This book is written for statisticians, data analysts, programmers, researchers, teachers, students, professionals, and general consumers on how to perform different types of statistical data analysis for research purposes using the R programming language. R is an open-source software and object-oriented programming language with a development environment (IDE) called RStudio for computing statistics and graphical displays through data manipulation, modelling, and calculation. R packages and supported libraries provides a wide range of functions for programming and analyzing of data. Unlike many of the existing statistical softwares, R has the added benefit of allowing the users to write more efficient codes by using command-line scripting and vectors. It has several built-in functions and libraries that are extensible and allows the users to define their own (customized) functions on how they expect the program to behave while handling the data, which can also be stored in the simple object system.For all intents and purposes, this book serves as both textbook and manual for R statistics particularly in academic research, data analytics, and computer programming targeted to help inform and guide the work of the R users or statisticians. It provides information about different types of statistical data analysis and methods, and the best scenarios for use of each case in R. It gives a hands-on step-by-step practical guide on how to identify and conduct the different parametric and non-parametric procedures. This includes a description of the different conditions or assumptions that are necessary for performing the various statistical methods or tests, and how to understand the results of the methods. The book also covers the different data formats and sources, and how to test for reliability and validity of the available datasets. Different research experiments, case scenarios and examples are explained in this book. It is the first book to provide a comprehensive description and step-by-step practical hands-on guide to carrying out the different types of statistical analysis in R particularly for research purposes with examples. Ranging from how to import and store datasets in R as Objects, how to code and call the methods or functions for manipulating the datasets or objects, factorization, and vectorization, to better reasoning, interpretation, and storage of the results for future use, and graphical visualizations and representations. Thus, congruence of Statistics and Computer programming for Research.

Statistical Analysis Software Market size was valued at USD 7,963.44 Million in 2023 and is projected to reach USD 13,023.63 Million by 2030, growing at a CAGR of 7.28% during the forecast period 2024-2030.

Global Statistical Analysis Software Market Drivers

The market drivers for the Statistical Analysis Software Market can be influenced by various factors. These may include:

Growing Data Complexity and Volume: The demand for sophisticated statistical analysis tools has been fueled by the exponential rise in data volume and complexity across a range of industries. Robust software solutions are necessary for organizations to evaluate and extract significant insights from huge datasets. Growing Adoption of Data-Driven Decision-Making: Businesses are adopting a data-driven approach to decision-making at a faster rate. Utilizing statistical analysis tools, companies can extract meaningful insights from data to improve operational effectiveness and strategic planning. Developments in Analytics and Machine Learning: As these fields continue to progress, statistical analysis software is now capable of more. These tools' increasing popularity can be attributed to features like sophisticated modeling and predictive analytics. A greater emphasis is being placed on business intelligence: Analytics and business intelligence are now essential components of corporate strategy. In order to provide business intelligence tools for studying trends, patterns, and performance measures, statistical analysis software is essential. Increasing Need in Life Sciences and Healthcare: Large volumes of data are produced by the life sciences and healthcare sectors, necessitating complex statistical analysis. The need for data-driven insights in clinical trials, medical research, and healthcare administration is driving the market for statistical analysis software. Growth of Retail and E-Commerce: The retail and e-commerce industries use statistical analytic tools for inventory optimization, demand forecasting, and customer behavior analysis. The need for analytics tools is fueled in part by the expansion of online retail and data-driven marketing techniques. Government Regulations and Initiatives: Statistical analysis is frequently required for regulatory reporting and compliance with government initiatives, particularly in the healthcare and finance sectors. In these regulated industries, statistical analysis software uptake is driven by this. Big Data Analytics's Emergence: As big data analytics has grown in popularity, there has been a demand for advanced tools that can handle and analyze enormous datasets effectively. Software for statistical analysis is essential for deriving valuable conclusions from large amounts of data. Demand for Real-Time Analytics: In order to make deft judgments fast, there is a growing need for real-time analytics. Many different businesses have a significant demand for statistical analysis software that provides real-time data processing and analysis capabilities. Growing Awareness and Education: As more people become aware of the advantages of using statistical analysis in decision-making, its use has expanded across a range of academic and research institutions. The market for statistical analysis software is influenced by the academic sector. Trends in Remote Work: As more people around the world work from home, they are depending more on digital tools and analytics to collaborate and make decisions. Software for statistical analysis makes it possible for distant teams to efficiently examine data and exchange findings.

ABSTRACT Experimental statistical procedures used in almost all scientific papers are fundamental for clearer interpretation of the results of experiments conducted in agrarian sciences. However, incorrect use of these procedures can lead the researcher to incorrect or incomplete conclusions. Therefore, the aim of this study was to evaluate the characteristics of the experiments and quality of the use of statistical procedures in soil science in order to promote better use of statistical procedures. For that purpose, 200 articles, published between 2010 and 2014, involving only experimentation and studies by sampling in the soil areas of fertility, chemistry, physics, biology, use and management were randomly selected. A questionnaire containing 28 questions was used to assess the characteristics of the experiments, the statistical procedures used, and the quality of selection and use of these procedures. Most of the articles evaluated presented data from studies conducted under field conditions and 27 % of all papers involved studies by sampling. Most studies did not mention testing to verify normality and homoscedasticity, and most used the Tukey test for mean comparisons. Among studies with a factorial structure of the treatments, many had ignored this structure, and data were compared assuming the absence of factorial structure, or the decomposition of interaction was performed without showing or mentioning the significance of the interaction. Almost none of the papers that had split-block factorial designs considered the factorial structure, or they considered it as a split-plot design. Among the articles that performed regression analysis, only a few of them tested non-polynomial fit models, and none reported verification of the lack of fit in the regressions. The articles evaluated thus reflected poor generalization and, in some cases, wrong generalization in experimental design and selection of procedures for statistical analysis.

The Best Management Practices Statistical Estimator (BMPSE) version 1.2.0 was developed by the U.S. Geological Survey (USGS), in cooperation with the Federal Highway Administration (FHWA) Office of Project Delivery and Environmental Review to provide planning-level information about the performance of structural best management practices for decision makers, planners, and highway engineers to assess and mitigate possible adverse effects of highway and urban runoff on the Nation's receiving waters (Granato 2013, 2014; Granato and others, 2021). The BMPSE was assembled by using a Microsoft Access® database application to facilitate calculation of BMP performance statistics. Granato (2014) developed quantitative methods to estimate values of the trapezoidal-distribution statistics, correlation coefficients, and the minimum irreducible concentration (MIC) from available data. Granato (2014) developed the BMPSE to hold and process data from the International Stormwater Best Management Practices Database (BMPDB, www.bmpdatabase.org). Version 1.0 of the BMPSE contained a subset of the data from the 2012 version of the BMPDB; the current version of the BMPSE (1.2.0) contains a subset of the data from the December 2019 version of the BMPDB. Selected data from the BMPDB were screened for import into the BMPSE in consultation with Jane Clary, the data manager for the BMPDB. Modifications included identifying water quality constituents, making measurement units consistent, identifying paired inflow and outflow values, and converting BMPDB water quality values set as half the detection limit back to the detection limit. Total polycyclic aromatic hydrocarbons (PAH) values were added to the BMPSE from BMPDB data; they were calculated from individual PAH measurements at sites with enough data to calculate totals. The BMPSE tool can sort and rank the data, calculate plotting positions, calculate initial estimates, and calculate potential correlations to facilitate the distribution-fitting process (Granato, 2014). For water-quality ratio analysis the BMPSE generates the input files and the list of filenames for each constituent within the Graphical User Interface (GUI). The BMPSE calculates the Spearman’s rho (ρ) and Kendall’s tau (τ) correlation coefficients with their respective 95-percent confidence limits and the probability that each correlation coefficient value is not significantly different from zero by using standard methods (Granato, 2014). If the 95-percent confidence limit values are of the same sign, then the correlation coefficient is statistically different from zero. For hydrograph extension, the BMPSE calculates ρ and τ between the inflow volume and the hydrograph-extension values (Granato, 2014). For volume reduction, the BMPSE calculates ρ and τ between the inflow volume and the ratio of outflow to inflow volumes (Granato, 2014). For water-quality treatment, the BMPSE calculates ρ and τ between the inflow concentrations and the ratio of outflow to inflow concentrations (Granato, 2014; 2020). The BMPSE also calculates ρ between the inflow and the outflow concentrations when a water-quality treatment analysis is done. The current version (1.2.0) of the BMPSE also has the option to calculate urban-runoff quality statistics from inflows to BMPs by using computer code developed for the Highway Runoff Database (Granato and Cazenas, 2009;Granato, 2019). Granato, G.E., 2013, Stochastic empirical loading and dilution model (SELDM) version 1.0.0: U.S. Geological Survey Techniques and Methods, book 4, chap. C3, 112 p., CD-ROM https://pubs.usgs.gov/tm/04/c03 Granato, G.E., 2014, Statistics for stochastic modeling of volume reduction, hydrograph extension, and water-quality treatment by structural stormwater runoff best management practices (BMPs): U.S. Geological Survey Scientific Investigations Report 2014–5037, 37 p., http://dx.doi.org/10.3133/sir20145037. Granato, G.E., 2019, Highway-Runoff Database (HRDB) Version 1.1.0: U.S. Geological Survey data release, https://doi.org/10.5066/P94VL32J. Granato, G.E., and Cazenas, P.A., 2009, Highway-Runoff Database (HRDB Version 1.0)--A data warehouse and preprocessor for the stochastic empirical loading and dilution model: Washington, D.C., U.S. Department of Transportation, Federal Highway Administration, FHWA-HEP-09-004, 57 p. https://pubs.usgs.gov/sir/2009/5269/disc_content_100a_web/FHWA-HEP-09-004.pdf Granato, G.E., Spaetzel, A.B., and Medalie, L., 2021, Statistical methods for simulating structural stormwater runoff best management practices (BMPs) with the stochastic empirical loading and dilution model (SELDM): U.S. Geological Survey Scientific Investigations Report 2020–5136, 41 p., https://doi.org/10.3133/sir20205136

This is the dataset used to generate the figures and information contained in the paper A Statistical Analysis of Error in MPI Reduction Operations by Samuel D. Pollard and Boyana Norris, to appear in IEEE's Fourth International Workshop on Software Correctness for HPC Applications, 2020.

A description is provided in the README.md as well as the software dependencies required to re-generate these data. The log files and tab-separated-values files (tsv) allows a user to analyze the same data we used for the paper. The file datasets-pollard-correctness2020.tar.bz2 decompresses to about 5.7GB.

The source code used to generate these data is available on Github.

This course is an introduction to the key ideas and principles of the collection, display, and analysis of data to guide you in making valid and appropriate conclusions about the world. We live in a world where data are increasingly available, in ever larger quantities, and are increasingly expected to form the basis for decisions by governments, businesses, and other organizations, as well as by individuals in their daily lives. To cope effectively, every informed citizen must be statistically literate. This course will provide an intuitive introduction to applied statistical reasoning, introducing fundamental statistical skills and acquainting students with the full process of inquiry and evaluation used in investigations in a wide range of fields.

Vision and Change in Undergraduate Biology Education encouraged faculty to focus on core concepts and competencies in undergraduate curriculum. We created a sophomore-level course, Biologists' Toolkit, to focus on the competencies of quantitative reasoning and scientific communication. We introduce students to the statistical analysis of data using the open source statistical language and environment, R and R Studio, in the first two-thirds of the course. During this time the students learn to write basic computer commands to input data and conduct common statistical analysis. The students also learn to graphically represent their data using R. In a final project, we assign students unique data sets that require them to develop a hypothesis that can be explored with the data, analyze and graph the data, search literature related to their data set, and write a report that emulates a scientific paper. The final report includes publication quality graphs and proper reporting of data and statistical results. At the end of the course students reported greater confidence in their ability to read and make graphs, analyze data, and develop hypotheses. Although programming in R has a steep learning curve, we found that students who learned programming in R developed a robust strategy for data analyses and they retained and successfully applied those skills in other courses during their junior and senior years.

Statistical Analysis Software Market Outlook

The global market size for statistical analysis software was estimated at USD 11.3 billion in 2023 and is projected to reach USD 21.6 billion by 2032, growing at a compound annual growth rate (CAGR) of 7.5% during the forecast period. This substantial growth can be attributed to the increasing complexity of data in various industries and the rising need for advanced analytical tools to derive actionable insights.

One of the primary growth factors for this market is the increasing demand for data-driven decision-making across various sectors. Organizations are increasingly recognizing the value of data analytics in enhancing operational efficiency, reducing costs, and identifying new business opportunities. The proliferation of big data and the advent of technologies such as artificial intelligence and machine learning are further fueling the demand for sophisticated statistical analysis software. Additionally, the growing adoption of cloud computing has significantly reduced the cost and complexity of deploying advanced analytics solutions, making them more accessible to organizations of all sizes.

Another critical driver for the market is the increasing emphasis on regulatory compliance and risk management. Industries such as finance, healthcare, and manufacturing are subject to stringent regulatory requirements, necessitating the use of advanced analytics tools to ensure compliance and mitigate risks. For instance, in the healthcare sector, statistical analysis software is used for clinical trials, patient data management, and predictive analytics to enhance patient outcomes and ensure regulatory compliance. Similarly, in the financial sector, these tools are used for fraud detection, credit scoring, and risk assessment, thereby driving the demand for statistical analysis software.

The rising trend of digital transformation across industries is also contributing to market growth. As organizations increasingly adopt digital technologies, the volume of data generated is growing exponentially. This data, when analyzed effectively, can provide valuable insights into customer behavior, market trends, and operational efficiencies. Consequently, there is a growing need for advanced statistical analysis software to analyze this data and derive actionable insights. Furthermore, the increasing integration of statistical analysis tools with other business intelligence and data visualization tools is enhancing their capabilities and driving their adoption across various sectors.

From a regional perspective, North America currently holds the largest market share, driven by the presence of major technology companies and a high level of adoption of advanced analytics solutions. However, the Asia Pacific region is expected to witness the highest growth rate during the forecast period, owing to the increasing adoption of digital technologies and the growing emphasis on data-driven decision-making in countries such as China and India. The region's rapidly expanding IT infrastructure and increasing investments in advanced analytics solutions are further contributing to this growth.

Component Analysis

The statistical analysis software market can be segmented by component into software and services. The software segment encompasses the core statistical analysis tools and platforms used by organizations to analyze data and derive insights. This segment is expected to hold the largest market share, driven by the increasing adoption of data analytics solutions across various industries. The availability of a wide range of software solutions, from basic statistical tools to advanced analytics platforms, is catering to the diverse needs of organizations, further driving the growth of this segment.

The services segment includes consulting, implementation, training, and support services provided by vendors to help organizations effectively deploy and utilize statistical analysis software. This segment is expected to witness significant growth during the forecast period, driven by the increasing complexity of data analytics projects and the need for specialized expertise. As organizations seek to maximize the value of their data analytics investments, the demand for professional services to support the implementation and optimization of statistical analysis solutions is growing. Furthermore, the increasing trend of outsourcing data analytics functions to third-party service providers is contributing to the growth of the services segment.

Within the software segment, the market can be further categori

ABSTRACT Meta-analysis is an adequate statistical technique to combine results from different studies, and its use has been growing in the medical field. Thus, not only knowing how to interpret meta-analysis, but also knowing how to perform one, is fundamental today. Therefore, the objective of this article is to present the basic concepts and serve as a guide for conducting a meta-analysis using R and RStudio software. For this, the reader has access to the basic commands in the R and RStudio software, necessary for conducting a meta-analysis. The advantage of R is that it is a free software. For a better understanding of the commands, two examples were presented in a practical way, in addition to revising some basic concepts of this statistical technique. It is assumed that the data necessary for the meta-analysis has already been collected, that is, the description of methodologies for systematic review is not a discussed subject. Finally, it is worth remembering that there are many other techniques used in meta-analyses that were not addressed in this work. However, with the two examples used, the article already enables the reader to proceed with good and robust meta-analyses. Level of Evidence V, Expert Opinion.

This publication provides all the information required to understand the PISA 2003 educational performance database and perform analyses in accordance with the complex methodologies used to collect and process the data. It enables researchers to both reproduce the initial results and to undertake further analyses. The publication includes introductory chapters explaining the statistical theories and concepts required to analyse the PISA data, including full chapters on how to apply replicate weights and undertake analyses using plausible values; worked examples providing full syntax in SAS®; and a comprehensive description of the OECD PISA 2003 international database. The PISA 2003 database includes micro-level data on student educational performance for 41 countries collected in 2003, together with students’ responses to the PISA 2003 questionnaires and the test questions. A similar manual is available for SPSS users.

Everyone is a data analyst. The purpose of this book is to inspire and enable anyone who reads it to reconsider the methods they currently employ to analyse data.

The validity of empirical research often relies upon the accuracy of self-reported behavior and beliefs. Yet, eliciting truthful answers in surveys is challenging especially when studying sensitive issues such as racial prejudice, corruption, and support for militant groups. List experiments have attracted much attention recently as a potential solution to this measurement problem. Many researchers, however, have used a simple difference-in-means estimator without being able to efficiently examine multivariate relationships between respondents' characteristics and their answers to sensitive items. Moreover, no systematic means exist to investigate role of underlying assumptions. We fill these gaps by developing a set of new statistical methods for list experiments. We identify the commonly invoked assumptions, propose new multivariate regression estimators, and develop methods to detect and adjust for potential violations of key assumptions. For empirical illustrations, we analyze list experiments concerning racial prejudice. Open-source software is made available to implement the proposed methodology.

We include the course syllabus used to teach quantitative research design and analysis methods to graduate Linguistics students using a blended teaching and learning approach. The blended course took place over two weeks and builds on a face to face course presented over two days in 2019. Students worked through the topics in preparation for a live interactive video session each Friday to go through the activities. Additional communication took place on Slack for two hours each week. A survey was conducted at the start and end of the course to ascertain participants' perceptions of the usefulness of the course. The links to online elements and the evaluations have been removed from the uploaded course guide.Participants who complete this workshop will be able to:- outline the steps and decisions involved in quantitative data analysis of linguistic data- explain common statistical terminology (sample, mean, standard deviation, correlation, nominal, ordinal and scale data)- perform common statistical tests using jamovi (e.g. t-test, correlation, anova, regression)- interpret and report common statistical tests- describe and choose from the various graphing options used to display data- use jamovi to perform common statistical tests and graph resultsEvaluationParticipants who complete the course will use these skills and knowledge to complete the following activities for evaluation:- analyse the data for a project and/or assignment (in part or in whole)- plan the results section of an Honours research project (where applicable)Feedback and suggestions can be directed to M Schaefer schaemn@unisa.ac.za

Social Scientists rarely take full advantage of the information available in their statistical results. As a consequence, they miss opportunities to present quantities that are of greatest substantive interest for their research and express the appropriate degree of certainty about these quantities. In this article, we offer an approach, built on the technique of statistical simulation, to extract the currently overlooked information from any statistical method and to interpret and present it in a reader-friendly manner. Using this technique requires some expertise, which we try to provide herein, but its application should make the results of quantitative articles more informative and transparent. To illustrate our recommendations, we replicate the results of several published works, showing in each case how the authors' own concl usions can be expressed more sharply and informatively, and, without changing any data or statistical assumptions, how our approach reveals important new information about the research questions at hand. We also offer very easy-to-use Clarify software that implements our suggestions. See also: Unifying Statistical Analysis

Statistics Software Market Outlook

The global statistics software market size is projected to grow from USD 10.5 billion in 2023 to USD 18.7 billion by 2032, exhibiting a CAGR of 6.5% over the forecast period. The growth of this market is driven by the increasing adoption of data-driven decision-making processes across various industries, the rising need for statistical modeling and analysis tools, and the growing emphasis on advanced analytics to gain competitive advantages. Additionally, the expanding use of artificial intelligence (AI) and machine learning (ML) technologies to enhance the capabilities of statistics software is contributing significantly to market growth.

One of the primary growth factors of the statistics software market is the increasing reliance on data analytics and business intelligence tools across different sectors. Organizations are leveraging statistical software to analyze large volumes of data generated through various digital channels, enabling them to make informed decisions and identify new business opportunities. This trend is particularly evident in the healthcare, finance, and retail sectors, where data-driven insights are crucial for improving operational efficiency, customer satisfaction, and overall performance.

Another key driver for the market is the proliferation of big data and the need for advanced data management solutions. With the exponential growth of data generated by various sources such as social media, IoT devices, and enterprise systems, there is a heightened demand for robust statistical software that can handle complex data sets and perform sophisticated analyses. This has led to increased investments in the development of innovative statistics software solutions that offer enhanced features and capabilities, such as real-time data processing, predictive analytics, and automated reporting.

The integration of AI and ML technologies into statistics software is also significantly boosting market growth. These technologies enable more accurate and efficient data analysis, allowing organizations to uncover hidden patterns and trends that were previously impossible to detect. AI-powered statistical tools can automate repetitive tasks, reduce human error, and provide deeper insights into data, thereby enhancing the overall decision-making process. As a result, there is a growing adoption of AI-driven statistics software across various industries, further propelling market expansion.

Regionally, North America is expected to maintain its dominance in the statistics software market, owing to the presence of numerous leading software providers, high adoption of advanced analytics solutions, and substantial investments in research and development. However, the Asia Pacific region is anticipated to witness the highest growth rate over the forecast period, driven by the rapid digital transformation of businesses, increasing awareness of data analytics benefits, and supportive government initiatives promoting technological advancements.

Component Analysis

The statistics software market is segmented by component into software and services. The software segment includes various types of statistical analysis tools, ranging from basic data visualization software to advanced predictive analytics platforms. This segment holds the largest market share due to the widespread adoption of software solutions that enable organizations to analyze and interpret data efficiently. The continuous development of innovative features, such as real-time analytics, data mining, and machine learning capabilities, is further driving the demand for statistics software.

In contrast, the services segment encompasses consulting, implementation, training, and support services provided by software vendors and third-party providers. These services are crucial for organizations to effectively utilize statistical software and maximize its benefits. The growing complexity of data and the need for specialized expertise in data analysis are driving the demand for professional services in the statistics software market. Moreover, as more businesses adopt advanced analytics solutions, the need for ongoing support and training services is expected to increase, contributing to the growth of the services segment.

The integration of cloud computing with statistics software is also influencing the component-wise growth of this market. Cloud-based solutions offer several advantages, such as scalability, flexibility, and cost-effectiveness, making them an attractive option for organizations of all sizes. As a result, there is a

The global market for Regression Data Analysis Software is experiencing robust growth, driven by increasing adoption across diverse sectors. While precise figures for market size and CAGR are absent from the provided data, a reasonable estimation can be made based on industry trends. Considering the significant presence of established players like Microsoft, SAS, and IBM, along with the rising demand for data-driven decision-making across healthcare, BFSI (Banking, Financial Services, and Insurance), and other sectors, we can project a 2025 market size of approximately $5 billion. The compound annual growth rate (CAGR) is likely to be in the range of 8-10% for the forecast period (2025-2033), propelled by factors such as the growing volume of big data, advancements in machine learning algorithms integrated into regression analysis software, and the increasing need for sophisticated predictive modeling in various industries. The market segmentation reveals strong demand across applications, with healthcare and BFSI sectors demonstrating significant growth potential due to their reliance on risk assessment, fraud detection, and personalized medicine. The type segmentation highlights a preference for commercial analysis software, reflecting the need for robust features and scalable solutions in enterprise settings. Geographic expansion is expected across North America and Europe, while the Asia-Pacific region presents significant untapped potential for future growth. Competitive dynamics indicate a landscape dominated by established players, yet opportunities exist for specialized software providers catering to niche industry needs. Overall, the market outlook for Regression Data Analysis Software remains optimistic, supported by ongoing technological advancements and expanding data-driven applications across various sectors. The continued expansion of the Regression Data Analysis Software market is anticipated to be influenced by several key factors. The rising adoption of cloud-based solutions offers enhanced scalability and accessibility. Furthermore, increasing integration with other analytical tools and platforms allows for more comprehensive data analysis and reporting. This trend will likely be amplified by the continued growth in big data and the subsequent demand for advanced analytics capabilities. Government initiatives promoting data science and analytics are likely to fuel this trend, along with the growing need for predictive modeling in areas such as risk management, personalized medicine, and fraud detection. However, challenges remain, including the high cost of sophisticated software and the need for skilled professionals to effectively utilize such tools. Despite these restraints, the long-term outlook remains positive, with continued growth expected as the demand for data-driven decision-making transcends various sectors and geographies.

The csv file contains aggregated data on the results of the experiment (user_id), treatment type (group) and key user metrics(views and clicks) The task is to analyze the results of the experiment and write your recommendations.

This resource contains a Jupyter Notebook that is used to introduce hydrologic data analysis and conservation laws. This resource is part of a HydroLearn Physical Hydrology learning module available at https://edx.hydrolearn.org/courses/course-v1:Utah_State_University+CEE6400+2019_Fall/about

In this activity, the student learns how to (1) calculate the residence time of water in land and rivers for the global hydrologic cycle; (2) quantify the relative and absolute uncertainties in components of the water balance; (3) navigate public websites and databases, extract key watershed attributes, and perform basic hydrologic data analysis for a watershed of interest; (4) assess, compare, and interpret hydrologic trends in the context of a specific watershed.

Please note that in problems 3-8, the user is asked to use an R package (i.e., dataRetrieval) and select a U.S. Geological Survey (USGS) streamflow gage to retrieve streamflow data and then apply the hydrological data analysis to the watershed of interest. We acknowledge that the material relies on USGS data that are only available within the U.S. If running for other watersheds of interest outside the U.S. or wishing to work with other datasets, the user must take some further steps and develop codes to prepare the streamflow dataset. Once a streamflow time series dataset is obtained for an international catchment of interest, the user would need to read that file into the workspace before working through subsequent analyses.

In the last decade, a plethora of algorithms have been developed for spatial ecology studies. In our case, we use some of these codes for underwater research work in applied ecology analysis of threatened endemic fishes and their natural habitat. For this, we developed codes in Rstudio® script environment to run spatial and statistical analyses for ecological response and spatial distribution models (e.g., Hijmans & Elith, 2017; Den Burg et al., 2020). The employed R packages are as follows: caret (Kuhn et al., 2020), corrplot (Wei & Simko, 2017), devtools (Wickham, 2015), dismo (Hijmans & Elith, 2017), gbm (Freund & Schapire, 1997; Friedman, 2002), ggplot2 (Wickham et al., 2019), lattice (Sarkar, 2008), lattice (Musa & Mansor, 2021), maptools (Hijmans & Elith, 2017), modelmetrics (Hvitfeldt & Silge, 2021), pander (Wickham, 2015), plyr (Wickham & Wickham, 2015), pROC (Robin et al., 2011), raster (Hijmans & Elith, 2017), RColorBrewer (Neuwirth, 2014), Rcpp (Eddelbeuttel & Balamura, 2018), rgdal (Verzani, 2011), sdm (Naimi & Araujo, 2016), sf (e.g., Zainuddin, 2023), sp (Pebesma, 2020) and usethis (Gladstone, 2022).

It is important to follow all the codes in order to obtain results from the ecological response and spatial distribution models. In particular, for the ecological scenario, we selected the Generalized Linear Model (GLM) and for the geographic scenario we selected DOMAIN, also known as Gower's metric (Carpenter et al., 1993). We selected this regression method and this distance similarity metric because of its adequacy and robustness for studies with endemic or threatened species (e.g., Naoki et al., 2006). Next, we explain the statistical parameterization for the codes immersed in the GLM and DOMAIN running:

In the first instance, we generated the background points and extracted the values of the variables (Code2_Extract_values_DWp_SC.R). Barbet-Massin et al. (2012) recommend the use of 10,000 background points when using regression methods (e.g., Generalized Linear Model) or distance-based models (e.g., DOMAIN). However, we considered important some factors such as the extent of the area and the type of study species for the correct selection of the number of points (Pers. Obs.). Then, we extracted the values of predictor variables (e.g., bioclimatic, topographic, demographic, habitat) in function of presence and background points (e.g., Hijmans and Elith, 2017).

Subsequently, we subdivide both the presence and background point groups into 75% training data and 25% test data, each group, following the method of Soberón & Nakamura (2009) and Hijmans & Elith (2017). For a training control, the 10-fold (cross-validation) method is selected, where the response variable presence is assigned as a factor. In case that some other variable would be important for the study species, it should also be assigned as a factor (Kim, 2009).

After that, we ran the code for the GBM method (Gradient Boost Machine; Code3_GBM_Relative_contribution.R and Code4_Relative_contribution.R), where we obtained the relative contribution of the variables used in the model. We parameterized the code with a Gaussian distribution and cross iteration of 5,000 repetitions (e.g., Friedman, 2002; kim, 2009; Hijmans and Elith, 2017). In addition, we considered selecting a validation interval of 4 random training points (Personal test). The obtained plots were the partial dependence blocks, in function of each predictor variable.

Subsequently, the correlation of the variables is run by Pearson's method (Code5_Pearson_Correlation.R) to evaluate multicollinearity between variables (Guisan & Hofer, 2003). It is recommended to consider a bivariate correlation ± 0.70 to discard highly correlated variables (e.g., Awan et al., 2021).

Once the above codes were run, we uploaded the same subgroups (i.e., presence and background groups with 75% training and 25% testing) (Code6_Presence&backgrounds.R) for the GLM method code (Code7_GLM_model.R). Here, we first ran the GLM models per variable to obtain the p-significance value of each variable (alpha ≤ 0.05); we selected the value one (i.e., presence) as the likelihood factor. The generated models are of polynomial degree to obtain linear and quadratic response (e.g., Fielding and Bell, 1997; Allouche et al., 2006). From these results, we ran ecological response curve models, where the resulting plots included the probability of occurrence and values for continuous variables or categories for discrete variables. The points of the presence and background training group are also included.

On the other hand, a global GLM was also run, from which the generalized model is evaluated by means of a 2 x 2 contingency matrix, including both observed and predicted records. A representation of this is shown in Table 1 (adapted from Allouche et al., 2006). In this process we select an arbitrary boundary of 0.5 to obtain better modeling performance and avoid high percentage of bias in type I (omission) or II (commission) errors (e.g., Carpenter et al., 1993; Fielding and Bell, 1997; Allouche et al., 2006; Kim, 2009; Hijmans and Elith, 2017).

Table 1. Example of 2 x 2 contingency matrix for calculating performance metrics for GLM models. A represents true presence records (true positives), B represents false presence records (false positives - error of commission), C represents true background points (true negatives) and D represents false backgrounds (false negatives - errors of omission).

We then calculated the Overall and True Skill Statistics (TSS) metrics. The first is used to assess the proportion of correctly predicted cases, while the second metric assesses the prevalence of correctly predicted cases (Olden and Jackson, 2002). This metric also gives equal importance to the prevalence of presence prediction as to the random performance correction (Fielding and Bell, 1997; Allouche et al., 2006).

The last code (i.e., Code8_DOMAIN_SuitHab_model.R) is for species distribution modelling using the DOMAIN algorithm (Carpenter et al., 1993). Here, we loaded the variable stack and the presence and background group subdivided into 75% training and 25% test, each. We only included the presence training subset and the predictor variables stack in the calculation of the DOMAIN metric, as well as in the evaluation and validation of the model.

Regarding the model evaluation and estimation, we selected the following estimators:

1) partial ROC, which evaluates the approach between the curves of positive (i.e., correctly predicted presence) and negative (i.e., correctly predicted absence) cases. As farther apart these curves are, the model has a better prediction performance for the correct spatial distribution of the species (Manzanilla-Quiñones, 2020).

2) ROC/AUC curve for model validation, where an optimal performance threshold is estimated to have an expected confidence of 75% to 99% probability (De Long et al., 1988).

Animal ecologists often collect hierarchically-structured data and analyze these with linear mixed-effects models. Specific complications arise when the effect sizes of covariates vary on multiple levels (e.g., within vs among subjects). Mean-centering of covariates within subjects offers a useful approach in such situations, but is not without problems. A statistical model represents a hypothesis about the underlying biological process. Mean-centering within clusters assumes that the lower level responses (e.g. within subjects) depend on the deviation from the subject mean (relative) rather than on absolute values of the covariate. This may or may not be biologically realistic. We show that mismatch between the nature of the generating (i.e., biological) process and the form of the statistical analysis produce major conceptual and operational challenges for empiricists. We explored the consequences of mismatches by simulating data with three response-generating processes differing in the source of correlation between a covariate and the response. These data were then analyzed by three different analysis equations. We asked how robustly different analysis equations estimate key parameters of interest and under which circumstances biases arise. Mismatches between generating and analytical equations created several intractable problems for estimating key parameters. The most widely misestimated parameter was the among-subject variance in response. We found that no single analysis equation was robust in estimating all parameters generated by all equations. Importantly, even when response-generating and analysis equations matched mathematically, bias in some parameters arose when sampling across the range of the covariate was limited. Our results have general implications for how we collect and analyze data. They also remind us more generally that conclusions from statistical analysis of data are conditional on a hypothesis, sometimes implicit, for the process(es) that generated the attributes we measure. We discuss strategies for real data analysis in face of uncertainty about the underlying biological process. Methods All data were generated through simulations, so included with this submission are a Read Me file containing general descriptions of data files, a code file that contains R code for the simulations and analysis data files (which will generate new datasets with the same parameters) and the analyzed results in the data files archived here. These data files form the basis for all results presented in the published paper. The code file (in R markdown) has more detailed descriptions of each file of analyzed results.