DOCSLIB.ORG

Lessons in Biostatistics

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Lessons in Biostatistics Lessons in biostatistics Resampling methods in Microsoft Excel® for estimating reference intervals Elvar Theodorsson Department of Clinical Chemistry and Department of Clinical and Experimental Medicine, Linköping University, Linköping, Sweden Corresponding author: [email protected] Abstract Computer- intensive resampling/bootstrap methods are feasible when calculating reference intervals from non-Gaussian or small reference sam- ples. Microsoft Excel® in version 2010 or later includes natural functions, which lend themselves well to this purpose including recommended inter- polation procedures for estimating 2.5 and 97.5 percentiles. The purpose of this paper is to introduce the reader to resampling estimation techniques in general and in using Microsoft Excel® 2010 for the purpo- se of estimating reference intervals in particular. Parametric methods are preferable to resampling methods when the distributions of observations in the reference samples is Gaussian or can tran- sformed to that distribution even when the number of reference samples is less than 120. Resampling methods are appropriate when the distribu- tion of data from the reference samples is non-Gaussian and in case the number of reference individuals and corresponding samples are in the order of 40. At least 500-1000 random samples with replacement should be taken from the results of measurement of the reference samples. Key words: reference interval; resampling method; Microsoft Excel; bootstrap method; biostatistics Received: May 18, 2015 Accepted: July 23, 2015 Description of the task Reference intervals (1,2) are amongst the essential are naturally determined in a ranked set of data tools for interpreting laboratory results. Excellent values if the number of observations is large, e.g. > theoretical and practical studies have been pub- 1000. When the number of values is small, e.g. in lished since the 1960ies for establishing reference the order of 40-120 and the data are non-Gaussian, intervals as a concept in contrast to “normal inter- resampling methods are useful to estimate the ref- vals” (3), establishing principles for selecting refer- erence interval. The reference population is com- ence persons (4) and performing the appropriate monly a population of apparently healthy individ- statistical data analysis (5-8). Reference intervals uals, but may also consist of any other well-de- continue to be an active area of research (2,9) and fined population of interest for diagnostic/com- at the core of practical work in clinical laboratories parative purposes. (6,10). The reference interval includes 95% the results/ Different methods for calculating values measured in a representative sample of ref- reference intervals erence subjects and is bounded by lower and up- per reference limits marking the 2.5 and 97.5 per- Estimating reference intervals means dealing with centiles respectively (Figure 1). The reference inter- uncertainties and probabilities. All probabilistic val including the upper and lower reference limits methods are based on assumptions about a theo- http://dx .doi .org/10 .11613/BM .2015 .031 Biochemia Medica 2015;25(3):311–9 ©Copyright by Croatian Society of Medical Biochemistry and Laboratory Medicine. This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc-nd/3.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited. 311 Theodorsson E. Microsoft Excel® for estimating reference intervals ductory literature on resampling methods in gen- eral (13) and resampling methods for Microsoft Ex- Reference population cel® in particular (14). Resampling with replacement means that a large number of samples with replacement are then tak- A representative reference sample en from the original sample and the statistic of in- e e r from the reference population terest is calculated from this pseudo-population as limit limit Lowe Upper estimate of the corresponding parameter of the referenc referenc Reference interval which includes population (Figure 2). 2.5% estimated 95% of the values 2.5% in the reference population FIGURE 1. General principles when calculating reference inter- vals. 50 77 91 107 50 53 79 91 109 retical distribution which fundamentally deter- 58 80 92 112 62 80 93 114 1000 copies 62 80 94 115 mines the conclusion that can be drawn from the 62 80 96 115 53 62 80 96 115 data. The most commonly used probabilistic 62 81 97 117 64 81 97 119 1000 copies methods are the parametric methods that assume 64 82 97 120 64 82 97 120 that observations in the population are distributed 67 82 99 120 67 83 99 124 according to the Gaussian/Normal distribution. 68 84 100 127 69 84 100 127 These are the methods of choice if the data are 71 84 101 141 71 87 106 146 Gaussian or can be transformed to that distribu- 71 88 106 147 tion since the data themselves with the added 72 88 106 168 177 72 89 107 177 knowledge of the distribution of the data in the 75 90 107 1000 copies sample and population enables the user of the Reference sample values data to draw firmer conclusions than if only the data are known. When the data are non-Gaussian and cannot be transformed to the Gaussian distribution the ana- lyst is left with non-parametric or resampling methods for determining reference intervals. Data Samples 177 88 72 from 120 reference intervals are needed for relia- 80 114 50 bly determining non-parametric reference inter- 120 84 89 112 67 115 vals (7,11). Resampling/bootstrap methods (12) 82 64 93 take numerous repeated sub- samples with re- 106 84 141 placement of the available data in order to esti- 82 127 100 62 79 69 mate the distribution of the data in the popula- 80 85 81 tion, including the reference intervals. 81 107 84 Resampling methods with replacement are com- FIGURE 2. Simplified illustration of the principles of resampling monly called bootstrap methods by many be- techniques as employed by resampling methods with replace- lieved to refer to the fairytale of Baron Munchaus- ment. This figure illustrates the use of 83 raw data observations ob- en pulling himself and his horse out of a swamp by tained from Geffré et al. (24) resampled 1000 times in this case. his hair. Bootstraps are in fact the tab, loop or han- One thousand copies of each observation are created and thor- dle at the top of boots allowing the use of fingers oughly mixed giving each of them identical possibility of being pull the boots on. The concept of bootstrap is selected. A multitude of random samples are then taken from the mixture, calculating the 0.025 and 0.975 percentiles for each therefore a metaphor for clever, self-induced sal- sample in order to create an estimate of these percentiles in the vaging efforts. There is a wealth of current intro- intended population. Biochemia Medica 2015;25(3):311–9 http://dx .doi .org/10 .11613/BM .2015 .031 312 Theodorsson E. Microsoft Excel® for estimating reference intervals Percentiles Geffré et al. published “Reference Value Advisor”, a set of comprehensive freeware macros for Micro- A proper start when calculating reference intervals soft Excel® to calculate reference intervals (24). It – is to estimate the observation(s) corresponding to together with the original paper - can be down- 2.5% and 97.5% in a ranked list of reference value loaded at http://www.biostat.envt.fr/spip/spip. data. Both International Federation of Clinical php?article63 which implements the procedures Chemistry (IFCC) (5-7,15) and Clinical and Labora- recommended e.g. by EP28-A3c. Increased availa- tory Standards Institute (CLSI) (16) recommend the bility of low-cost computing machinery and resa- following formulas: lower limit has the rank num- mpling methods has made distribution independ- ber 0.025 x (n+1) and the upper limit the rank num- ent computer intensive methods accessible in rou- ber 0.975 x (n+1). This method is practicable mainly tine work (25). when the number of reference samples is 120 or more. The fundamental purpose of statistics in general and statistics in reference interval estimation is to While there is agreement on how to calculate the extrapolate from a limited number of observa- median, agreement on how to calculate quantiles tions/data to the whole population of observa- including percentiles is lacking due to the fact that tions. All statistical methods are based on assump- interpolation is frequently needed, especially tions which fundamentally decide the conclusion when the number of observations is small. Unfor- that can be made from the data. Parametric statis- tunately there is no general agreement on the tical methods which are the most widely used, as- best way of performing interpolations. In 1996 sume that the population values are distributed Hyndman and Fan published an influential paper according to a mathematically well-defined distri- on calculating quantiles (17). It evaluated the bution - the Gaussian/Normal distribution. Para- methods used by popular statistics packages with metric methods were initially described in the first the intention to find a consensus and basis for half of the twentieth century when methods for standardization. Of the nine formulas commonly performing extensive calculations were primarily used, four satisfied five of the six properties desir- manual and semi-automated at best. Using distri- able for a sample quantile. Hyndman and Fan felt bution functions to describe natural phenomena that the “Linear interpolation of the approximate including research data, substantially simplified medians for order statistics” (used by the Excel the calculations required for statistical analysis. =PERCENTILE.EXC function) was best due to the Without these known statistical distribution func- approximately median-unbiased estimates of the tions it would have been impossible to use ad- quantiles, regardless of the distribution (17).
Load more

Recommended publications
  • Analysis of Imbalance Strategies Recommendation Using a Meta-Learning Approach
    7th ICML Workshop on Automated Machine Learning (2020) Analysis of Imbalance Strategies Recommendation using a Meta-Learning Approach Afonso Jos´eCosta [email protected] CISUC, Department of Informatics Engineering, University of Coimbra, Portugal Miriam Seoane Santos [email protected] CISUC, Department of Informatics Engineering, University of Coimbra, Portugal Carlos Soares [email protected] Fraunhofer AICOS and LIACC, Faculty of Engineering, University of Porto, Portugal Pedro Henriques Abreu [email protected] CISUC, Department of Informatics Engineering, University of Coimbra, Portugal Abstract Class imbalance is known to degrade the performance of classifiers. To address this is- sue, imbalance strategies, such as oversampling or undersampling, are often employed to balance the class distribution of datasets. However, although several strategies have been proposed throughout the years, there is no one-fits-all solution for imbalanced datasets. In this context, meta-learning arises a way to recommend proper strategies to handle class imbalance, based on data characteristics. Nonetheless, in related work, recommendation- based systems do not focus on how the recommendation process is conducted, thus lacking interpretable knowledge. In this paper, several meta-characteristics are identified in order to provide interpretable knowledge to guide the selection of imbalance strategies, using Ex- ceptional Preferences Mining. The experimental setup considers 163 real-world imbalanced datasets, preprocessed with 9 well-known resampling algorithms. Our findings elaborate on the identification of meta-characteristics that demonstrate when using preprocessing algo- rithms is advantageous for the problem and when maintaining the original dataset benefits classification performance. 1. Introduction Class imbalance is known to severely affect the data quality.
    [Show full text]
  • Particle Filtering-Based Maximum Likelihood Estimation for Financial Parameter Estimation
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Spiral - Imperial College Digital Repository Particle Filtering-based Maximum Likelihood Estimation for Financial Parameter Estimation Jinzhe Yang Binghuan Lin Wayne Luk Terence Nahar Imperial College & SWIP Techila Technologies Ltd Imperial College SWIP London & Edinburgh, UK Tampere University of Technology London, UK London, UK [email protected] Tampere, Finland [email protected] [email protected] [email protected] Abstract—This paper presents a novel method for estimating result, which cannot meet runtime requirement in practice. In parameters of financial models with jump diffusions. It is a addition, high performance computing (HPC) technologies are Particle Filter based Maximum Likelihood Estimation process, still new to the finance industry. We provide a PF based MLE which uses particle streams to enable efficient evaluation of con- straints and weights. We also provide a CPU-FPGA collaborative solution to estimate parameters of jump diffusion models, and design for parameter estimation of Stochastic Volatility with we utilise HPC technology to speedup the estimation scheme Correlated and Contemporaneous Jumps model as a case study. so that it would be acceptable for practical use. The result is evaluated by comparing with a CPU and a cloud This paper presents the algorithm development, as well computing platform. We show 14 times speed up for the FPGA as the pipeline design solution in FPGA technology, of PF design compared with the CPU, and similar speedup but better convergence compared with an alternative parallelisation scheme based MLE for parameter estimation of Stochastic Volatility using Techila Middleware on a multi-CPU environment.
    [Show full text]
  • Resampling Hypothesis Tests for Autocorrelated Fields
    JANUARY 1997 WILKS 65 Resampling Hypothesis Tests for Autocorrelated Fields D. S. WILKS Department of Soil, Crop and Atmospheric Sciences, Cornell University, Ithaca, New York (Manuscript received 5 March 1996, in ®nal form 10 May 1996) ABSTRACT Presently employed hypothesis tests for multivariate geophysical data (e.g., climatic ®elds) require the as- sumption that either the data are serially uncorrelated, or spatially uncorrelated, or both. Good methods have been developed to deal with temporal correlation, but generalization of these methods to multivariate problems involving spatial correlation has been problematic, particularly when (as is often the case) sample sizes are small relative to the dimension of the data vectors. Spatial correlation has been handled successfully by resampling methods when the temporal correlation can be neglected, at least according to the null hypothesis. This paper describes the construction of resampling tests for differences of means that account simultaneously for temporal and spatial correlation. First, univariate tests are derived that respect temporal correlation in the data, using the relatively new concept of ``moving blocks'' bootstrap resampling. These tests perform accurately for small samples and are nearly as powerful as existing alternatives. Simultaneous application of these univariate resam- pling tests to elements of data vectors (or ®elds) yields a powerful (i.e., sensitive) multivariate test in which the cross correlation between elements of the data vectors is successfully captured by the resampling, rather than through explicit modeling and estimation. 1. Introduction dle portion of Fig. 1. First, standard tests, including the t test, rest on the assumption that the underlying data It is often of interest to compare two datasets for are composed of independent samples from their parent differences with respect to particular attributes.
    [Show full text]
  • Receiver Operating Characteristic (ROC) Methods in Diagnostic Imaging
    8/2/2017 Receiver Operating Characteristic (ROC) Methods in Diagnostic Imaging Elizabeth A. Krupinski, PhD Department Radiology & Imaging Sciences Emory University Bit of History • Developed early 1950s based on principles SDT for eval radar operators detecting enemy aircraft & missiles • Contributions from engineering, psychology & mathematics • Lee Lusted introduced medicine 1960s with significant effort on gaining better understanding decision-making • Result of radiology studies after WWII to determine which of 4 radiographic & fluoroscopic techniques better for TB screening • Goal = single imaging technique outperform others • Found intra & inter-observer variation so high impossible determine • Necessary to build systems generate better images so radiologists’ performance could improve (i.e., reduce observer variability) & develop methods evaluate these new systems & assess impact on observer performance Basics • ROC traditionally binary decision task – target/signal (e.g., lesion, disease, missile) present versus target/signal absent, or in case classification rather than detection target/signal belongs to class 1 (e.g., cancer, enemy) or class 2 (e.g., not cancer, friend) • ROC analysis these two conditions must be mutually exclusive 1 8/2/2017 2 x 2 Matrix Decision = Target Decision = Target Present Absent Truth = Target Present True Positive (TP) False Negative (FN) Truth = Target Absent False Positive (FP) True Negative (TN) Common Performance Metrics • Sensitivity = TP/(TP + FN) • Specificity = TN/(TN + FP) • Accuracy = (TP
    [Show full text]
  • Sampling and Resampling
    Sampling and Resampling Thomas Lumley Biostatistics 2005-11-3 Basic Problem (Frequentist) statistics is based on the sampling distribution of statistics: Given a statistic Tn and a true data distribution, what is the distribution of Tn • The mean of samples of size 10 from an Exponential • The median of samples of size 20 from a Cauchy • The difference in Pearson’s coefficient of skewness ((X¯ − m)/s) between two samples of size 40 from a Weibull(3,7). This is easy: you have written programs to do it. In 512-3 you learn how to do it analytically in some cases. But... We really want to know: What is the distribution of Tn in sampling from the true data distribution But we don’t know the true data distribution. Empirical distribution On the other hand, we do have an estimate of the true data distribution. It should look like the sample data distribution. (we write Fn for the sample data distribution and F for the true data distribution). The Glivenko–Cantelli theorem says that the cumulative distribution function of the sample converges uniformly to the true cumulative distribution. We can work out the sampling distribution of Tn(Fn) by simulation, and hope that this is close to that of Tn(F ). Simulating from Fn just involves taking a sample, with replace- ment, from the observed data. This is called the bootstrap. We ∗ write Fn for the data distribution of a resample. Too good to be true? There are obviously some limits to this • It requires large enough samples for Fn to be close to F .
    [Show full text]
  • Kwame Nkrumah University of Science and Technology, Kumasi
    KWAME NKRUMAH UNIVERSITY OF SCIENCE AND TECHNOLOGY, KUMASI, GHANA Assessing the Social Impacts of Illegal Gold Mining Activities at Dunkwa-On-Offin by Judith Selassie Garr (B.A, Social Science) A Thesis submitted to the Department of Building Technology, College of Art and Built Environment in partial fulfilment of the requirement for a degree of MASTER OF SCIENCE NOVEMBER, 2018 DECLARATION I hereby declare that this work is the result of my own original research and this thesis has neither in whole nor in part been prescribed by another degree elsewhere. References to other people’s work have been duly cited. STUDENT: JUDITH S. GARR (PG1150417) Signature: ........................................................... Date: .................................................................. Certified by SUPERVISOR: PROF. EDWARD BADU Signature: ........................................................... Date: ................................................................... Certified by THE HEAD OF DEPARTMENT: PROF. B. K. BAIDEN Signature: ........................................................... Date: ................................................................... i ABSTRACT Mining activities are undertaken in many parts of the world where mineral deposits are found. In developing nations such as Ghana, the activity is done both legally and illegally, often with very little or no supervision, hence much damage is done to the water bodies where the activities are carried out. This study sought to assess the social impacts of illegal gold mining activities at Dunkwa-On-Offin, the capital town of Upper Denkyira East Municipality in the Central Region of Ghana. The main objectives of the research are to identify factors that trigger illegal mining; to identify social effects of illegal gold mining activities on inhabitants of Dunkwa-on-Offin; and to suggest effective ways in curbing illegal mining activities. Based on the approach to data collection, this study adopts both the quantitative and qualitative approach.
    [Show full text]
  • The Association Between Four Scoring Systems and 30-Day Mortality Among Intensive Care Patients with Sepsis
    www.nature.com/scientificreports OPEN The association between four scoring systems and 30‑day mortality among intensive care patients with sepsis: a cohort study Tianyang Hu 1,4, Huajie Lv2,4 & Youfan Jiang3* Several commonly used scoring systems (SOFA, SAPS II, LODS, and SIRS) are currently lacking large sample data to confrm the predictive value of 30‑day mortality from sepsis, and their clinical net benefts of predicting mortality are still inconclusive. The baseline data, LODS score, SAPS II score, SIRS score, SOFA score, and 30‑day prognosis of patients who met the diagnostic criteria of sepsis were retrieved from the Medical Information Mart for Intensive Care III (MIMIC‑III) intensive care unit (ICU) database. Receiver operating characteristic (ROC) curves and comparisons between the areas under the ROC curves (AUC) were conducted. Decision curve analysis (DCA) was performed to determine the net benefts between the four scoring systems and 30‑day mortality of sepsis. For all cases in the cohort study, the AUC of LODS, SAPS II, SIRS, SOFA were 0.733, 0.787, 0.597, and 0.688, respectively. The diferences between the scoring systems were statistically signifcant (all P‑values < 0.0001), and stratifed analyses (the elderly and non‑elderly) also showed the superiority of SAPS II among the four systems. According to the DCA, the net beneft ranges in descending order were SAPS II, LODS, SOFA, and SIRS. For stratifed analyses of the elderly or non‑elderly groups, the results also showed that SAPS II had the most net beneft. Among the four commonly used scoring systems, the SAPS II score has the highest predictive value for 30‑day mortality from sepsis, which is better than LODS, SIRS, and SOFA.
    [Show full text]
  • Investigating Data Management Practices in Australian Universities
    Investigating Data Management Practices in Australian Universities Margaret Henty, The Australian National University Belinda Weaver, The University of Queensland Stephanie Bradbury, Queensland University of Technology Simon Porter, The University of Melbourne http://www.apsr.edu.au/investigating_data_management July, 2008 ii Table of Contents Introduction ...................................................................................... 1 About the survey ................................................................................ 1 About this report ................................................................................ 1 The respondents................................................................................. 2 The survey results............................................................................... 2 Tables and Comments .......................................................................... 3 Digital data .................................................................................... 3 Non-digital data forms....................................................................... 3 Types of digital data ......................................................................... 4 Size of data collection ....................................................................... 5 Software used for analysis or manipulation .............................................. 6 Software storage and retention ............................................................ 7 Research Data Management Plans.........................................................
    [Show full text]
  • Quality Assurance
    500A ANNUAL MEETING ABSTRACTS 2051 Synchronous Lung Adenocarcinoma and Primary Pulmonary MALT there are no established guidelines for storage methods of precut controls, patient tissue, Lymphoma: An Underdiagnosed Entity Associated with KRAS Mutations or microarrays (TMAs). We sought to determine loss of antigenicity and potential for J Yao, N Rehktman, K Nafa, A Dogan, M Ladanyi, ME Arcila. Memorial Sloan-Kettering preservation by refrigeration in a longitudinal prospective study. Cancer Center, New York, NY. Design: Selected diagnostic or prognostic antibodies included p53, IDH-1, Ki67, Background: Pulmonary extranodal marginal zone lymphoma (MZL / MALT) is a synaptophysin, and androgen receptor (AR). TMA with 22 cores from small cell rare entity accounting for less than 0.5% of primary pulmonary malignancies. The carcinomas, prostatic adenocarcinomas, and gliomas was constructed; 125 slides were occurrence of lung adenocarcinoma (AD) and primary pulmonary MALT lymphoma cut at 4 microns at time 0. Slides were stored exposed to air at room temperature (RT), as collision tumors have only been rarely reported. We investigated the concurrent 4C, or -20C; IHC was performed on the Leica Bond III at time 0, weeks 1, 2, 4, and 6. incidence of these two entities in a large cohort of lung AD cases submitted for routine Each tissue core was scored for overall intensity (0 to 3+) and % of cells staining (100 molecular diagnostic testing. cells within hotspot). Loss of antigenicity was defi ned as a decrease of staining intensity Design: Consecutive lung AD cases were reviewed and categorized based on the by one order and/or loss of≥10% of positive cells compared to time 0.
    [Show full text]
  • Efficient Computation of Adjusted P-Values for Resampling-Based Stepdown Multiple Testing
    University of Zurich Department of Economics Working Paper Series ISSN 1664-7041 (print) ISSN 1664-705X (online) Working Paper No. 219 Efficient Computation of Adjusted p-Values for Resampling-Based Stepdown Multiple Testing Joseph P. Romano and Michael Wolf February 2016 Efficient Computation of Adjusted p-Values for Resampling-Based Stepdown Multiple Testing∗ Joseph P. Romano† Michael Wolf Departments of Statistics and Economics Department of Economics Stanford University University of Zurich Stanford, CA 94305, USA 8032 Zurich, Switzerland [email protected] [email protected] February 2016 Abstract There has been a recent interest in reporting p-values adjusted for resampling-based stepdown multiple testing procedures proposed in Romano and Wolf (2005a,b). The original papers only describe how to carry out multiple testing at a fixed significance level. Computing adjusted p-values instead in an efficient manner is not entirely trivial. Therefore, this paper fills an apparent gap by detailing such an algorithm. KEY WORDS: Adjusted p-values; Multiple testing; Resampling; Stepdown procedure. JEL classification code: C12. ∗We thank Henning M¨uller for helpful comments. †Research supported by NSF Grant DMS-1307973. 1 1 Introduction Romano and Wolf (2005a,b) propose resampling-based stepdown multiple testing procedures to control the familywise error rate (FWE); also see Romano et al. (2008, Section 3). The procedures as described are designed to be carried out at a fixed significance level α. Therefore, the result of applying such a procedure to a set of data will be a ‘list’ of binary decisions concerning the individual null hypotheses under study: reject or do not reject a given null hypothesis at the chosen significance level α.
    [Show full text]
  • Resampling Methods: Concepts, Applications, and Justification
    Practical Assessment, Research, and Evaluation Volume 8 Volume 8, 2002-2003 Article 19 2002 Resampling methods: Concepts, Applications, and Justification Chong Ho Yu Follow this and additional works at: https://scholarworks.umass.edu/pare Recommended Citation Yu, Chong Ho (2002) "Resampling methods: Concepts, Applications, and Justification," Practical Assessment, Research, and Evaluation: Vol. 8 , Article 19. DOI: https://doi.org/10.7275/9cms-my97 Available at: https://scholarworks.umass.edu/pare/vol8/iss1/19 This Article is brought to you for free and open access by ScholarWorks@UMass Amherst. It has been accepted for inclusion in Practical Assessment, Research, and Evaluation by an authorized editor of ScholarWorks@UMass Amherst. For more information, please contact [email protected]. Yu: Resampling methods: Concepts, Applications, and Justification A peer-reviewed electronic journal. Copyright is retained by the first or sole author, who grants right of first publication to Practical Assessment, Research & Evaluation. Permission is granted to distribute this article for nonprofit, educational purposes if it is copied in its entirety and the journal is credited. PARE has the right to authorize third party reproduction of this article in print, electronic and database forms. Volume 8, Number 19, September, 2003 ISSN=1531-7714 Resampling methods: Concepts, Applications, and Justification Chong Ho Yu Aries Technology/Cisco Systems Introduction In recent years many emerging statistical analytical tools, such as exploratory data analysis (EDA), data visualization, robust procedures, and resampling methods, have been gaining attention among psychological and educational researchers. However, many researchers tend to embrace traditional statistical methods rather than experimenting with these new techniques, even though the data structure does not meet certain parametric assumptions.
    [Show full text]
  • Monte Carlo Simulation and Resampling
    Monte Carlo Simulation and Resampling Tom Carsey (Instructor) Jeff Harden (TA) ICPSR Summer Course Summer, 2011 | Monte Carlo Simulation and Resampling 1/68 Resampling Resampling methods share many similarities to Monte Carlo simulations { in fact, some refer to resampling methods as a type of Monte Carlo simulation. Resampling methods use a computer to generate a large number of simulated samples. Patterns in these samples are then summarized and analyzed. However, in resampling methods, the simulated samples are drawn from the existing sample of data you have in your hands and NOT from a theoretically defined (researcher defined) DGP. Thus, in resampling methods, the researcher DOES NOT know or control the DGP, but the goal of learning about the DGP remains. | Monte Carlo Simulation and Resampling 2/68 Resampling Principles Begin with the assumption that there is some population DGP that remains unobserved. That DGP produced the one sample of data you have in your hands. Now, draw a new \sample" of data that consists of a different mix of the cases in your original sample. Repeat that many times so you have a lot of new simulated \samples." The fundamental assumption is that all information about the DGP contained in the original sample of data is also contained in the distribution of these simulated samples. If so, then resampling from the one sample you have is equivalent to generating completely new random samples from the population DGP. | Monte Carlo Simulation and Resampling 3/68 Resampling Principles (2) Another way to think about this is that if the sample of data you have in your hands is a reasonable representation of the population, then the distribution of parameter estimates produced from running a model on a series of resampled data sets will provide a good approximation of the distribution of that statistics in the population.
    [Show full text]