Robust Statistical Approaches for Stratified Data of Municipal Solid Waste Composition: A Case Study of the Czech Republic

Abstract

Accurate information on waste composition is essential for strategic planning in waste management and developing environmental technologies. However, detailed analyses of individual waste containers are both time- and cost-intensive, resulting in a limited number of available samples. Therefore, it is crucial to apply statistical methods that enable reliable estimation of average waste composition and its variability, while accounting for territorial differences. This study presents a statistical approach based on territorial stratification, aggregating data from individual waste container analyses to higher geographic units. The methodology was applied in a case study conducted in the Czech Republic, where 19.4 tons of mixed municipal waste (MMW) were manually analyzed in selected representative municipalities. The method considers regional heterogeneity, monitors the precision of partial estimates, and supports reliable aggregation across stratified regions. Three alternative approaches for constructing interval estimates of individual waste components are presented. Each interval estimate addresses variability from the random selection of waste containers and the selection of strata representatives at multiple levels. The proposed statistical framework is particularly suited to situations where the number of samples is small, a common scenario in waste composition analysis. The approach provides a practical tool for generating statistically sound insights under limited data conditions. The main fractions of MMW identified in the Czech Republic were as follows: paper 6.7%, plastic 7.3%, glass 3.6%, bio-waste 28.4%, metal 2.1%, and textile 3.0%. The methodology is transferable to other regions with similar waste management systems.

1. Introduction

Changing current waste management (WM) systems towards increased recycling and resource recovery is complex and financially demanding [1]. However, this transition is necessary to reduce environmental impacts, particularly emissions associated with waste disposal [2]. To plan and implement such system changes effectively, it is essential to use modeling approaches that can simulate different management scenarios [3]. These models depend critically on accurate estimates of waste composition, which serve as input data for predicting outcomes and planning interventions [4].

Mixed municipal waste (MMW), representing the main unsorted waste stream, provides essential information for evaluating separation potential and improving recycling processes [5]. Accurate knowledge of its composition allows targeted WM development, supporting decision-making related to sorting efficiency [6], recyclability of plastic waste [7], potential for pyrolysis [8], and processing of food waste through fermentation [9]. Moreover, the composition of solid waste strongly affects the applicability of existing treatment technologies, including energy recovery [10]. Waste composition data are also increasingly integrated into sustainable management strategies [11].

Obtaining reliable estimates of MMW composition requires both physical waste analyses and robust statistical evaluation methods. Data processing methodology plays a key role in ensuring the applicability and credibility of the results. A novel approach based on zero-intercept regression, proposed by Ezennia et al. [12], has demonstrated the potential for improving the accuracy of composition estimates through statistical modeling. Recent studies further highlight that significant spatial variability in waste composition can be observed even within homogeneous administrative units. For example, Tonjes et al. [13] analyzed waste composition in New York State and reported notable differences between and within WM systems. These findings confirm the importance of using stratified sampling and statistical approaches to obtain representative estimates.

This study aims to analyze current methodologies for statistical evaluation of waste composition, identify their limitations, and propose improvements towards a comprehensive and practical tool for waste composition assessment. The description of the procedures for the analysis of solid waste is already presented as a part of the standardized methodology with recommendations SWA-Tool (solid waste analysis) [14]. The main idea of waste composition evaluation is based on the stratification of the investigated territory and the statistical evaluation of collected data. The stratification is necessary to select the most representative samples across the territory, as regions can differ in the character and WM system, possibly resulting in a considerable impact on the MMW composition [15].

The generally recommended methodology is divided into three levels described in Figure 1. The individual steps are strongly interconnected, and it is necessary to consider this aspect when designing the solution. This paper focuses on the statistical evaluation of the obtained data (using point and interval estimates of waste composition) and aggregating the results from collection containers or municipalities into a larger territorial unit (e.g., region or state). For relevant results, it is necessary to achieve a certain precision according to statistical assumptions at each level of stratification. It is essential to estimate the required number of samples to achieve the desired precision, which further allows for effective investigation planning from the point of view of costs and staffing.

However, the results processed in the third level (Figure 1) are significantly influenced by the choice of location and container, and subsequently by the analysis method. Before starting the analyses, it is necessary to appropriately divide the examined territory into clusters. In clusters, waste sample analyses are performed in only a few selected localities (representatives of clusters) that probably best describe the whole territory (e.g., the state) [16]. The principles of stratification are used for this purpose and are commonly used in various branches such as sociology [17], climatology [18], and others. Based on the stratification of the territory, the best representatives are determined, and in these selected parts of the territory (e.g., municipalities), the actual waste composition analyses will be carried out. Stratification will enable waste composition analyses to be more efficient, i.e., to reduce their number while maintaining the quality of the results. It is also necessary to select the waste fractions that will be monitored. The sample’s content should be investigated using a predetermined methodology. In some cases, it is also appropriate to perform stratification at the level of collection containers to ensure a description of variability within the municipality. A key factor is the coherence of stratification, sampling methodology, and suitable statistical methods. The statistical methods will evaluate the collected data and the aggregation results, which can be applied with a meaningful value.

This work is focused on the third part of the approach described above, i.e., on the statistical evaluation of the data obtained and the aggregation of the evaluated results. As Figure 1 shows, the third level is directly influenced by the approach to the levels of waste analyses that precede it. Concerning the complex methodology, including feedback in the process, and an iterative approach to refining the results, it is necessary to describe the whole process. In the follow-up research, it is therefore recommended to focus on the approaches to stratification and the performance of waste analyses. The quality of waste composition estimation is an interplay at all three levels.

The main objective of this study is to develop a general statistical approach for processing waste composition data in the context of territorial stratification, using a real case study based on MMW in the Czech Republic. Although designed primarily for MMW, the presented methodology applies to any waste type requiring stratified sampling and analysis. The key contribution of this work lies in enabling the aggregation of results from stratified territories to provide composition estimates for larger units, such as regions or entire countries. This approach improves existing methodologies by systematically considering sample-level variability and the variability from selecting representative locations. Additionally, the results from the Czech case study, covering approximately 19.4 tons of MMW analyzed across 10 clusters, provide valuable reference data for comparable regions, especially in Central and Eastern Europe. The methodology also supports practical applications in waste management planning, including economic evaluation of analysis campaigns and setting of data collection priorities based on the required precision.

1.1. Research Gap and Challenges

Current research into the production and composition of MMW is limited by economic and time constraints for carrying out waste composition analyses to the necessary extent. While numerous studies address waste composition, most are constrained by simple sampling strategies and basic statistical methods that fail to capture waste streams’ spatial and socio-economic variability fully. A critical review of available methodologies revealed that many studies apply random sampling or single-level stratification without properly treating variability between regions or sampling units. Furthermore, data aggregation into larger territorial units is often performed without rigorous statistical justification, potentially leading to biased or misleading results. Part of this work was a search for statistical methods used in the research on the production and composition of MMW. The articles to be studied were selected from the Scopus database based on the following keywords: stratification, waste composition, waste sampling, stratum characterization, waste components, waste classification, and SWA-Tool. Monitored parameters are as follows:

• Assumptions check—many statistical methods have defined assumptions, which should be verified, e.g., data normality.
• Point/interval estimate—point estimate represents a result with a simple application. On the other hand, its probability is considered zero and does not give information about variability.
• Relative/absolute estimate—relative and absolute estimates complement each other. In the context of waste composition, the relative is considered more utilizable and gives clear insight into the obtained results.
• Necessary number of samples—precision of statistical evaluation is very dependent on dataset size. Required precision should be suggested regarding the application and assessed from the results.
• Testing of statistical hypotheses—analysis of obtained estimates to detect significant behavior of evaluated data.
• Aggregation of results—in the case of stratification, it is necessary to propose a statistical method for aggregating the obtained results into a higher territorial level.

The results of the search are summarized in

Table 1. An overview of reviewed publications focused on the statistical evaluation of the composition of municipal solid waste.

Paper	Assumptions Check	Point/Interval Estimate	Absolute/Relative Estimate	Number of Samples	Statistical Hypotheses	Aggregation of Results
[4]	no	point, interval, log interval, correlation	relative	no	yes	no
[16]	no	point, interval	relative	no	yes	only results
[19]	no	no	no	no	no	no
[20]	no	point	absolute	no	yes	no
[21]	no	point	relative	no	yes	no
[22]	no	point	relative	no	yes	no
[23]	no	point	relative	no	no	no
[24]	yes	point, interval	both	no	no	no
[25]	no	point	relative	no	no	no
[26]	no	interval	both	yes	no	no
[27]	no	point	relative	no	no	only results
[28]	no	point	relative	no	no	no
[29]	no	point 1	relative	yes	no	no
[30]	no	point	relative	no	yes	only results
[31]	no	point	relative	no	no	brief description
[32]	no	point 1	relative	yes	no	only results
[33]	yes	point, interval	relative	yes	yes	only results
[34]	no	point, interval	relative	yes	yes	brief description
[35]	no	point 1	relative	yes	yes	no
[36]	yes	point	relative	yes 2	yes	only results
[37]	no	point 1	relative	yes	yes	brief description
[38]	yes	point, interval	relative	yes	no	no

¹ Interval set in an equation for n by a given level of precision. ² Expert estimation of the necessary number of samples.

. Almost all the studies below focused on research into the production and composition of MMW, except for the study of specific electrical waste [19] and anaerobic swine waste [20]. It was also noted that methodologies differ significantly in how waste types are described and results reported, making comparisons between studies difficult.

The most critical gap identified relates to insufficient treatment of spatial variability and the lack of robust aggregation methods linked to stratification. Most existing publications rely on random sampling without systematic territory division. Variability due to regional differences or representative selection is rarely quantified. Results are often generalized to higher territorial units without proper statistical foundations, which increases the risk of biased conclusions and misapplication in waste management planning. Only a small number of publications focusing on waste composition estimation describe in detail statistical methods that would extend the commonly used approaches.

In general, all the above articles use the same method to describe the main characteristics of the sought unknown quantity—the ratio of selected waste fractions in the total weight. However, the calculations assume a normal distribution of data, which is usually not verified by the appropriate statistical method. For fractions that are abundant in waste (e.g., paper, plastic), this strict assumption is not a considerable problem. For fractions with a small proportion (e.g., electrical waste, metal), the confidence interval also contains negative values that do not reflect reality. Another neglected factor is the achieved precision of interval estimates and feedback for the required number of samples. Most approaches focus solely on relative precision, which becomes impractical for fractions with small shares, where achieving the required precision would demand an excessive number of samples. This issue can be addressed using absolute precision, but choosing the appropriate form of precision requires a methodological framework not discussed in the current literature.

Currently, only a few specialized approaches seek to address the issue comprehensively. The description of the procedures for statistical evaluation of stratified territory is part of the methodological recommendations of the SWA-Tool [14]. Similar statistical procedures are given in the ASTM methodology [39], which is confirmed by [40]. It uses the ASTM to process the results of 37 studies and states the standard deviation and coefficient of variation. Another guideline published in Scotland provides the basis for determining the minimum number of samples depending on the variation and confidence interval [39].

However, these existing guidelines rely on standard formulas and do not sufficiently address data aggregation from stratified territories, nor account for variability arising from the selection of representative locations. A structured approach combining stratification, variability control, and iterative precision evaluation is lacking. The limitations of existing methods—namely insufficient stratification, neglect of representative selection variability, reliance on symmetric intervals, and missing iterative precision control—highlight the need for a more comprehensive framework. This study addresses these gaps by introducing a statistical framework based on multi-stage stratification, combined with advanced aggregation methods and interval estimation approaches that account for both container-level and territorial-level variability. The methodology also supports optimization of sampling based on defined precision criteria, providing a structured and reproducible process for waste composition estimation.

One of the recent studies by [28] specifically focused on waste analysis in the Czech Republic, an EU member state, which is also the source of the case study presented in this article. However, the previous research did not apply territorial stratification; municipalities were divided into two groups based on size. The specific collection containers for waste analysis were then selected randomly within 35 municipalities and evaluated without distinction or further aggregation. Additionally, the data were used solely for point estimation, significantly reducing the explanatory value and the efficiency of resources invested in waste analysis. Most similar studies follow this approach, making a comprehensive statistical evaluation methodology a necessary step towards sustainability and increasing the efficiency of available resources.

1.2. Novelty and Main Contribution

This work suggests a theoretical approach for statistical data processing (from waste analysis) for general stratification and its application to the case study based on a real dataset. The presented methodology is generally defined for any waste type’s composition analysis, but it is primarily designed for MMW. The main benefit of the proposed procedure is the possible aggregation of results from different areas for an overall estimate of a higher territorial unit. Based on partial waste composition analyses in predetermined localities, it is then possible to evaluate waste composition at the levels of micro-regions, regions, or the entire state. Another benefit of the contribution is the results of the composition of MMW in locations with specific characteristics. This information can be further used in case studies and applications of WM in various locations.

At the same time, data from an extensive case study are provided, in which about 19.4 t of MMW were analyzed in 10 clusters on the territory of the Czech Republic. The composition results, including interval estimates, are presented in Section 3. Each cluster represents a particular group of municipalities with similar characteristics. A significant output is also a discussion on the results of individual clusters, which have a general overlap, especially for representatives of Central and Eastern Europe, but also in other parts of the world.

Legislative and industrial use of the results is the main benefit. An example is the TIRSMZP719 2019–2021 project [41], which addresses the average composition of the MMW for the Ministry of the Environment of the Czech Republic and follows this methodology. Estimating the necessary number of samples is a direct prerequisite for planning the economic costs of analysis. Cost planning is possible not only from the municipality’s point of view but also for regions and states. Using the presented approach, it is possible to plan the costs of local surveys in this area from a global perspective.

The authors of this article set the following requirements for the statistical processing of data from waste sample analyses. All these points are addressed within the presented approach in Section 2 and Appendix A.

• Point and interval estimates—it is advisable to design asymmetric interval estimates that better describe the properties of the data. The interval should be limited to non-negative values.
• The results must consider the different waste weights of the individual MMW composition analyses.
• It must be possible to aggregate partial results into higher territorial units. The stratification results and the variability in individual waste composition analyses must be considered.
• It is advisable to choose a precision criterion for interval estimates. A tool should be provided to decide on relative or absolute precision.
• It is advisable to estimate the required number of samples based on partial waste composition analyses, allowing for initial data variability estimates.
• It is appropriate to have an approach for estimating the waste composition of all territorial units based on the characteristics of territorial stratification.

Unlike existing approaches to the statistical evaluation of waste analyses, the newly proposed method utilizes results more comprehensively, especially regarding result aggregations. It not only considers variability caused by the selection of collection containers but also accounts for variability arising from the selection of representatives of individual strata at different levels. At the same time, the formulas offer a solution for cases where the number of representatives and individual waste samples is small. This is a typical scenario in waste analysis evaluations, as these are both time-consuming and financially demanding. The approach thus presents a comprehensive methodology with recommendations and possible alternatives for specific scenarios in waste composition analysis.

2. Methodology

This section briefly outlines the methodology for estimating the composition of the MMW fraction. A detailed description is available in Appendix A. It is possible to use several approaches to estimate waste composition in the investigated territory, as is shown in Figure 2. The most straightforward approach is a statistical evaluation of samples selected without any stratification or further knowledge. Another approach is one-level stratification, which involves analyzing waste in each stratum and performing aggregation to estimate the investigated territory. The most suitable way is a comprehensive methodology consisting of multi-stage stratification, complex statistical methods, and iterative assessment of estimate precision.

An important distinction must be made between the number of representative locations and the number of samples. Representative locations (municipalities) are selected to reflect the entire territory’s spatial, socio-economic, and waste-production diversity. Multiple samples (individual container analyses) are collected within each representative location to capture local variability and ensure statistical reliability. While the number of samples directly determines the statistical precision of the estimates, the number of representatives defines the territorial and population coverage of the analysis. Both quantities are essential for proper waste composition assessment and cost planning.

The proposed data processing process incorporates a sequence of seven consecutive steps shown in Figure 2. For clarity, it is possible to consider the evaluated territory as a state and the lowest territorial units as municipalities.

• The evaluated territory is subjected to a cluster analysis in the first phase. Based on the selected parameters, the territory is divided into several clusters (A to H in Figure 2).
• One representative from each cluster who best represents the group in the cluster according to the given criteria is selected.
• The collection containers are selected. If the representative is a larger city, it is appropriate to efficiently and economically obtain relevant results and stratify this city based on selected characteristics (e.g., describing individual build-up areas).
• Waste composition analyses will be performed in the selected location (representative) using a predetermined methodology.
• The empirical data are then statistically evaluated; point and interval estimates are determined for each monitored fraction. Sufficient precision is based on an iterative statistical evaluation of the individual waste composition analyses until the criterion of precision in the individual strata is met.
• Subsequently, these strata estimates are aggregated for the actual representative, who describes the whole cluster.
• In the last step, all clusters are aggregated to estimate the overall composition in the evaluated territory.

As already mentioned, this article’s research subject is the statistical evaluation of the obtained data and determining the waste composition in the selected territory (i.e., points 5, 6, and 7). However, it is necessary to describe the entire complex methodology due to feedback in the process and an iterative approach involved in refining the results.

Statistical processing of waste composition analyses is described in detail in Appendix A. The mathematical apparatus evaluates the percentage composition of waste by predetermined fractions. The absolute amount can be calculated from the total production. Furthermore, there is a brief description of four approaches to statistical processing of waste composition analyses:

• Estimation without stratification: This is a situation where the waste composition analysis was performed without previous stratification. It is helpful for an application on small territorial units (e.g., village, municipality).
• Estimation for stratified locality/municipality: Stratification is beneficial if heterogeneity of the analyzed area is expected. The samples are representative of a particular locality.
• Estimation for stratum consisting of many localities: Waste composition estimates have only been considered for individual municipalities. However, the goal of waste composition analysis can often be to estimate for regions or even for the whole state.
• Estimation at a national level: The last approach to statistical processing of analyses is based on aggregating results for several strata. In this way, estimating the waste composition for a higher territorial unit is possible.

3. Results for the Case Study of the Czech Republic

The mathematical method described in Section 2 and in more detail in Appendix A is applied to data from the Czech Republic. The presented methodology is based on theoretical statistics and is generally applicable. The example of the Czech Republic provides the MMW composition for different clusters (C1–C10).

3.1. Waste Analysis Information

Within this work, a demonstration of the presented methodology was performed using an example focused on the Czech Republic. The territory of the Czech Republic, with an area of 78,870 km² and a population of over 10.5 million inhabitants, is administratively divided into 14 regions. These are divided into 206 micro-regions and further into 6258 municipalities. Based on stratification, 19.4 t of MMW were selected and analyzed for the territory of the Czech Republic.

According to the proposed methodology, the area was stratified using a multi-level approach. The method combines socio-economic, demographic, and waste-related parameters (such as waste production and heating type) to divide municipalities into homogeneous groups and select representative locations for analysis. The detailed description of the stratification process, including the criteria and clustering steps, is presented in the study by Šomplák et al. [42]. In brief, hierarchical clustering based on Euclidean distance was applied to population density, waste generation per capita, settlement type, and socio-economic indicators. Representative municipalities were selected as those closest to the cluster centroid [42]. A similar procedure was used for the container selection within each investigated municipality. Based on this approach, the area of the Czech Republic was stratified into 10 clusters (C1–C10), as seen in Figure 3. Representatives were selected to reflect the diversity of settlement types and waste production patterns (see points 1 and 2 in Figure 2). Seasonal variability, which is known to affect household waste composition [43], was considered during sampling design according to the methodology described by Šomplák et al. [42], recommending the distribution of analyses between heating and non-heating seasons. However, due to dataset limitations, seasonal effects could not be quantitatively evaluated in this study. Waste analyses were subsequently performed in the selected representative locations.

Analyses of the MMW were performed for representatives of each cluster (C1–C10), as seen in point 4 in Figure 2. The aim was to obtain knowledge and key information for identifying individual fractions of the MMW based on certified methodology. Namely, paper, plastic, glass, biowaste, metals, textiles, composite packaging, electrical equipment, others, and the fraction of waste smaller than 40 mm were sorted out. The waste analysis aimed to identify the composition of the MMW, i.e., weighing and recording the weight and percentage of individual monitored fractions.

Manual analyses of MMW from randomly selected collection containers from the given housing types were performed. At first, a sieve (with a mesh size of 40 mm) was used for sorting—the result was an under-sieve fraction and an over-sieve fraction. The over-sieve fraction was further manually sorted and weighted. Furthermore, the total weight of the analyzed waste and the average weight in one sample are given. The average weights differ in different localities regarding the predominant type of housing. In the case of housing estates type, the analysis involved large collection containers (with a volume of 1100 L), where, due to the large volume of waste, only part of the waste was used for the analysis. In the case of the rural type, there were relatively small point samples in the form of waste from small bins (usually with a volume of 240 L). The single-family detached house type then combined the two previous variants.

3.2. Statistical Evaluation

The following part of the case example will focus on the statistical evaluation of available data from the waste analysis using the statistical methodology described in Section 2 and Appendix A. At the start, it is necessary to select appropriate weights for strata, significance level, and desired precision. The weights were determined according to the produced quantity; these are approximately the same values for any cluster. It is necessary to normalize weights in all aggregations. The confidence level is set at the usual value of 95%. A combination of absolute (0.5%) and relative precision (30%) is used to assess the precision of the waste analyses. An estimate is considered precise if at least one of these precisions is met. Bootstrap construction uses 5000 generated samples from the available dataset.

The C1 cluster is selected to describe the results and differences between approaches for confidence intervals. First, the individual strata of the representative must be evaluated, and the precision of the obtained estimates must be reviewed. According to the diagram in Figure 2, this step is point 5. The formulas (described in Appendix A) are used for the calculation, which do not assume further stratification of the examined area. Figure 4 shows important statistical outputs describing the composition of MMW in the housing estate of the cluster C1. A total of 55 samples with a total weight of 6747 kg were analyzed for C1.

Looking at interval estimates, the suitability of individual approaches can be assessed. The common construction of interval estimation represents a symmetric interval. The disadvantage of this approach is that, in the case of a small percentage of waste fraction and a large variance, it can give negative values which do not correspond to reality. For this reason, an alternative construction is proposed. The logit transformation provides an asymmetric interval and satisfies non-negativity. From Figure 4, it can be observed that the alternative interval is shifted to higher values even in the case of non-negative values. However, this occurrence with a larger number of samples is negligible. The bootstrap percentile method is an easy construction for non-negative interval estimation, but in the case of a smaller number of examined samples, it provides a too-narrow confidence interval. This is mainly because the range of the confidence interval is limited by the range of the observed individual ratios, which leads to too optimistic results in the case of less investigated waste. Based on the presented methodology, the necessary number of samples can be effectively changed during the waste analyses. This aspect is crucial, especially in terms of economic costs, which can be minimized. The MMW composition for each cluster is evaluated in the same way.

According to Figure 5, the aggregation of results is performed at the end to evaluate the entire examined territory, corresponding to point 7. The formulas related to Section 2 (described in Appendix A) are used for the calculation. The statistical evaluation of the Czech Republic also includes methodology from Section 2, which characterizes the composition of waste in strata and represents input data for aggregation at the level of the whole territory. During the investigation of the composition of MMW in the Czech Republic, 634 samples were taken with a total amount of waste of 19,401 kg.

The summary estimates are shown in Figure 5. The results of the bootstrap percentile method are not included, as it is unclear how to incorporate this additional variability to aggregate the results. In contrast to previous calculations, the number of required samples is not estimated. Instead, the total number of investigated localities (representatives) is given, where the waste analyses should meet the required precision. The estimate for the necessary number of representatives is 17. This value is due to the significant variance in the glass, and it can be expected that including other localities will reduce the variance. The expected additional cost required to achieve the desired precision by conducting further analysis in 7 localities is discussed in Section 4.

In summary, the statistical evaluation shows that the most represented fractions are bio (with a dominant share of food waste), the under-sieve fraction, and other waste. Information related to food waste can be utilized for measures aiming at higher separation, and for planning treatment infrastructure of new, effective technologies [44]. Common commodities such as plastic, paper, and glass each account for up to 10% of MMW. However, significant differences are evident for individual clusters. The other factions represent a minority stake in MMW. The results were aggregated into three strata, as indicated in

Table 2. Point and interval estimates resulting from analyses of the composition of MMW in the Czech Republic, for representatives C1–C9 using logit transformation.

		S1	S1	S2	S2	S2	S3	S3	S3	S3
		C1	C2	C3	C4	C5	C6	C7	C8	C9
Paper	Point	7.70%	9.50%	5.10%	9.90%	4.10%	5.20%	3.60%	3.00%	4.80%
	Interval	5.70%	8.23%	3.18%	7.31%	3.14%	3.45%	2.72%	1.90%	3.46%
		10.26%	10.89%	8.12%	13.18%	5.38%	7.64%	4.64%	4.65%	6.69%
Plastic	Point	8.50%	9.00%	4.20%	10.90%	6.70%	5.90%	4.40%	5.20%	6.00%
	Interval	6.20%	8.05%	3.56%	9.21%	5.25%	4.26%	3.33%	3.78%	4.79%
		11.54%	10.13%	4.93%	12.75%	8.59%	8.03%	5.79%	7.23%	7.44%
Glass	Point	3.70%	4.00%	2.30%	6.50%	2.80%	2.20%	2.20%	5.40%	2.10%
	Interval	2.66%	3.43%	1.61%	4.90%	1.59%	1.00%	1.19%	2.95%	1.38%
		5.18%	4.75%	3.39%	8.55%	4.85%	4.61%	4.00%	9.51%	3.21%
Bio waste	Point	25.10%	25.10%	27.50%	27.70%	28.10%	43.00%	26.30%	29.60%	33.80%
	Interval	21.89%	21.98%	21.66%	24.53%	23.77%	34.51%	20.81%	22.57%	27.07%
		28.52%	28.45%	34.21%	31.14%	32.78%	52.01%	32.63%	37.71%	41.25%
Metal	Point	1.90%	2.00%	2.50%	2.10%	2.70%	1.60%	1.70%	1.70%	2.50%
	Interval	1.57%	1.72%	1.72%	1.50%	2.18%	0.88%	1.25%	1.05%	1.06%
		2.20%	2.23%	3.54%	3.04%	3.38%	3.05%	2.35%	2.64%	5.95%
Textile	Point	4.00%	2.90%	4.90%	2.40%	2.80%	1.90%	2.20%	2.30%	2.20%
	Interval	2.44%	2.23%	3.28%	1.25%	1.81%	1.14%	1.33%	1.22%	1.35%
		6.59%	3.66%	7.25%	4.70%	4.41%	3.10%	3.55%	4.13%	3.71%
Composite	Point	2.00%	2.00%	1.60%	2.40%	2.30%	1.70%	2.00%	1.60%	1.80%
	Interval	1.50%	1.71%	1.18%	2.01%	1.77%	1.18%	1.50%	1.21%	1.39%
		2.61%	2.25%	2.05%	2.84%	2.86%	2.57%	2.55%	2.17%	2.36%
Electrical	Point	0.40%	0.50%	0.70%	1.00%	0.20%	0.30%	0.40%	1.30%	0.10%
	Interval	0.19%	0.31%	0.30%	0.31%	0.07%	0.11%	0.12%	0.44%	0.04%
		0.75%	0.83%	1.80%	3.10%	0.53%	0.65%	1.25%	3.93%	0.20%
Others	Point	21.60%	23.10%	22.20%	24.50%	26.20%	14.00%	20.00%	20.30%	19.90%
	Interval	17.42%	19.28%	16.97%	18.67%	21.46%	10.30%	15.20%	15.20%	15.85%
		26.84%	27.75%	30.73%	32.49%	32.41%	18.95%	25.89%	26.55%	25.00%
<40 mm	Point	25.20%	22.00%	29.00%	12.60%	24.10%	24.20%	37.30%	29.70%	26.70%
	Interval	19.90%	18.81%	18.29%	10.48%	20.73%	17.15%	28.91%	19.39%	19.14%
		31.32%	25.46%	42.72%	15.06%	27.78%	33.07%	46.63%	42.58%	35.83%

, to describe the outputs. These are S1 (C1, C2), S2 (C3–C5), and S3 (C6–C9). Cluster C10 is not listed here because it includes only one location (Capital City Prague), where the analyses have not yet been carried out according to the valid methodology, and therefore, no data is available.

Simplistically, S1 is an aggregation for cities, S2 for transitional areas, and S3 represents an aggregation of rural settlements. In this way of representation, trends are already visible for some fractions of waste. Commonly separated fractions, such as paper, plastic, and glass, are most abundant in MMW in cities (S1) and gradually decrease in quantity. In the rural localities, the balances of these fractions in MMW are significantly lower. The opposite trend is visible for bio waste; the balance in MMW is considerably lower in cities than in rural areas. The remaining factions either have too little representation in MMW or do not reflect the character of the territory. Therefore, their occurrence in MMW is not linked to the type of housing.

The following

Table 3. Results of analyses of the composition of MMW in the Czech Republic, for representatives C1–C9 using logit transformation.

	Presented Approach		Simple Evaluation
	Point Estimate	Variance (10-7)	Point Estimate	Variance (10-7)
Paper	6.75%	1020.4	6.64%	102.1
Plastic	7.32%	851.7	7.06%	71.8
Glass	3.59%	392.9	3.35%	30.5
Bio waste	28.37%	2289.4	28.74%	885.1
Metal	2.06%	36.7	2.06%	15.7
Textile	2.96%	204.3	3.11%	55.5
Composite	1.93%	96.4	1.90%	5.1
Electrical	0.53%	26.2	0.51%	5.4
Others	21.86%	1777.9	21.92%	519.7
<40 mm	24.63%	8301.9	24.71%	997.1

provides a comparison of the presented approach with the generally known statistical evaluation of the analyzed samples without considering stratification, and therefore, without considering gradual aggregation. The results are related to the highest level of stratification, i.e., for the entire Czech Republic. The results show that the point estimates of waste composition do not differ significantly. The simple evaluation works only with the weighted average according to the size of the individual samples. The presented approach additionally considers information from stratification, where individual clusters are weighted according to the amount of production they represent. However, stratification aims to design clusters of approximately equal size, so this aspect does not significantly impact the results.

However, a significant difference can be observed in the case of variance. Simple statistics do not consider that individual samples are taken from different locations, and the data is thus evaluated as a single set. The presented approach also considers the variability arising from the selection of representatives, i.e., that a representative might not have an average cluster composition. To reduce the impact of this contribution to variability, it is advisable to evaluate multiple representatives to minimize the uncertainty arising from this fact. This aspect, however, conflicts with the financial demands of waste analysis. Nevertheless, it is essential to consider this variability in subsequent studies and applications.

4. Discussion

Waste analysis statistical processing significantly impacts the applicability of the results in practice. According to the stated research gap and given requirements for statistical apparatus, three approaches for constructing interval estimates were introduced. The advantages and disadvantages were progressively discussed with appropriate recommendations. Given the economic demands of waste analyses, suggesting how to monitor the precision of results was a requisite.

The presented approach provides the necessary number of samples and representatives to satisfy the desired precision and allows for planning the whole project by properly assigning financial resources. It is closely connected with the choice between relative and absolute precision, and a combination of both is recommended due to their properties. The main benefit of the proposed procedure is the possible aggregation of results from different areas for a comprehensive view of the higher territorial unit. Based on partial waste composition analyses in predetermined localities, it is then possible to evaluate waste composition at the levels of micro-regions, regions, or the entire state. The approach limitation lies clearly in a small database, and from a statistical point of view, precision can be handled only by using a larger number of samples. The results are further influenced by the quality of stratification and own waste analyses in the field, which is beyond the scope of this work.

Although the stratification framework aims to mitigate sampling bias, the total analyzed waste mass of 19.4 t remains relatively small considering the national scope of the study. This limited database increases sensitivity to geographic and socio-economic heterogeneity, which may affect the representativeness of the composition estimates. In particular, regions underrepresented within the stratification process, such as certain rural or industrial areas, may exhibit different waste composition patterns. Therefore, while the methodology itself is designed to be broadly applicable, the specific composition results presented in this study should primarily be interpreted as representative of municipalities with characteristics similar to the selected clusters. A larger, more geographically balanced dataset would allow for more robust generalization to the entire national territory. However, in relative terms (population and waste production), the waste fraction analyzed in our study aligns with or exceeds common practice. The analyzed amounts are often limited to just a few tons, and sample sizes in the hundreds of tons are exceptional.

From a practical perspective, the sampling campaign conducted in the Czech Republic required approximately 79 working days, with a field team consisting of four sampling technicians and one supervisor. Considering the supervisor’s costs were approximately double those of a technician, the total personnel effort was equivalent to six full-time workers. This corresponds to approximately 474 person-days, or about 3800 working hours, excluding material, equipment, and transportation costs. This metric is used because each country has different wage levels based on its GDP. In our case study, an average of 8 working days is needed per locality. For seven more localities resulting from national evaluation in Figure 5, this would amount to up to 336 person-days. In addition to labor costs, protective gear, essential equipment, and transportation expenses must also be considered. Although a detailed cost analysis was beyond the scope of this study, these figures highlight the labor-intensive nature of waste composition analysis.

Based on the presented study and our experience in developing the improved approach, the following recommendations could be given for statistical evaluation of waste composition.

• Investigated territory should be stratified in advance; multi-stage stratification based on multiple parameters is recommended.
• To obtain relevant results, it is appropriate to stratify even the representatives according to significant parameters influencing the waste composition. Then, a random sampling procedure in individual strata will be performed.
• Confidence intervals (for instance, with the standard 95% precision) provide a valuable tool to assess the quality (variability) of estimates of waste composition.
• From the presented methods of constructing confidence intervals, the logit transformation method performs best in the context of waste composition estimation.
• The required precision should be defined at the beginning of the process concerning economic possibilities and the application of results.
• It is suitable for evaluating absolute and relative precision at the same time. The results should achieve at least one of them.
• To achieve defined precision in the required detail, having the same precision in all lower strata is recommended.
• The sample size should be at least 10. It should be proportional to the required precision and iteratively evaluated with new data.
• In the case of using the absolute precision of 0.5%, and the relative precision of 30%, a requirement of at least 10 representatives can be stated, and at least 30 samples should be performed in each sub-area. However, these numbers depend on the variability of data from waste analyses.

A comparative summary of the three interval estimation methods, including their practical advantages and limitations, is presented in

Table 4. Comparison of interval estimation methods.

Method	Advantages	Limitations
Standard asymptotic	– Simple and fast to compute – Suitable for large samples	– Unreliable for small samples – Performs poorly for extreme proportions – Confidence intervals may exceed [0, 1]
Logit-transformed	– Reliable for small samples – Handles extreme proportions well – Keeps intervals within [0, 1]	– Requires logit transformations – Slightly more complex
Bootstrap	– Non-parametric (no distribution assumptions) – Intuitive and flexible	– Less stable with small samples or stratified data – Computationally intensive – Less reliable than the logit method in this study

. The results indicate that, while the symmetric interval is straightforward to compute, it may yield negative values for small waste fractions with high variance. The logit-transformed interval addresses this issue by ensuring non-negativity, although it can be slightly biased upwards. The bootstrap percentile method is easy to implement but tends to underestimate uncertainty with small sample sizes and cannot account for additional variability when aggregating estimates. These findings underscore the importance of choosing an appropriate method based on the characteristics of the data and the number of available samples.

5. Conclusions

A general methodology for statistical processing of analysis data was created. The results will reduce the analysis cost by minimizing the number of collection containers analyzed in each location. The developed statistical apparatus allows the estimation of the minimum required number of representative localities to achieve the desired precision of the aggregated result. This approach provides for gradually optimizing localities and samples based on currently available data. Accurate estimates of the MMW composition will make it possible to plan WM and the necessary treatment infrastructure. The results will form the basis for setting suitable WM goals and identifying locations where waste separation can be improved. High-quality data evaluation will help identify the potential for using environmentally friendly technology and effectively plan the development of WM and processing infrastructure. In this way, it is possible to reduce the environmental burden due to the production of MSW.

The presented framework was applied to a case study in the Czech Republic, where 19.4 tons of MMW were manually analyzed. The dominant component was bio-waste, especially food waste, which represents a significant potential for further utilization. The share of paper and plastics was also identified, which could be materially recovered with higher separation rates. The evaluation results were compared with the standard sample assessment, revealing that point estimates showed only minor differences. However, significant discrepancies were observed in the variability of estimates, as the proposed method also accounts for the influence of representative selection within stratification. It can be seen that the different characteristics of municipalities affect the composition of MMW. The approach further provides recommendations, alternative evaluations, and modifications to calculations in cases where the number of samples and representatives is limited. These insights are crucial for waste analyses, as the high demands of their implementation allow only a limited number of studies to be conducted.

The main fractions of MMW in the Czech Republic are estimated as follows: paper 6.7%, plastic 7.3%, glass 3.6%, bio-waste 28.4%, metal 2.1%, and textile 3.0%. While comparable statistics for all fractions across the EU are inaccessible, existing data suggest that organic waste often accounts for 30–50% of MMW in Western Europe (approximately 34% as reported by the European Compost Network [45]). Differences in composition between countries may be affected by the sampling process and data variability—and therefore sample size requirements to achieve desired precision—but do not limit the applicability of the proposed methodology, which remains valid across distinct waste composition profiles. In general, the presented methodology supports optimization of sampling design during the investigation, which can significantly reduce resource demands by minimizing the number of necessary samples and representative locations without compromising the quality of the results.

In future research, extensive datasets such as the Waste Data and Analysis Center repository (wastedata.info [46]), which aggregates over 300 waste composition reports from the United States, could be used to validate the presented stratification approach in different regional and legislative contexts.