BackgroundIndividual participant data (IPD) meta-analyses that obtain “raw” data from studies rather than summary data typically adopt a “two-stage” approach to analysis whereby IPD within trials generate summary measures, which are combined using standard meta-analytical methods. Recently, a range of “one-stage” approaches which combine all individual participant data in a single meta-analysis have been suggested as providing a more powerful and flexible approach. However, they are more complex to implement and require statistical support. This study uses a dataset to compare “two-stage” and “one-stage” models of varying complexity, to ascertain whether results obtained from the approaches differ in a clinically meaningful way. Methods and FindingsWe included data from 24 randomised controlled trials, evaluating antiplatelet agents, for the prevention of pre-eclampsia in pregnancy. We performed two-stage and one-stage IPD meta-analyses to estimate overall treatment effect and to explore potential treatment interactions whereby particular types of women and their babies might benefit differentially from receiving antiplatelets. Two-stage and one-stage approaches gave similar results, showing a benefit of using anti-platelets (Relative risk 0.90, 95% CI 0.84 to 0.97). Neither approach suggested that any particular type of women benefited more or less from antiplatelets. There were no material differences in results between different types of one-stage model. ConclusionsFor these data, two-stage and one-stage approaches to analysis produce similar results. Although one-stage models offer a flexible environment for exploring model structure and are useful where across study patterns relating to types of participant, intervention and outcome mask similar relationships within trials, the additional insights provided by their usage may not outweigh the costs of statistical support for routine application in syntheses of randomised controlled trials. Researchers considering undertaking an IPD meta-analysis should not necessarily be deterred by a perceived need for sophisticated statistical methods when combining information from large randomised trials.

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.

This dataset contains all of the supporting materials to accompany Helsel, D.R., Hirsch, R.M., Ryberg, K.R., Archfield, S.A., and Gilroy, E.J., 2020, Statistical methods in water resources: U.S. Geological Survey Techniques and Methods, book 4, chapter A3, 454 p., https://doi.org/10.3133/tm4a3. [Supersedes USGS Techniques of Water-Resources Investigations, book 4, chapter A3, version 1.1.]. Supplemental material (SM) for each chapter are available to re-create all examples and figures, and to solve the exercises at the end of each chapter, with relevant datasets provided in an electronic format readable by R. The SM provide (1) datasets as .Rdata files for immediate input into R, (2) datasets as .csv files for input into R or for use with other software programs, (3) R functions that are used in the textbook but not part of a published R package, (4) R scripts to produce virtually all of the figures in the book, and (5) solutions to the exercises as .html and .Rmd files. The suff ...

Australian and New Zealand journal of statistics Impact Factor 2024-2025 - ResearchHelpDesk - The Australian & New Zealand Journal of Statistics is an international journal managed jointly by the Statistical Society of Australia and the New Zealand Statistical Association. Its purpose is to report significant and novel contributions in statistics, ranging across articles on statistical theory, methodology, applications and computing. The journal has a particular focus on statistical techniques that can be readily applied to real-world problems, and on application papers with an Australasian emphasis. Outstanding articles submitted to the journal may be selected as Discussion Papers, to be read at a meeting of either the Statistical Society of Australia or the New Zealand Statistical Association. The main body of the journal is divided into three sections. The Theory and Methods Section publishes papers containing original contributions to the theory and methodology of statistics, econometrics and probability, and seeks papers motivated by a real problem and which demonstrate the proposed theory or methodology in that situation. There is a strong preference for papers motivated by, and illustrated with, real data. The Applications Section publishes papers demonstrating applications of statistical techniques to problems faced by users of statistics in the sciences, government and industry. A particular focus is the application of newly developed statistical methodology to real data and the demonstration of better use of established statistical methodology in an area of application. It seeks to aid teachers of statistics by placing statistical methods in context. The Statistical Computing Section publishes papers containing new algorithms, code snippets, or software descriptions (for open source software only) which enhance the field through the application of computing. Preference is given to papers featuring publically available code and/or data, and to those motivated by statistical methods for practical problems. In addition, suitable review papers and articles of historical and general interest will be considered. The journal also publishes book reviews on a regular basis. Abstracting and Indexing Information Academic Search (EBSCO Publishing) Academic Search Alumni Edition (EBSCO Publishing) Academic Search Elite (EBSCO Publishing) Academic Search Premier (EBSCO Publishing) CompuMath Citation Index (Clarivate Analytics) Current Index to Statistics (ASA/IMS) Journal Citation Reports/Science Edition (Clarivate Analytics) Mathematical Reviews/MathSciNet/Current Mathematical Publications (AMS) RePEc: Research Papers in Economics Science Citation Index Expanded (Clarivate Analytics) SCOPUS (Elsevier) Statistical Theory & Method Abstracts (Zentralblatt MATH) ZBMATH (Zentralblatt MATH)

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

Sir R.A. Fisher said of simulation and permutation methods in 1936: "Actually, the statistician does not carry out this very simple and very tedious process, but his conclusions have no justification beyond the fact that they agree with those which could have been arrived at by this elementary method." These methods, too ‘tedious’ to apply in 1936, are now readily accessible. As George Cobb (2007) wrote in his lead article for the journal Technology Innovations in Statistical Education, “... despite broad acceptance and rapid growth in enrollments, the consensus curriculum is still an unwitting prisoner of history. What we teach is largely the technical machinery of numerical approximations based on the normal distribution and its many subsidiary cogs. This machinery was once necessary, because the conceptually simpler alternative based on permutations was computationally beyond our reach. Before computers statisticians had no choice. These days we have no excuse. Randomization-based inference makes a direct connection between data production and the logic of inference that deserves to be at the core of every introductory course.” It is our hope that the textbook we are writing will help move the introductory statistics curriculum in the directions advocated by Professor Cobb. We use ideas such as randomization tests and bootstrap intervals to introduce the fundamental ideas of statistical inference. These methods are surprisingly intuitive to novice students and, with proper use of computer support, are accessible at very early stages of a course. Our text introduces statistical inference through these resampling methods, not only because these methods are becoming increasingly important for statisticians in their own right but also because randomization methods are outstanding in building students’ conceptual understanding of the key ideas. Our text includes the more traditional methods such as t-tests, chi-square tests, etc., but only after students have developed a strong intuitive understanding of inference through randomization methods. At this point students have a conceptual understanding and appreciation for the results they can then compute using the more traditional methods. We believe that this approach helps students realize that although the formulae may take different forms for different types of data, the conceptual framework underlying most statistical methods remains the same. Furthermore, our experience has been that after using these new methods in intuitive ways to introduce the core ideas, students understand and can move quickly through most of the standard techniques. Our goal is a text that gently moves the curriculum in innovative ways while still looking relatively familiar. Instructors won’t need to completely abandon their current syllabi and students will be well-prepared for more traditional follow-up courses.

Course materials for BIO 439/539: Big Data Analysis

Health registries record data about patients with a specific health problem. These data may include age, weight, blood pressure, health problems, medical test results, and treatments received. But data in some patient records may be missing. For example, some patients may not report their weight or all of their health problems. Research studies can use data from health registries to learn how well treatments work. But missing data can lead to incorrect results. To address the problem, researchers often exclude patient records with missing data from their studies. But doing this can also lead to incorrect results. The fewer records that researchers use, the greater the chance for incorrect results. Missing data also lead to another problem: it is harder for researchers to find patient traits that could affect diagnosis and treatment. For example, patients who are overweight may get heart disease. But if data are missing, it is hard for researchers to be sure that trait could affect diagnosis and treatment of heart disease. In this study, the research team developed new statistical methods to fill in missing data in large studies. The team also developed methods to use when data are missing to help find patient traits that could affect diagnosis and treatment. To access the methods, software, and R package, please visit the Long Research Group website.

Australian and New Zealand journal of statistics Acceptance Rate - ResearchHelpDesk - The Australian & New Zealand Journal of Statistics is an international journal managed jointly by the Statistical Society of Australia and the New Zealand Statistical Association. Its purpose is to report significant and novel contributions in statistics, ranging across articles on statistical theory, methodology, applications and computing. The journal has a particular focus on statistical techniques that can be readily applied to real-world problems, and on application papers with an Australasian emphasis. Outstanding articles submitted to the journal may be selected as Discussion Papers, to be read at a meeting of either the Statistical Society of Australia or the New Zealand Statistical Association. The main body of the journal is divided into three sections. The Theory and Methods Section publishes papers containing original contributions to the theory and methodology of statistics, econometrics and probability, and seeks papers motivated by a real problem and which demonstrate the proposed theory or methodology in that situation. There is a strong preference for papers motivated by, and illustrated with, real data. The Applications Section publishes papers demonstrating applications of statistical techniques to problems faced by users of statistics in the sciences, government and industry. A particular focus is the application of newly developed statistical methodology to real data and the demonstration of better use of established statistical methodology in an area of application. It seeks to aid teachers of statistics by placing statistical methods in context. The Statistical Computing Section publishes papers containing new algorithms, code snippets, or software descriptions (for open source software only) which enhance the field through the application of computing. Preference is given to papers featuring publically available code and/or data, and to those motivated by statistical methods for practical problems. In addition, suitable review papers and articles of historical and general interest will be considered. The journal also publishes book reviews on a regular basis. Abstracting and Indexing Information Academic Search (EBSCO Publishing) Academic Search Alumni Edition (EBSCO Publishing) Academic Search Elite (EBSCO Publishing) Academic Search Premier (EBSCO Publishing) CompuMath Citation Index (Clarivate Analytics) Current Index to Statistics (ASA/IMS) Journal Citation Reports/Science Edition (Clarivate Analytics) Mathematical Reviews/MathSciNet/Current Mathematical Publications (AMS) RePEc: Research Papers in Economics Science Citation Index Expanded (Clarivate Analytics) SCOPUS (Elsevier) Statistical Theory & Method Abstracts (Zentralblatt MATH) ZBMATH (Zentralblatt MATH)

Exploratory data analysis.

The biostatistics software market is experiencing robust growth, driven by the increasing adoption of data-driven approaches in pharmaceutical research, clinical trials, and academic studies. The market, valued at approximately $2.5 billion in 2025, is projected to exhibit a Compound Annual Growth Rate (CAGR) of 12% from 2025 to 2033. This expansion is fueled by several key factors. Firstly, the rising volume of complex biological data necessitates sophisticated software solutions for analysis and interpretation. Secondly, advancements in machine learning and artificial intelligence are enhancing the capabilities of biostatistics software, enabling more accurate and efficient data processing. Thirdly, regulatory pressures demanding robust data analysis in the pharmaceutical and healthcare sectors are boosting demand for validated and compliant biostatistics tools. The market is segmented by software type (general-purpose versus specialized) and end-user (pharmaceutical companies, academic institutions, and others). Pharmaceutical companies represent a significant portion of the market due to their extensive reliance on clinical trial data analysis. However, the academic and research segments are also exhibiting strong growth due to increased research activities and funding. Geographically, North America and Europe currently dominate the market, but Asia-Pacific is expected to witness substantial growth in the coming years due to increasing healthcare spending and technological advancements in the region. The competitive landscape is characterized by a mix of established players offering comprehensive suites and specialized niche vendors. While leading players like IBM SPSS Statistics and Minitab enjoy significant market share based on their brand recognition and established user bases, smaller companies specializing in specific statistical methods or user interfaces are gaining traction by catering to niche demands. This competitive dynamic will likely drive innovation and further segmentation within the market, resulting in specialized software offerings tailored to particular research areas and user requirements. The challenges the market faces include the high cost of software licensing, the need for specialized training for effective utilization, and the potential integration complexities with existing data management systems. However, the overall growth trajectory remains positive, driven by the inherent need for sophisticated biostatistical analysis in various sectors.

Data Analysis is the process that supports decision-making and informs arguments in empirical studies. Descriptive statistics, Exploratory Data Analysis (EDA), and Confirmatory Data Analysis (CDA) are the approaches that compose Data Analysis (Xia & Gong; 2014). An Exploratory Data Analysis (EDA) comprises a set of statistical and data mining procedures to describe data. We ran EDA to provide statistical facts and inform conclusions. The mined facts allow attaining arguments that would influence the Systematic Literature Review of DL4SE.

The Systematic Literature Review of DL4SE requires formal statistical modeling to refine the answers for the proposed research questions and formulate new hypotheses to be addressed in the future. Hence, we introduce DL4SE-DA, a set of statistical processes and data mining pipelines that uncover hidden relationships among Deep Learning reported literature in Software Engineering. Such hidden relationships are collected and analyzed to illustrate the state-of-the-art of DL techniques employed in the software engineering context.

Our DL4SE-DA is a simplified version of the classical Knowledge Discovery in Databases, or KDD (Fayyad, et al; 1996). The KDD process extracts knowledge from a DL4SE structured database. This structured database was the product of multiple iterations of data gathering and collection from the inspected literature. The KDD involves five stages:

Selection. This stage was led by the taxonomy process explained in section xx of the paper. After collecting all the papers and creating the taxonomies, we organize the data into 35 features or attributes that you find in the repository. In fact, we manually engineered features from the DL4SE papers. Some of the features are venue, year published, type of paper, metrics, data-scale, type of tuning, learning algorithm, SE data, and so on.

Preprocessing. The preprocessing applied was transforming the features into the correct type (nominal), removing outliers (papers that do not belong to the DL4SE), and re-inspecting the papers to extract missing information produced by the normalization process. For instance, we normalize the feature “metrics” into “MRR”, “ROC or AUC”, “BLEU Score”, “Accuracy”, “Precision”, “Recall”, “F1 Measure”, and “Other Metrics”. “Other Metrics” refers to unconventional metrics found during the extraction. Similarly, the same normalization was applied to other features like “SE Data” and “Reproducibility Types”. This separation into more detailed classes contributes to a better understanding and classification of the paper by the data mining tasks or methods.

Transformation. In this stage, we omitted to use any data transformation method except for the clustering analysis. We performed a Principal Component Analysis to reduce 35 features into 2 components for visualization purposes. Furthermore, PCA also allowed us to identify the number of clusters that exhibit the maximum reduction in variance. In other words, it helped us to identify the number of clusters to be used when tuning the explainable models.

Data Mining. In this stage, we used three distinct data mining tasks: Correlation Analysis, Association Rule Learning, and Clustering. We decided that the goal of the KDD process should be oriented to uncover hidden relationships on the extracted features (Correlations and Association Rules) and to categorize the DL4SE papers for a better segmentation of the state-of-the-art (Clustering). A clear explanation is provided in the subsection “Data Mining Tasks for the SLR od DL4SE”. 5.Interpretation/Evaluation. We used the Knowledge Discover to automatically find patterns in our papers that resemble “actionable knowledge”. This actionable knowledge was generated by conducting a reasoning process on the data mining outcomes. This reasoning process produces an argument support analysis (see this link).

We used RapidMiner as our software tool to conduct the data analysis. The procedures and pipelines were published in our repository.

Overview of the most meaningful Association Rules. Rectangles are both Premises and Conclusions. An arrow connecting a Premise with a Conclusion implies that given some premise, the conclusion is associated. E.g., Given that an author used Supervised Learning, we can conclude that their approach is irreproducible with a certain Support and Confidence.

Support = Number of occurrences this statement is true divided by the amount of statements Confidence = The support of the statement divided by the number of occurrences of the premise

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 to express their degree of certainty about these quantities. In this article, the authors offer an approach, built on the technique of statistical simulation, to extract the currently overlooked information from any statistical method, no matter how complicated, and to interpret and present it in a reader-friendly manner. Using this technique requires some sophistication, but its application should make the results of quantitative articles more informative and transparent to all. To illustrate their recommendations, the authors replicate the results of several published works, showing in each case how the authors' own conclusions could be expressed more sharply and informatively, and how this approach reveals important new information about the research questions at hand.

Background Microarray experiments offer a potent solution to the problem of making and comparing large numbers of gene expression measurements either in different cell types or in the same cell type under different conditions. Inferences about the biological relevance of observed changes in expression depend on the statistical significance of the changes. In lieu of many replicates with which to determine accurate intensity means and variances, reliable estimates of statistical significance remain problematic. Without such estimates, overly conservative choices for significance must be enforced. Results A simple statistical method for estimating variances from microarray control data which does not require multiple replicates is presented. Comparison of datasets from two commercial entities using this difference-averaging method demonstrates that the standard deviation of the signal scales at a level intermediate between the signal intensity and its square root. Application of the method to a dataset related to the β-catenin pathway yields a larger number of biologically reasonable genes whose expression is altered than the ratio method. Conclusions The difference-averaging method enables determination of variances as a function of signal intensities by averaging over the entire dataset. The method also provides a platform-independent view of important statistical properties of microarray data.

This dataset is about books. It has 2 rows and is filtered where the book is Statistical and computational methods in data analysis. It features 7 columns including author, publication date, language, and book publisher.

A summary of the statistical methods used to assess whether the relationship between obligatory future tense (FTR) and the propensity to save money is robust to controlling for shared cultural history. Some methods aggregate the data over languages (column 3). Columns 4, 5 and 6 state whether the method implements a control for language family, geographic area and country, respectively. The mixed effects model is the only method that does not aggregate the data and which provides an explicit control for language family, geographic area and country. The final column suggests whether the overall result for the given method demonstrates that the relationship between FTR and savings behaviour is robust. However, this does indicate the status of tests for a given method (see text for details).Summary of statistical methods used in this paper.

This is the replication package for the analysis done in the paper "Evolution of statistical analysis in empirical software engineering research: Current state and steps forward" (DOI: https://doi.org/10.1016/j.jss.2019.07.002, preprint: https://arxiv.org/abs/1706.00933).

The package includes CSV files with data on statistical usage extracted from 5 journals in SE (EMSE, IST, JSS, TOSEM, TSE). The data was extracted from papers between 2001 - 2015. The package also contains forms, scripts and figures (generated using the scripts) used in the paper.

The extraction tool mentioned in the paper is available in dockerhub via: https://hub.docker.com/r/robertfeldt/sept

List of Top Authors of Statistical Methods in Medical Research sorted by articles.

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.

The graph shows the changes in the impact factor of ^ and its corresponding percentile for the sake of comparison with the entire literature. Impact Factor is the most common scientometric index, which is defined by the number of citations of papers in two preceding years divided by the number of papers published in those years.