Exploring Data and Descriptive Statistics (Using R)
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A Review on Outlier/Anomaly Detection in Time Series Data
A review on outlier/anomaly detection in time series data ANE BLÁZQUEZ-GARCÍA and ANGEL CONDE, Ikerlan Technology Research Centre, Basque Research and Technology Alliance (BRTA), Spain USUE MORI, Intelligent Systems Group (ISG), Department of Computer Science and Artificial Intelligence, University of the Basque Country (UPV/EHU), Spain JOSE A. LOZANO, Intelligent Systems Group (ISG), Department of Computer Science and Artificial Intelligence, University of the Basque Country (UPV/EHU), Spain and Basque Center for Applied Mathematics (BCAM), Spain Recent advances in technology have brought major breakthroughs in data collection, enabling a large amount of data to be gathered over time and thus generating time series. Mining this data has become an important task for researchers and practitioners in the past few years, including the detection of outliers or anomalies that may represent errors or events of interest. This review aims to provide a structured and comprehensive state-of-the-art on outlier detection techniques in the context of time series. To this end, a taxonomy is presented based on the main aspects that characterize an outlier detection technique. Additional Key Words and Phrases: Outlier detection, anomaly detection, time series, data mining, taxonomy, software 1 INTRODUCTION Recent advances in technology allow us to collect a large amount of data over time in diverse research areas. Observations that have been recorded in an orderly fashion and which are correlated in time constitute a time series. Time series data mining aims to extract all meaningful knowledge from this data, and several mining tasks (e.g., classification, clustering, forecasting, and outlier detection) have been considered in the literature [Esling and Agon 2012; Fu 2011; Ratanamahatana et al. -
Mean, Median and Mode We Use Statistics Such As the Mean, Median and Mode to Obtain Information About a Population from Our Sample Set of Observed Values
INFORMATION AND DATA CLASS-6 SUB-MATHEMATICS The words Data and Information may look similar and many people use these words very frequently, But both have lots of differences between What is Data? Data is a raw and unorganized fact that required to be processed to make it meaningful. Data can be simple at the same time unorganized unless it is organized. Generally, data comprises facts, observations, perceptions numbers, characters, symbols, image, etc. Data is always interpreted, by a human or machine, to derive meaning. So, data is meaningless. Data contains numbers, statements, and characters in a raw form What is Information? Information is a set of data which is processed in a meaningful way according to the given requirement. Information is processed, structured, or presented in a given context to make it meaningful and useful. It is processed data which includes data that possess context, relevance, and purpose. It also involves manipulation of raw data Mean, Median and Mode We use statistics such as the mean, median and mode to obtain information about a population from our sample set of observed values. Mean The mean/Arithmetic mean or average of a set of data values is the sum of all of the data values divided by the number of data values. That is: Example 1 The marks of seven students in a mathematics test with a maximum possible mark of 20 are given below: 15 13 18 16 14 17 12 Find the mean of this set of data values. Solution: So, the mean mark is 15. Symbolically, we can set out the solution as follows: So, the mean mark is 15. -
Synthpop: Bespoke Creation of Synthetic Data in R
synthpop: Bespoke Creation of Synthetic Data in R Beata Nowok Gillian M Raab Chris Dibben University of Edinburgh University of Edinburgh University of Edinburgh Abstract In many contexts, confidentiality constraints severely restrict access to unique and valuable microdata. Synthetic data which mimic the original observed data and preserve the relationships between variables but do not contain any disclosive records are one possible solution to this problem. The synthpop package for R, introduced in this paper, provides routines to generate synthetic versions of original data sets. We describe the methodology and its consequences for the data characteristics. We illustrate the package features using a survey data example. Keywords: synthetic data, disclosure control, CART, R, UK Longitudinal Studies. This introduction to the R package synthpop is a slightly amended version of Nowok B, Raab GM, Dibben C (2016). synthpop: Bespoke Creation of Synthetic Data in R. Journal of Statistical Software, 74(11), 1-26. doi:10.18637/jss.v074.i11. URL https://www.jstatsoft. org/article/view/v074i11. 1. Introduction and background 1.1. Synthetic data for disclosure control National statistical agencies and other institutions gather large amounts of information about individuals and organisations. Such data can be used to understand population processes so as to inform policy and planning. The cost of such data can be considerable, both for the collectors and the subjects who provide their data. Because of confidentiality constraints and guarantees issued to data subjects the full access to such data is often restricted to the staff of the collection agencies. Traditionally, data collectors have used anonymisation along with simple perturbation methods such as aggregation, recoding, record-swapping, suppression of sensitive values or adding random noise to prevent the identification of data subjects. -
Bootstrapping Regression Models
Bootstrapping Regression Models Appendix to An R and S-PLUS Companion to Applied Regression John Fox January 2002 1 Basic Ideas Bootstrapping is a general approach to statistical inference based on building a sampling distribution for a statistic by resampling from the data at hand. The term ‘bootstrapping,’ due to Efron (1979), is an allusion to the expression ‘pulling oneself up by one’s bootstraps’ – in this case, using the sample data as a population from which repeated samples are drawn. At first blush, the approach seems circular, but has been shown to be sound. Two S libraries for bootstrapping are associated with extensive treatments of the subject: Efron and Tibshirani’s (1993) bootstrap library, and Davison and Hinkley’s (1997) boot library. Of the two, boot, programmed by A. J. Canty, is somewhat more capable, and will be used for the examples in this appendix. There are several forms of the bootstrap, and, additionally, several other resampling methods that are related to it, such as jackknifing, cross-validation, randomization tests,andpermutation tests. I will stress the nonparametric bootstrap. Suppose that we draw a sample S = {X1,X2, ..., Xn} from a population P = {x1,x2, ..., xN };imagine further, at least for the time being, that N is very much larger than n,andthatS is either a simple random sample or an independent random sample from P;1 I will briefly consider other sampling schemes at the end of the appendix. It will also help initially to think of the elements of the population (and, hence, of the sample) as scalar values, but they could just as easily be vectors (i.e., multivariate). -
A Survey on Data Collection for Machine Learning a Big Data - AI Integration Perspective
1 A Survey on Data Collection for Machine Learning A Big Data - AI Integration Perspective Yuji Roh, Geon Heo, Steven Euijong Whang, Senior Member, IEEE Abstract—Data collection is a major bottleneck in machine learning and an active research topic in multiple communities. There are largely two reasons data collection has recently become a critical issue. First, as machine learning is becoming more widely-used, we are seeing new applications that do not necessarily have enough labeled data. Second, unlike traditional machine learning, deep learning techniques automatically generate features, which saves feature engineering costs, but in return may require larger amounts of labeled data. Interestingly, recent research in data collection comes not only from the machine learning, natural language, and computer vision communities, but also from the data management community due to the importance of handling large amounts of data. In this survey, we perform a comprehensive study of data collection from a data management point of view. Data collection largely consists of data acquisition, data labeling, and improvement of existing data or models. We provide a research landscape of these operations, provide guidelines on which technique to use when, and identify interesting research challenges. The integration of machine learning and data management for data collection is part of a larger trend of Big data and Artificial Intelligence (AI) integration and opens many opportunities for new research. Index Terms—data collection, data acquisition, data labeling, machine learning F 1 INTRODUCTION E are living in exciting times where machine learning expertise. This problem applies to any novel application that W is having a profound influence on a wide range of benefits from machine learning. -
Uses for Census Data in Market Research
Uses for Census Data in Market Research MRS Presentation 4 July 2011 Andrew Zelin, Director, Sampling & RMC, Ipsos MORI Why Census Data is so critical to us Use of Census Data underlies almost all of our quantitative work activities and projects Needed to ensure that: – Samples are balanced and representative – ie Sampling; – Results derived from samples reflect that of target population – ie Weighting; – Understanding how demographic and geographic factors affect the findings from surveys – ie Analysis. How would we do our jobs without the use of Census Data? Our work withoutCensusData Our work Regional Assembly What I will cover Introduction, overview and why Census Data is so critical; Census data for sampling; Census data for survey weighting; Census data for statistical analysis; Use of SARs; The future (eg use of “hypercubes”); Our work without Census Data / use of alternatives; Conclusions Census Data for Sampling For Random (pre-selected) Samples: – Need to define stratum sample sizes and sampling fractions; – Need to define cluster size, esp. if PPS – (Need to define stratum / cluster) membership; For any type of Sample: – To balance samples across demographics that cannot be included as quota controls or stratification variables – To determine number of sample points by geography – To create accurate booster samples (eg young people / ethnic groups) Census Data for Sampling For Quota (non-probability) Samples: – To set appropriate quotas (based on demographics); Data are used here at very localised level – ie Census Outputs Census Data for Sampling Census Data for Survey Weighting To ensure that the sample profile balances the population profile Census Data are needed to tell you what the population profile is ….and hence provide accurate weights ….and hence provide an accurate measure of the design effect and the true level of statistical reliability / confidence intervals on your survey measures But also pre-weighting, for interviewer field dept. -
Accelerating Raw Data Analysis with the ACCORDA Software and Hardware Architecture
Accelerating Raw Data Analysis with the ACCORDA Software and Hardware Architecture Yuanwei Fang Chen Zou Andrew A. Chien CS Department CS Department University of Chicago University of Chicago University of Chicago Argonne National Laboratory [email protected] [email protected] [email protected] ABSTRACT 1. INTRODUCTION The data science revolution and growing popularity of data Driven by a rapid increase in quantity, type, and number lakes make efficient processing of raw data increasingly impor- of sources of data, many data analytics approaches use the tant. To address this, we propose the ACCelerated Operators data lake model. Incoming data is pooled in large quantity { for Raw Data Analysis (ACCORDA) architecture. By ex- hence the name \lake" { and because of varied origin (e.g., tending the operator interface (subtype with encoding) and purchased from other providers, internal employee data, web employing a uniform runtime worker model, ACCORDA scraped, database dumps, etc.), it varies in size, encoding, integrates data transformation acceleration seamlessly, en- age, quality, etc. Additionally, it often lacks consistency or abling a new class of encoding optimizations and robust any common schema. Analytics applications pull data from high-performance raw data processing. Together, these key the lake as they see fit, digesting and processing it on-demand features preserve the software system architecture, empower- for a current analytics task. The applications of data lakes ing state-of-art heuristic optimizations to drive flexible data are vast, including machine learning, data mining, artificial encoding for performance. ACCORDA derives performance intelligence, ad-hoc query, and data visualization. Fast direct from its software architecture, but depends critically on the processing on raw data is critical for these applications. -
A First Step Into the Bootstrap World
INSTITUTE FOR DEFENSE ANALYSES A First Step into the Bootstrap World Matthew Avery May 2016 Approved for public release. IDA Document NS D-5816 Log: H 16-000624 INSTITUTE FOR DEFENSE ANALYSES 4850 Mark Center Drive Alexandria, Virginia 22311-1882 The Institute for Defense Analyses is a non-profit corporation that operates three federally funded research and development centers to provide objective analyses of national security issues, particularly those requiring scientific and technical expertise, and conduct related research on other national challenges. About This Publication This briefing motivates bootstrapping through an intuitive explanation of basic statistical inference, discusses the right way to resample for bootstrapping, and uses examples from operational testing where the bootstrap approach can be applied. Bootstrapping is a powerful and flexible tool when applied appropriately. By treating the observed sample as if it were the population, the sampling distribution of statistics of interest can be generated with precision equal to Monte Carlo error. This approach is nonparametric and requires only acceptance of the observed sample as an estimate for the population. Careful resampling is used to generate the bootstrap distribution. Applications include quantifying uncertainty for availability data, quantifying uncertainty for complex distributions, and using the bootstrap for inference, such as the two-sample t-test. Copyright Notice © 2016 Institute for Defense Analyses 4850 Mark Center Drive, Alexandria, Virginia 22311-1882 -
CORRELATION COEFFICIENTS Ice Cream and Crimedistribute Difficulty Scale ☺ ☺ (Moderately Hard)Or
5 COMPUTING CORRELATION COEFFICIENTS Ice Cream and Crimedistribute Difficulty Scale ☺ ☺ (moderately hard)or WHAT YOU WILLpost, LEARN IN THIS CHAPTER • Understanding what correlations are and how they work • Computing a simple correlation coefficient • Interpretingcopy, the value of the correlation coefficient • Understanding what other types of correlations exist and when they notshould be used Do WHAT ARE CORRELATIONS ALL ABOUT? Measures of central tendency and measures of variability are not the only descrip- tive statistics that we are interested in using to get a picture of what a set of scores 76 Copyright ©2020 by SAGE Publications, Inc. This work may not be reproduced or distributed in any form or by any means without express written permission of the publisher. Chapter 5 ■ Computing Correlation Coefficients 77 looks like. You have already learned that knowing the values of the one most repre- sentative score (central tendency) and a measure of spread or dispersion (variability) is critical for describing the characteristics of a distribution. However, sometimes we are as interested in the relationship between variables—or, to be more precise, how the value of one variable changes when the value of another variable changes. The way we express this interest is through the computation of a simple correlation coefficient. For example, what’s the relationship between age and strength? Income and years of education? Memory skills and amount of drug use? Your political attitudes and the attitudes of your parents? A correlation coefficient is a numerical index that reflects the relationship or asso- ciation between two variables. The value of this descriptive statistic ranges between −1.00 and +1.00. -
Notes Mean, Median, Mode & Range
Notes Mean, Median, Mode & Range How Do You Use Mode, Median, Mean, and Range to Describe Data? There are many ways to describe the characteristics of a set of data. The mode, median, and mean are all called measures of central tendency. These measures of central tendency and range are described in the table below. The mode of a set of data Use the mode to show which describes which value occurs value in a set of data occurs most frequently. If two or more most often. For the set numbers occur the same number {1, 1, 2, 3, 5, 6, 10}, of times and occur more often the mode is 1 because it occurs Mode than all the other numbers in the most frequently. set, those numbers are all modes for the data set. If each number in the set occurs the same number of times, the set of data has no mode. The median of a set of data Use the median to show which describes what value is in the number in a set of data is in the middle if the set is ordered from middle when the numbers are greatest to least or from least to listed in order. greatest. If there are an even For the set {1, 1, 2, 3, 5, 6, 10}, number of values, the median is the median is 3 because it is in the average of the two middle the middle when the numbers are Median values. Half of the values are listed in order. greater than the median, and half of the values are less than the median. -
Common Data Set 2020-2021 University of Pennsylvania
Common Data Set 2020-2021 University of Pennsylvania Table of Contents A General Information page 3 B Enrollment and Persistence 5 C First Time, First Year Admission 8 D Transfer Admission 14 E Academic Offerings and Policies 16 F Student Life 18 G Annual Expenses 20 H Financial Aid 22 I Instructional Faculty and Class Size 28 J Disciplinary Areas of Degrees Conferred 30 Common Data Set Definitions 32 Common Data Set 2020-21 1 25 Jun 2021 Common Data Set 2020-21 2 25 Jun 2021 A. General Information return to Table of Contents A1 Address Information A1 University of Pennsylvania A1 Mailing Address: 1 College Hall, Room 100 A1 City/State/Zip/Country: Philadelphia, PA 19104-6228 A1 Main Phone Number: 215-898-5000 A1 Home Page Address www.upenn.edu A1 Admissions Phone Number: 215-898-7507 A1 Admissions Office Mailing Address: 1 College Hall A1 City/State/Zip/Country: Philadelphia, PA 19104 A1 Admissions Fax Number: 215-898-9670 A1 Admissions E-mail Address: [email protected] A1 Online application www.admissions.upenn.edu A2 Source of institutional control (Check only one): A2 Public A2 Private (nonprofit) x A2 Proprietary A3 Classify your undergraduate institution: A3 Coeducational college A3 Men's college A3 Women's college A4 Academic year calendar: A4 Semester x A4 Quarter A4 Trimester A4 4-1-4 A4 Continuous A5 Degrees offered by your institution: A5 Certificate x A5 Diploma A5 Associate x A5 Transfer Associate A5 Terminal Associate x A5 Bachelor's x A5 Postbachelor's certificate x A5 Master's x A5 Post-master's certificate x A5 Doctoral degree - research/scholarship x A5 Doctoral degree - professional practice x A5 Doctoral degree - other x A5 Doctoral degree -- other Common Data Set 2020-21 3 25 Jun 2021 Common Data Set 2020-21 4 25 Jun 2021 B. -
Lecture 14 Testing for Kurtosis
9/8/2016 CHE384, From Data to Decisions: Measurement, Kurtosis Uncertainty, Analysis, and Modeling • For any distribution, the kurtosis (sometimes Lecture 14 called the excess kurtosis) is defined as Testing for Kurtosis 3 (old notation = ) • For a unimodal, symmetric distribution, Chris A. Mack – a positive kurtosis means “heavy tails” and a more Adjunct Associate Professor peaked center compared to a normal distribution – a negative kurtosis means “light tails” and a more spread center compared to a normal distribution http://www.lithoguru.com/scientist/statistics/ © Chris Mack, 2016Data to Decisions 1 © Chris Mack, 2016Data to Decisions 2 Kurtosis Examples One Impact of Excess Kurtosis • For the Student’s t • For a normal distribution, the sample distribution, the variance will have an expected value of s2, excess kurtosis is and a variance of 6 2 4 1 for DF > 4 ( for DF ≤ 4 the kurtosis is infinite) • For a distribution with excess kurtosis • For a uniform 2 1 1 distribution, 1 2 © Chris Mack, 2016Data to Decisions 3 © Chris Mack, 2016Data to Decisions 4 Sample Kurtosis Sample Kurtosis • For a sample of size n, the sample kurtosis is • An unbiased estimator of the sample excess 1 kurtosis is ∑ ̅ 1 3 3 1 6 1 2 3 ∑ ̅ Standard Error: • For large n, the sampling distribution of 1 24 2 1 approaches Normal with mean 0 and variance 2 1 of 24/n 3 5 • For small samples, this estimator is biased D. N. Joanes and C. A. Gill, “Comparing Measures of Sample Skewness and Kurtosis”, The Statistician, 47(1),183–189 (1998).