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Compositional Data Analysis: Theory and Applications
Abstract
It is difficult to imagine that the statistical analysis of compositional data has been a major issue of concern for more than 100 years. It is even more difficult to realize that so many statisticians and users of statistics are unaware of the particular problems affecting compositional data, as well as their solutions. The issue of spurious correlation'', as the situation was phrased by Karl Pearson back in 1897, affects all data that measures parts of some whole, such as percentages, proportions, ppm and ppb. Such measurements are present in all fields of science, ranging from geology, biology, environmental sciences, forensic sciences, medicine and hydrology. This book presents the history and development of compositional data analysis along with Aitchison's log-ratio approach. Compositional Data Analysis describes the state of the art both in theoretical fields as well as applications in the different fields of science.
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“Indeed, the distribution of time spent in physical behaviors is by nature intrinsically compositional[11,12].”
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Broséus, L., Vaiman, D., Tost, J., Ruano, C. S. M., Jacobi, M., Schwartz, J. D., Béranger, R., Slama, R., Heude, B., & Lepeule, J. (2022) · BMC Medicine · doi:10.1186/s12916-022-02610-y · Cited by 20
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“Data were transformed with clr transformation [34, 37] and mean centered.”
MethodRasmussen, C. L., Palarea‐Albaladejo, J., Korshøj, M., Gupta, N., Nabe‐Nielsen, K., Holtermann, A., & Jørgensen, M. B. (2019) · PLoS ONE · doi:10.1371/journal.pone.0217024 · Cited by 16
Motyka, O., Pavlíková, I., Bitta, J., et al. (2020) · Environmental Science and Pollution Research · doi:10.1007/s11356-020-09466-w · Cited by 16
Preprocessing alternatives for compositional data related to water, sanitation and hygiene
Quispe-Coica, A., & Foguet, A. P. (2020) · The Science of The Total Environment · doi:10.1016/j.scitotenv.2020.140519 · Cited by 16
Spatial interpolation of coal properties using geographic quantile regression forest
Maxwell, K., Rajabi, M., & Esterle, J. (2021) · International Journal of Coal Geology · doi:10.1016/j.coal.2021.103869 · Cited by 16
Mineral Balance Plasticity of Cloudberry (Rubus chamaemorus) in Quebec-Labrador Bogs
Parent, L. É., Parent, S.-É., Hébert-Gentile, V., et al. (2013) · American Journal of Plant Sciences · doi:10.4236/ajps.2013.47183 · Cited by 16
Stanimirova, I. (2013) · Analytica Chimica Acta · doi:10.1016/j.aca.2013.08.026 · Cited by 16
Arbel, J., Mengersen, K. L., & Rousseau, J. (2016) · The Annals of Applied Statistics · doi:10.1214/16-aoas944 · Cited by 16
Flem, B., Moen, V., Finne, T. E., et al. (2017) · Fisheries Research · doi:10.1016/j.fishres.2017.02.010 · Cited by 16
Prenatal exposure to triclosan assessed in multiple urine samples and placental DNA methylation.
Jedynak, P., Broséus, L., Tost, J., Busato, F., Gabet, S., Thomsen, C., Sakhi, A., Pin, I., Slama, R., Lepeule, J., et al. (2023) · Environmental Pollution · doi:10.1016/j.envpol.2023.122197 · Cited by 15
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Garrido-Fernández, A., Montaño, A., Sánchez, A. H., et al. (2017) · Talanta · doi:10.1016/j.talanta.2017.03.066 · Cited by 15
“The length of the rays can usually be interpreted with caution when the comparisons include subcompositions because their values depend on each sub-composition throughout their geometric mean (which may differ between the full and any considered subcomposition) [27].”
BackgroundInfluentialDo Hotels Talk on Facebook About Themselves or About Their Destinations?
Ferrer-Rosell, B., Martín-Fuentes, E., & Mariné-Roig, E. (2018) · Springer eBooks · doi:10.1007/978-3-030-05940-8_27 · Cited by 15
Generalized discrete autoregressive moving‐average models
Möller, T. A., & Weiß, C. H. (2020) · Applied Stochastic Models in Business and Industry · doi:10.1002/asmb.2520 · Cited by 15
Weighted Symmetric Pivot Coordinates for Compositional Data with Geochemical Applications
Hron, K., Engle, M. A., Filzmoser, P., et al. (2020) · Mathematical Geosciences · doi:10.1007/s11004-020-09862-5 · Cited by 15
Laurent, C. W. S., Burkart, S. A., Rodheim, K., Marcotte, R. T., & Spencer, R. M. C. (2020) · International Journal of Environmental Research and Public Health · doi:10.3390/ijerph17197148 · Cited by 15
Impact of Covariates in Compositional Models and Simplicial Derivatives
Morais, J., & Thomas‐Agnan, C. (2021) · Austrian Journal of Statistics · doi:10.17713/ajs.v50i2.1069 · Cited by 15
“Theory for inference in these models is developed for example in Pawlowsky-Glahn and Buccianti (2011), Van Den Boogaart and Tolosana-Delgado (2013), Pawlowsky-Glahn, Egozcue, and Tolosana-Delgado (2015b), and Filzmoser, Hron, and Templ (2018).”
MethodWood, J. R., & Greenacre, M. J. (2021) · Archaeological and Anthropological Sciences · doi:10.1007/s12520-021-01341-0 · Cited by 15
Yang, J., & Cheng, Q. (2014) · Journal of Geochemical Exploration · doi:10.1016/j.gexplo.2014.11.014 · Cited by 15
“Nevertheless, for capturing their scale invariance, a log-ratiomethodology should be employed (Pawlowsky-Glahn and Buccianti, 2011).”
MethodExploratory tools for outlier detection in compositional data with structural zeros
Templ, M., Hron, K., & Filzmoser, P. (2016) · Journal of Applied Statistics · doi:10.1080/02664763.2016.1182135 · Cited by 15
“Such data occur frequently in many practical situations [1,31,32].”
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Pavlíková, I., Motyka, O., Plášek, V., et al. (2021) · Applied Sciences · doi:10.3390/app11178262 · Cited by 14
Ratio product model: A rank‐preserving normalization‐agnostic multi‐criteria decision‐making method
Mohammadi, M., & Rezaei, J. (2023) · Journal of Multi-Criteria Decision Analysis · doi:10.1002/mcda.1806 · Cited by 14
A nonlinear principal component analysis to study archeometric data
Bitetto, A., Mangone, A., Mininni, R. M., et al. (2016) · Journal of Chemometrics · doi:10.1002/cem.2807 · Cited by 14
“Furthermore, a multivariate statistical technique (Wilks’ lambda test [33,34]) was applied as a criterion to discard those chemical elements that make more difficult a good archeological classification or are redundants.”
MethodÀvila, N., López‐Flores, R., Boix, D., Gascón, S., & Quintana, X. D. (2016) · Hydrobiologia · doi:10.1007/s10750-016-2897-1 · Cited by 14
“This balance takes the form of a log ratio, where 1 ffiffiffi 2 p is added for normalization (Pawlowsky-Glahn & Buccianti, 2011).”
BackgroundMethodWan, H., Jiang, L., Shang, S., et al. (2021) · Journal of Soils and Sediments · doi:10.1007/s11368-021-03044-4 · Cited by 14
A new class of α -transformations for the spatial analysis of Compositional Data
Clarotto, L., Allard, D., & Menafoglio, A. (2021) · Spatial Statistics · doi:10.1016/j.spasta.2021.100570 · Cited by 14
Taussi, M., Gozzi, C., Vaselli, O., Cabassi, J., Menichini, M., Doveri, M., Romei, M., Ferretti, A., Gambioli, A., & Nisi, B. (2022) · International Journal of Environmental Research and Public Health · doi:10.3390/ijerph191912231 · Cited by 14
Robustness for Compositional Data
Filzmoser, P., & Hron, K. (2013) · Springer eBooks · doi:10.1007/978-3-642-35494-6_8 · Cited by 14
Geboy, N. J., Olea, R. A., Engle, M. A., et al. (2012) · International Journal of Coal Geology · doi:10.1016/j.coal.2012.10.010 · Cited by 14
Cokriging of compositional balances including a dimension reduction and retrieval of original units
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Self-citationChen, J., Zhang, X., Hron, K., et al. (2017) · Journal of Applied Statistics · doi:10.1080/02664763.2017.1410524 · Cited by 14
“Compositional data or compositions carrying only relative information can be represented by vectors, where all its elements are positive numbers [1,17].”
BackgroundGozzi, C., Graziano, R. S., Frondini, F., et al. (2018) · Environmental Earth Sciences · doi:10.1007/s12665-018-7756-0 · Cited by 14
Self-citationCompositional Analysis of Microbiome Data
Xia, Y., Sun, J., & Chen, D. (2018) · ICSA book series in statistics · doi:10.1007/978-981-13-1534-3_10 · Cited by 17
Grillo, H., Alemany, M. M. E., Ortíz, Á., et al. (2019) · International Journal of Production Research · doi:10.1080/00207543.2019.1574039 · Cited by 14
“For reviews on the topic, we refer to Aitchison and Egozcue (2005), Pawlowsky-Glahn and Buccianti (2011), and Pawlowsky-Glahn and Egozcue (2016).”
MethodLin, X., Hu, Y., Meng, G., et al. (2019) · Journal of Geochemical Exploration · doi:10.1016/j.gexplo.2019.106457 · Cited by 14
Part–Whole Relations: New Insights about the Dynamics of Complex Geochemical Riverine Systems
Gozzi, C., Graziano, R. S., & Buccianti, A. (2020) · Minerals · doi:10.3390/min10060501 · Cited by 14
Self-citationSánchez‐Rodríguez, M. I., Sánchez‐López, E. M., Marinas, A., et al. (2022) · Journal of Chemical Information and Modeling · doi:10.1021/acs.jcim.2c00964 · Cited by 13
Lim, R., Dumuid, D., Parfitt, G., et al. (2023) · Maturitas · doi:10.1016/j.maturitas.2023.03.006 · Cited by 13
Usman, M., Clift, P. D., Pastore, G., et al. (2024) · Earth-Science Reviews · doi:10.1016/j.earscirev.2024.104674 · Cited by 13
A New Look at the Dirichlet Distribution: Robustness, Clustering, and Both Together
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A Logistic Normal Mixture Model for Compositional Data Allowing Essential Zeros
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Adeli, A., & Emery, X. (2020) · Journal of Geochemical Exploration · doi:10.1016/j.gexplo.2020.106661 · Cited by 13
Toller, S., Funari, V., Vasumini, I., et al. (2021) · Journal of Geochemical Exploration · doi:10.1016/j.gexplo.2021.106863 · Cited by 13
Compositional Classification of Financial Statement Profiles: The Weighted Case
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Borgheresi, M., Buccianti, A., Benedetto, F. D., & Vaughan, D. J. (2012) · Mathematical Geosciences · doi:10.1007/s11004-012-9422-5 · Cited by 13
“…to induced (numerical) and natural (stoichiometric) phenomena, with no way of separating the two contributions (Rollinson 1992; Aitchison and Greenacre 2002; Pawlowsky-Glahn and Buccianti 2002, 2011; Buccianti and Pawlowsky-Glahn 2005; Nisi et al. 2008; Buccianti 2011; Buccianti and Magli 2011).”
BackgroundSelf-citationOlszowski, T., & Ziembik, Z. (2018) · Journal of Aerosol Science · doi:10.1016/j.jaerosci.2018.04.001 · Cited by 13
Human prostate cancer bone metastases have an actionable immunosuppressive microenvironmentPreprint
Baryawno, N., Kfoury, Y. S., Sévère, N., Mei, S., Gustafsson, K. U., Hirz, T., Brouse, T., Scadden, E. W., Igolkina, A. A., Choi, B. D., et al. (2020) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2020.03.19.998658 · Cited by 12
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“All statistical procedures (i.e., CoDa and RPCA) of this study was carried out using the robCompositions 53 package in R software 54 .”
Bescós, R., Toit, L. D., Redondo-Río, Á., Warburton, P., Nicholas, T. L., Kiernan, M., Burton, R. A., Belfield, L., Montagut, G., Benavente, A., et al. (2024) · Journal of Oral Microbiology · doi:10.1080/20002297.2024.2439636 · Cited by 16
Potential modeling: conditional independence matters
Schaeben, H. (2014) · GEM - International Journal on Geomathematics · doi:10.1007/s13137-014-0059-z · Cited by 12
Treatment of the Airbnb controversy by the press
Huertas, A., Ferrer-Rosell, B., Mariné-Roig, E., & Fransi, E. C. (2020) · International Journal of Hospitality Management · doi:10.1016/j.ijhm.2020.102762 · Cited by 12
Social and Material Vulnerability in the Face of Seismic Hazard: An Analysis of the Italian Case
Didkovskyi, O., AZZONE, G. F., Menafoglio, A., et al. (2021) · Journal of the Royal Statistical Society Series A (Statistics in Society) · doi:10.1111/rssa.12739 · Cited by 12
“Aitchison (1982) firstly proposed the use of a log-ratio approach to the analysis of compositional data, defining a set of principles that such analyses should fulfill (see Pawlowsky-Glahn and J. (2001) Pawlowsky-Glahn and Buccianti (2011) Pawlowsky-Glahn et al. (2015)).”
MethodA Sparse Oblique-Manifold Nonnegative Matrix Factorization for Hyperspectral Unmixing
Guo, Z., Min, A., Yang, B., et al. (2021) · IEEE Transactions on Geoscience and Remote Sensing · doi:10.1109/tgrs.2021.3082255 · Cited by 12
“Inspired by the knowledge of compositional data analysis [43], [44], we consider the ASC constraint from the perspective of longitudinal compositional data Then, we apply root transformations to the longtitudinal compositional data S , obtaining and thus, There is no problem with zeros as with some…”
MethodThree approaches to supervised learning for compositional data with pairwise logratios
Coenders, G., & Greenacre, M. J. (2022) · Journal of Applied Statistics · doi:10.1080/02664763.2022.2108007 · Cited by 12
Toward an Efficient and Integrative Analysis of Limited-Choice Behavioral Experiments: Figure 1.
Schilling, K., Oberdick, J., & Schilling, R. L. (2012) · Journal of Neuroscience · doi:10.1523/jneurosci.1452-12.2012 · Cited by 12
“The rationale and the formalism of this approach, its technical details, and its benefits have been extensively described (for review, see Billheimer et al., 2001; Weltje, 2002; Egozcue et al., 2003; Aitchison and Egozcue, 2005; Pawlowsky-Glahn and Buccianti, 2011).”
BackgroundIntroductory Overview of Statistical Analysis of Microbiome Data
Xia, Y., Sun, J., & Chen, D. (2018) · ICSA book series in statistics · doi:10.1007/978-981-13-1534-3_3 · Cited by 14
Bergeron-Boucher, M.-P., Oeppen, J., Holm, N. V., et al. (2019) · International Journal of Environmental Research and Public Health · doi:10.3390/ijerph16173093 · Cited by 12
“There is a rich literature on how to treat compositional data [28,29], labeled compositional data analysis (CoDA).”
BackgroundMethodEPR discrimination of microcrystalline calcite geomaterials
Benedetto, F. D., Buccianti, A., Montegrossi, G., et al. (2012) · American Mineralogist · doi:10.2138/am.2012.4168 · Cited by 12
“…temperatures of three related parameters, aiso, ∆6, and W6) was performed by means of a statistical analysis for constrained (compositional) data (Aitchinson 1986; Buccianti and Esposito 2004; Buccianti et al. 2006; Buccianti 2011; Buccianti and Magli 2011; Pawlowsky-Glahn and Buccianti 2011).”
MethodSelf-citationFoliar Nutrient Balance Standards for Maize (Zea mays L.) at High-Yield Level
Modesto, V. C., Parent, S.-É., Natale, W., et al. (2014) · American Journal of Plant Sciences · doi:10.4236/ajps.2014.54064 · Cited by 12
Gini index estimation in randomized response surveys
Barabesi, L., Diana, G., & Perri, P. F. (2014) · AStA Advances in Statistical Analysis · doi:10.1007/s10182-014-0230-8 · Cited by 12
Metabolic status of CSF distinguishes rats with tauopathy from controls
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“The data were analysed as compositional using centred log ratio (clr) transformation and mean centring [25].”
MethodLog-Ratio and Parallel Factor Analysis: An Approach to Analyze Three-Way Compositional Data
Gallo, M. (2012) · Studies in computational intelligence · doi:10.1007/978-3-642-32903-6_15 · Cited by 12
Is Active Moss Biomonitoring Comparable to Air Filter Standard Sampling?
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Be aware of the allele-specific bias and compositional effects in multi-template PCR
Korvigo, I. O., Igolkina, A. A., Kichko, A. A., Aksenova, T. S., & Andronov, E. E. (2022) · PeerJ · doi:10.7717/peerj.13888 · Cited by 11
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Robust differential abundance test in compositional data
Wang, S. (2022) · Biometrika · doi:10.1093/biomet/asac029 · Cited by 12
“As every piece of information introduced by compositional data is relative, reference frames are necessary to analyze the compositional data, as noted in Pawlowsky-Glahn and Buccianti (2011) and Morton et al. (2019).”
BackgroundMethodHydrogeochemical processes controlling groundwater in Western Sohag Governorate, Upper Egypt
Embaby, A., & Ali, M. (2021) · Arabian Journal of Geosciences · doi:10.1007/s12517-021-07097-0 · Cited by 11
Emotion recognition: A smoothed Dirichlet multinomial solution
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“While there is a tremendous effort, such as several books (Aitchison, 1982; Pawlowsky-Glahn and Buccianti, 2011; Buccianti et al., 2006; Mohammadi and Rezaei, 2023), in providing proper statistical tools and methods for analyzing compositional data, MCDM researchers often neglect them, resulting in improper statistica…”
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Frequency Distributions of Geochemical Data, Scaling Laws, and Properties of Compositions
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Self-citationRegression for compositions based on a generalization of the Dirichlet distribution
Graf, M. (2020) · Statistical Methods & Applications · doi:10.1007/s10260-020-00512-y · Cited by 11
“Monti et al. (2011) defined the scaled Dirichlet by introducing a constant scale composition.”
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Garrido-Fernández, A., Montaño, A., Cortés‐Delgado, A., Rodríguez‐Gómez, F., & Arroyo‐López, F. N. (2021) · Foods · doi:10.3390/foods10061182 · Cited by 11
Compositional DuPont Analysis. A Visual Tool for Strategic Financial Performance Assessment
Saus–Sala, E., Farreras–Noguer, À., Serrat, N. A., et al. (2021) · Springer eBooks · doi:10.1007/978-3-030-71175-7_10 · Cited by 11
Numerical Stability Analysis of the Centered Log-Ratio Transformation
Galletti, A., & Maratea, A. (2016) · International Conference on Signal-Image Technology & Internet-Based Systems (SITIS) · doi:10.1109/sitis.2016.119 · Cited by 11
The shifted-scaled Dirichlet distribution in the simplex
Monti, G. S., Mateu‐Figueras, G., Pawlowsky-Glahn, et al. (2011) · BOA (University of Milano-Bicocca) · Cited by 11
Sadeghi, B., Grunsky, E. C., & Pawlowsky‐Glahn, V. (2023) · Encyclopedia of earth sciences series/Encyclopedia of earth sciences · doi:10.1007/978-3-030-85040-1_334 · Cited by 11
Self-citationAustin, G. I., & Korem, T. (2025) · mSystems · doi:10.1128/msystems.00021-25 · Cited by 12
“Most microbiome data sets have an arbitrary total read count that is not reflective of sample properties and should therefore be interpreted as relative abundances that are compositional (5, 8, 9).”
Puris, E., Kouřil, Š., Najdekr, L., Loppi, S. H., Korhonen, P., Kanninen, K. M., Malm, T., Koıstınaho, J., Friedecký, D., & Gynther, M. (2021) · Scientific Reports · doi:10.1038/s41598-021-92602-4 · Cited by 11
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“Pearson correlations calculation, Principal Component Analysis (PCA) and the visualizations of the results were performed in the R environment [41], package FactoMineR [42,43], Openair [44] and ggplot2 [45].”
MethodMeasurement, selection, and visualization of association rules: A compositional data perspective
Vives‐Mestres, M., Kenett, R. S., Thió‐Henestrosa, S., et al. (2021) · Quality and Reliability Engineering International · doi:10.1002/qre.2910 · Cited by 10
Evaluating supervised and unsupervised background noise correction in human gut microbiome data
Briscoe, L., Balliu, B., Sankararaman, S., Halperin, E., & Garud, N. R. (2022) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1009838 · Cited by 11
Locally polynomial Hilbertian additive regression
Jeon, J. M., Lee, Y. K., Mammen, E., et al. (2022) · Bernoulli · doi:10.3150/21-bej1410 · Cited by 10
Gascón, E. M., Garrigós, J. B. I., Day, P. M., et al. (2023) · Applied Sciences · doi:10.3390/app13063733 · Cited by 10
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“A problem of application of CoDA in this field is that a subset of the components may not be related directly to the mass balance, i.e. be outside of the multidimensional simplex; for example, when a sum of impurities’ contents is a member of the mass balance, but individual impurities or a subset of those impurities…”
MethodInfluentialSadeghi, B., Grunsky, E. C., & Pawlowsky‐Glahn, V. (2021) · Encyclopedia of earth sciences series/Encyclopedia of earth sciences · doi:10.1007/978-3-030-26050-7_334-1 · Cited by 10
Self-citationModelling Compositional Data. The Sample Space Approach
Egozcue, J. J., & Pawlowsky‐Glahn, V. (2018) · Springer eBooks · doi:10.1007/978-3-319-78999-6_4 · Cited by 9
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Metadata
- Authors
- Glahn, V. P., & Buccianti, A.
- ORCID
- Antonella Buccianti
- Venue
- Wiley eBooks
- Publisher
- Wiley
- Published
- 2011-07-28
- OpenAlex
- W571770348
- Cited by
- 704
- References
- 0
- Citations by year
- 2026: 30 · 2025: 38 · 2024: 34 · 2023: 40 · 2022: 45 · 2021: 71 · 2020: 71 · 2019: 46 · 2018: 61 · 2017: 60 · 2016: 52 · 2015: 42 · 2014: 47 · 2013: 37 · 2012: 22
- FWCI
- 14.85
- Type
- book
- Language
- en
- Open access
- closed
- Locations
- Wiley eBooks (publishedVersion)
- Florence Research (University of Florence) (submittedVersion)
- Topics
- Physical Sciences › Earth and Planetary Sciences › Geochemistry and Petrology › Geochemistry and Geologic Mapping
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Statistical Methods and Models
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Applications
- Keywords
- compositional data analysis, spurious correlations, parts and wholes
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