directionally biased yet distributionally homogeneous.

5.4 Methodological and practical implications

Four main methodological implications arise:

• (1)

  Conversion of ordinal responses: To harmonize ordinal and numeric formats, the fixed-interval mapping approach proved to be more stable in preserving observed distributional properties. Snell’s conversion, based on latent threshold modeling, offers perceptual calibration by adapting to empirical distributions, but it can also introduce attribute-specific redistributions. When applied, sensitivity analyses or transparent supplemental reporting are recommended to ensure interpretability.

• (2)

  Configuration of the PAQ questionnaire: The four bipolar adjective-pair format yielded consistently tighter circumplex clusters, whereas the eight single-attribute version reflected a wider spread of perceptual responses. Accordingly, configuration choice should follow the intended use: bipolar pairs support focused, quadrant-based profiling, while the expanded attribute set is more appropriate for exploratory mapping of perceptual heterogeneity.

• (3)

  Integration of statistical and perceptual tools: Soundscape circumplex graphs enhanced with KDE are not merely illustrative; they make distributional structure visible (e.g., multimodality, directional elongation, and clustering) in ways that summary statistics alone cannot capture. In this study, these distributional signatures were consistent with the interaction between questionnaire configuration and location-specific context: acoustically heterogeneous settings with multiple concurrent sources (e.g., P1: low traffic, pedestrians, and biophonic sounds; P2: a reverberant entrance hall with intense circulation and partial exposure to external noise; P3: a semi-open transitional space near circulation/parking; P4: human activities with distant traffic and natural sounds) tended to produce broader and more anisotropic KDE contours, whereas more source-limited indoor conditions (P5: indoor space dominated by human activity and room acoustics/reverberation) tended to concentrate responses. Taken together, combining non-parametric inference with KDE-based circumplex mapping and a minimal description of site characteristics establishes a more rigorous and context-sensitive framework for interpreting PAQ-based soundscape outcomes.

• (4)

  Socio-cultural and cross-location generalization: The effects observed here were obtained with a homogeneous sample (architecture students, single campus, Brazilian Portuguese speakers), which represents a specific socio-cultural profile. Evidence from cross-cultural soundscape research [18, 19] suggests that attributes along the Eventful–Uneventful axis carry particular semantic fragility in Portuguese, and broader psychometric literature indicates that bipolar scale formats and response tendencies vary systematically across cultural groups [51–53]. Future applications should therefore test whether the configuration effects reported here are stable across populations with different linguistic backgrounds, acoustic familiarity, or urban experience. Incorporating measurement invariance testing across groups would be a concrete methodological improvement.

6 Conclusion

This study demonstrated that methodological decisions concerning both the conversion of ordinal responses and the configuration of PAQ questionnaires significantly influence the statistical and perceptual representation of soundscape evaluations. In this context, effectiveness is understood as the extent to which a given response format supports the intended analytical objective while maintaining sensitivity, distributional stability, and interpretative clarity. By integrating inferential statistics, descriptive parameters, and two-dimensional soundscape circumplex graphs, the analyses provided a multidimensional assessment that not only quantifies differences but also reveals their perceptual manifestations.

In the comparison between ordinal-to-metric conversions, Snell’s method produced attribute-specific redistributions, altering medians, kurtosis, and perceptual density contours, whereas fixed-value mapping remained closely aligned with the native metric scale (0–100). These findings indicate that conversion methods are not interchangeable. Snell’s method can enhance sensitivity to certain perceptual nuances but may also reshape response distributions, potentially affecting subsequent analyses. Fixed-value mapping, on the other hand, offers greater stability when the analytical objective is harmonization across formats.

Regarding questionnaire configuration, the bipolar four-adjective pair configuration tended to yield more compact density clusters, particularly at locations with lower acoustic complexity and reduced source heterogeneity (P3, P4, and P5), whereas the eight single-attribute configuration better captured perceptual variability in acoustically heterogeneous environments with multiple concurrent sources (P2). A systematic analysis of sound-source dominance as an independent variable, however, would require a dedicated experimental design and is suggested as a direction for future research. A salient finding concerns the attributes Uneventful and Monotonous, which showed the greatest distributional instability under methodological conditions. This variability cannot be explained solely by scale conversion. Previous studies [18–20] reported semantic ambiguity and low spontaneous usage of these attributes, indicating conceptual fragility of the Eventful–Uneventful axis. Recognizing this limitation is essential for adapting ISO 12913 PAQs to Brazilian Portuguese and improving the cross-cultural robustness of soundscape tools.

A key strength of this work lies in the convergence between statistics and perceptual soundscape circumplex graphs, reinforcing the validity of the observed effects. Attributes that differed significantly in non-parametric tests also showed corresponding shifts in centroid positions, contour shapes, and quadrant distribution in the circumplex graphs. The combined use of descriptive statistics (including kurtosis and skewness) and KDE-based visualizations allowed a richer interpretation of distributional characteristics beyond central tendency alone.

By reporting these results, the study advances methodological transparency, explicitly demonstrating how variations in response scale format and PAQ questionnaire configuration influence both statistical outcomes and circumplex-based perceptual representations in soundscape analysis. On this basis, it provides empirically grounded recommendations for selecting conversion methods and questionnaire designs according to analytical objectives, whether prioritizing perceptual sensitivity, distributional stability, or cross-study comparability.

Ultimately, these findings contribute to the refinement of ISO/TS 12913-3 [11] applications, offering a replicable analytical framework that integrates psychometric rigor with perceptual mapping. Such an approach enhances the interpretative power of soundscape analyses and may contribute to more informed, evidence-based decisions in urban acoustic planning and environmental quality assessment.

By demonstrating how specific questionnaire configurations and scale conversions affect both statistical outcomes and perceptual circumplex graphs, the study provides a transferable framework for optimizing public surveys, refining noise mapping practices, and integrating perceptual indicators into environmental quality standards. This alignment between methodological precision and practical applicability points to the broader potential of PAQ-based instruments to contribute to soundscape assessment in urban planning contexts, as discussed by Michalski et al. [20] in the Brazilian standardization framework. Since the observed trends were obtained from a sample within a specific sociocultural and location context, the generalizability of these results to other contexts is necessarily limited. The effects associated with questionnaire configuration and the distributional stability of fixed-value mapping relative to Snell’s conversion were consistent across all comparison sets, supporting the internal validity of the results. Replication studies employing diverse population profiles, urban typologies, and linguistic backgrounds are nonetheless needed to determine the extent to which the effects are stable across broader contexts. Incorporating formal measurement invariance testing between questionnaire formats would represent a concrete and recommended methodological advance in this direction.

Finally, the study provides consistent evidence within the scope investigated, offering a solid basis for comparing response formats and questionnaire structures. Nevertheless, some limitations should be acknowledged when interpreting the reach of these results. The sample consisted of university students, and data collection was conducted within the urban context of a university campus; therefore, extrapolation to more diverse sociodemographic profiles and to other urban typologies should be undertaken with due caution. In addition, formal measurement invariance was not examined at this stage. Future research can strengthen and extend these conclusions by replicating the protocol across different population groups and urban contexts, explicitly testing invariance between formats and questionnaire structures, and integrating these findings with objective acoustic indicators, thereby advancing more comprehensive and multimodal approaches to soundscape assessment.

Funding

This study was partially supported by grants number #2021/14221-5 and #2021/02915-2 from the São Paulo Research Foundation (FAPESP), and by project number 406603/2023-5 from the National Council for Scientific and Technological Developmentnd by grants number 16159/2021-2 and 308206/2025-8, (Conselho Nacional de Desenvolvimento Científico e Tecnológico, CNPq – Brazil).

Conicts of interest

The authors declare they have nothing to disclose.

Data availability statement

Data are available on request from the authors.

Author contribution statement

Lucas Rafael Ferreira: conceptualization, data curation, formal analysis, investigation, methodology, validation, visualization, writing – original draft, writing – review & editing. Leonardo Marques Monteiro: project administration, supervision, writing – review & editing. Nara Gabriela de Mesquita Peixoto: conceptualization, data curation, formal analysis, investigation, methodology, validation, visualization, writing – original draft, writing – review & editing. Ranny Loureiro Xavier Nascimento Michalski: conceptualization, data curation, formal analysis, investigation, methodology, validation, visualization, writing – original draft, writing – review & editing

Ethics approval

This study was approved by the Research Ethics Committee (CEP) of the University of São Paulo (CAEE 80357224.1.0000.5390 and 63954322.4.0000.5390).

References

All Tables

All Figures

	Figure 1. Spatial distribution and visual characterization of the five selected locations.
In the text

	Figure 2. Response scales used across questionnaire configurations: (1) eight single-attributes PAQ metric scale; (2) eight single-attributes PAQ ordinal scale; and (3) four bipolar adjective pairs (PAQ) metric scale.
In the text

	Figure 3. Soundscape circumplex graphs: Snell conversion (G1_S), fixed-value mapping (G1_i), and data collected in metric scale (G2) for Point P1 (open green area).
In the text

	Figure 4. Soundscape circumplex graphs for Point 2 (P2): G3_1 (eight single-attribute PAQs) and G4_1 (four bipolar adjective pairs) at point P2 (entrance hall).
In the text

	Figure 5. Soundscape circumplex graphs for Point 3 (P3): G3_2 (eight single-attribute PAQs) and G4_2 (four bipolar adjective pairs) at point P3 (transitional area).
In the text

	Figure 6. Soundscape circumplex graphs for Point 4 (P4): G3_3 (eight single-attribute PAQs) and G4_3 (four bipolar adjective pairs) at point P (open green area).
In the text

	Figure 7. Soundscape circumplex graphs for Point 5 (P5): G3_4 (eight single-attribute PAQs) and G4_4 (four bipolar adjective pairs) at point P5 (classroom).
In the text

	Figure 8. Comparative soundscape circumplex graphs between Group 2 (metric scale), in blue, and Group 1 conversed using Snell’s method (left) or fixed-value (right), both in orange, for Point P1 (open green area).
In the text

	Figure 9. Comparative soundscape circumplex graphs for Group 3 (eight single-attributes), in blue, and Group 4 (four bipolar adjective pairs), in orange, across the four locations (P2 to P5).
In the text