Characteristics and statistics of digital remote sensing imagery


 Pierce Butler
 2 years ago
 Views:
Transcription
1 Characteristics and statistics of digital remote sensing imagery There are two fundamental ways to obtain digital imagery: Acquire remotely sensed imagery in an analog format (often referred to as hardcopy) and then convert it to a digital format through the process of digitization, and Acquire remotely sensed imagery already in a digital format, such as that obtained by a Landsat sensor system. 1
2 Image Digitization: Analog to Digital (A/D) Conversion Using Linear Array Scanners Image digitization is the process of turning a hardcopy analog imagery into a digital image. (e.g., a destop scanner)
3 RGB = True Color. Any addition array that collect spectral information beyond visible light will be able to generate pseudo color image. Additional array? 3
4 Panchromatic Blac & White Infrared Truecolor vs. Pseudo (false)color 4
5 With all images are digital, nowledge and sills in digital image processing are necessary. Digital Image With raster data structure, each image is treated as an array of values of the pixels. Image data is organized as rows and columns (or lines and pixels) start from the upper left corner of the image. Each pixel (picture element) is treated as a separate unite. 5
6 Statistics of Digital Images: Looing at the frequency of occurrence of individual brightness values in the image displayed in a histogram Viewing individual pixel brightness values at specific locations or within a geographic area; Computing univariate descriptive statistics to determine if there are unusual anomalies in the image data; and Computing multivariate statistics to determine the amount of betweenband correlation (e.g., to identify redundancy). Statistics of Digital Images It is useful to calculate fundamental univariate and multivariate statistics of the multispectral remote sensor data. This normally involved computing of maximum and minimum value for each band of imagery, the range, mean, standard deviation, betweenband variancecovariance matrix, correlation matrix, and frequencies of brightness values for each band, which are used to produce histograms. Such statistics provide valuable information necessary for processing and analyzing remote sensing data. 6
7 Digital Images: A population is an infinite or finite set of elements. A sample is a subset of the elements taen from a population used to mae inferences about certain characteristics of the population. (e.g., training signatures) Large samples drawn randomly from natural populations usually produce a symmetrical frequency distribution. Most values are clustered around some central value, and the frequency of occurrence declines away from this central point. A graph of the distribution appears bell shaped is called a normal distribution. 7
8 Histogram and Its Significance to Digital Remote Sensing Image Processing Many statistical tests used in the analysis of remotely sensed data assume that the brightness values recorded in a scene are normally distributed. Unfortunately, remotely sensed data may not be normally distributed. In such instance, nonparametric statistical theory may be preferred. Forest Water 8
9 Histogram and Its Significance to Digital Remote Sensing Image Processing The histogram is a useful graphic representation of the information content of a remote sensing image, which provide readers with an appreciation of the quality of the original data, e.g. whether it is low in contrast, high in contrast, or multimodal in nature. Univariate Descriptive Image Statistics Measures of Central Tendency in Remote Sensor Data Mode: is the value that occurs most frequently in a distribution and is usually the highest point on the curve. Multiple modes are common in image dataset. Median: is the value midway in the frequency distribution. Mean: is the arithmetic average and if defined as the sum of all observations divided by the number of observations. 9
10 Measures of Central Tendency in Remote Sensor Data The mean is the arithmetic average and is defined as the sum of all brightness value observations divided by the number of observations. It is the most commonly used measure of central tendency. The mean ( ) of a single band of imagery composed of n brightness values (BV i ) is computed using the formula: Sample mean is a poor measure of central tendency when the set of observations is sewed or contains an outlier. 9 Further measurements are needed. Outlier Mean = 7/9 = 3 (Does not represent the dataset well) Sewed Mean = 9/9 = 1 Mean = 9/9 = 1 10
11 Measures of Dispersion Measures of the dispersion about the mean of a distribution provide valuable information about the image. For example, the range of a band of imagery (range ) is computed as the difference between the maximum (max ) and minimum (min ) values: Measures of Dispersion Unfortunately, when the minimum or maximum values are extreme or unusual observations, the range could be a misleading measure of dispersion. Such extreme values are not uncommon because the remote sensor data are often collected by detector systems with delicate electronics that can experience spies in voltage and other unfortunate malfunctions. When unusual values are not encountered, the range is a very important statistic often used in image enhancement functions such as min max contrast stretching. 11
12 Measures of Dispersion Variance: is the average squared deviation of all possible observations from the sample mean. The variance of a band of imagery, var, is computed using the equation: BV 11 BV 1 BV 13 BV 1 BV BV 3 BV 31 BV 3 BV 33 var n ( i 1 BV n i 1 ) BV 11 BV 1 BV 13 BV 1 BV BV 3 var n ( i 1 BV i n 1 ) BV 31 BV 3 BV 33 var 9 i 1 (1 1 ) var ( n i 1 54 ( BV i ) n 1 (1 (1 (18 (1 8 (13 ( (14 (1 1
13 Standard Deviation (s ): is the positive square root of the variance. s var A small s. suggests that observations clustered tightly around a central value. A large s indicates that values are scattered widely about the mean. The sample having the largest variance or standard deviation has the greater spread among the values of the observations. Mean Standard Deviations Standard Deviation (s ): is the positive square root of the variance. s var var ( n i 1 54 ( BV i n 1 (1 ) (1 (18 (1 8 (13 (1 (14 (1 s var
14 Measures of Distribution (Histogram) Asymmetry and Pea Sharpness Sewness is a measure of the asymmetry of a histogram and is computed using the formula: BV 11 BV 1 BV 13 BV 1 BV BV 3 BV 31 BV 3 BV 33 A perfectly symmetric histogram has a sewness value of zero. Histogram of A Single Band of Landsat Thematic Mapper Data Max. = 10 Min. = 6 Mean = 7 Median = 5 Mode = 9 14
15 Histogram of Thermal Infrared Imagery of a Thermal Plume in the Savannah River Max. = 188 Min. = 38 Mean = 73 Median = 68 Mode = 75 Remote Sensing Multivariate Statistics Remote sensing is often concerned with the measurement of how much radiant flux is reflected or emitted from an object in more than one band (e.g., in red and nearinfrared bands). It is useful to compute multivariate statistical measures such as covariance and correlation among the several bands to determine how the measurements covary. 15
16 Remote Sensing Multivariate Statistics The different remotesensingderived spectral measurements for each pixel often change together in some predictable fashion. Landsat7 ETM+ Band 1 (Blue band) Landsat7 ETM+ Band (Green band) Remote Sensing Multivariate Statistics If there is no relationship between the brightness value in one band and that of another for a given pixel, the values are mutually independent; i.e., an increase or decrease in one band s brightness value is not accompanied by a predictable change in another band s brightness value. Landsat7 ETM+ Band 3 (Red band) Landsat7 ETM+ Band 4 (Near IR band) 16
17 Correlation between Multiple Bands of Remotely Sensed Data To estimate the degree of interrelation between variables in a manner not influenced by measurement units, the correlation coefficient, r, is commonly used. The correlation between two bands of remotely sensed data, r l, is the ratio of their covariance (cov l ) to the product of their standard deviations (s s l ); thus: r l cov s s l l Correlation Coefficient: A correlation coefficient of +1 indicates a positive, perfect relationship between the brightness values of the two bands. A correlation coefficient of 1 indicates that the two bands are inversely related. A correlation coefficient of zero suggests that there is no linear relationship between the two bands of data. 17
18 Remote Sensing Multivariate Statistics Because spectral measurements of individual pixels may not be independent, some measure of their mutual interaction is needed. This measure, called the covariance, is the joint variation of two variables about their common mean. To calculate covariance, we first compute the corrected sum of products (SP) defined by the equation: 18
19 Remote Sensing Multivariate Statistics It is computationally more efficient to use the following formula to arrive at the same result: This quantity is called the uncorrected sum of products. Remote Sensing Multivariate Statistics Covariance is calculated by dividing SP by (n 1). Therefore, the covariance between brightness values in bands and l, cov l, is equal to: 19
20 Covariance: is the joint variation of two variables about their common mean. SP l is the corrected Sum of Products between bands and l. SP cov l l n 1 SP l n ( i 1 BV i )( BV il l ) Band = Band l l = 1 SP l = (199)x(11)+(19)x(11)+(19)x(11)+(189)x(11)+(19)x(11)+(139)x(11)+ (19)x(11)+(149)x(11)+(19)x(11) = 0 Cov l = 0 Covariance: A more efficient formula is: n SP l ( BV i BV il ) i 1 n BV i 1 n i BV i 1 n il Band Band l Total = Total = 9 SP l = [(19x1)+(1x1)+(1x1)+(18x1)+(1x1)+(13x1)+(1x1)+(14x1)+(1x1)] [91x9/9] = 0 Cov l = 0 The sums of products (SP) and sums of squares (SS) can be computed for all possible band combinations. 0
21 Format of a VarianceCovariance Matrix Band 1 (green) Band (red) Band 3 (nearinfrared) Band 4 (nearinfrared) Band 1 SS 1 cov 1, cov 1,3 cov 1,4 Band cov,1 SS cov,3 cov,4 Band 3 cov 3,1 cov 3, SS 3 cov 3,4 Band 4 cov 4,1 cov 4, cov 4,3 SS 4 1
22 Remote Sensing Multivariate Statistics Variance covariance and correlation matrices are the ey for principal components analysis (PCA), feature selection, classification and accuracy assessment.
Data Mining Part 2. Data Understanding and Preparation 2.1 Data Understanding Spring 2010
Data Mining Part 2. and Preparation 2.1 Spring 2010 Instructor: Dr. Masoud Yaghini Introduction Outline Introduction Measuring the Central Tendency Measuring the Dispersion of Data Graphic Displays References
More informationSAMPLE MIDTERM QUESTIONS
Geography 309 Sample MidTerm Questions Page 1 SAMPLE MIDTERM QUESTIONS Textbook Questions Chapter 1 Questions 4, 5, 6, Chapter 2 Questions 4, 7, 10 Chapter 4 Questions 8, 9 Chapter 10 Questions 1, 4, 7
More information1) Write the following as an algebraic expression using x as the variable: Triple a number subtracted from the number
1) Write the following as an algebraic expression using x as the variable: Triple a number subtracted from the number A. 3(x  x) B. x 3 x C. 3x  x D. x  3x 2) Write the following as an algebraic expression
More information103 Measures of Central Tendency and Variation
103 Measures of Central Tendency and Variation So far, we have discussed some graphical methods of data description. Now, we will investigate how statements of central tendency and variation can be used.
More informationContent DESCRIPTIVE STATISTICS. Data & Statistic. Statistics. Example: DATA VS. STATISTIC VS. STATISTICS
Content DESCRIPTIVE STATISTICS Dr Najib Majdi bin Yaacob MD, MPH, DrPH (Epidemiology) USM Unit of Biostatistics & Research Methodology School of Medical Sciences Universiti Sains Malaysia. Introduction
More informationResolutions of Remote Sensing
Resolutions of Remote Sensing 1. Spatial (what area and how detailed) 2. Spectral (what colors bands) 3. Temporal (time of day/season/year) 4. Radiometric (color depth) Spatial Resolution describes how
More informationData Exploration Data Visualization
Data Exploration Data Visualization What is data exploration? A preliminary exploration of the data to better understand its characteristics. Key motivations of data exploration include Helping to select
More informationSTATS8: Introduction to Biostatistics. Data Exploration. Babak Shahbaba Department of Statistics, UCI
STATS8: Introduction to Biostatistics Data Exploration Babak Shahbaba Department of Statistics, UCI Introduction After clearly defining the scientific problem, selecting a set of representative members
More informationChapter 2: Systems of Linear Equations and Matrices:
At the end of the lesson, you should be able to: Chapter 2: Systems of Linear Equations and Matrices: 2.1: Solutions of Linear Systems by the Echelon Method Define linear systems, unique solution, inconsistent,
More informationDESCRIPTIVE STATISTICS. The purpose of statistics is to condense raw data to make it easier to answer specific questions; test hypotheses.
DESCRIPTIVE STATISTICS The purpose of statistics is to condense raw data to make it easier to answer specific questions; test hypotheses. DESCRIPTIVE VS. INFERENTIAL STATISTICS Descriptive To organize,
More informationModule 3: Correlation and Covariance
Using Statistical Data to Make Decisions Module 3: Correlation and Covariance Tom Ilvento Dr. Mugdim Pašiƒ University of Delaware Sarajevo Graduate School of Business O ften our interest in data analysis
More informationData. ECON 251 Research Methods. 1. Data and Descriptive Statistics (Review) CrossSectional and TimeSeries Data. Population vs.
ECO 51 Research Methods 1. Data and Descriptive Statistics (Review) Data A variable  a characteristic of population or sample that is of interest for us. Data  the actual values of variables Quantitative
More informationA Introduction to Matrix Algebra and Principal Components Analysis
A Introduction to Matrix Algebra and Principal Components Analysis Multivariate Methods in Education ERSH 8350 Lecture #2 August 24, 2011 ERSH 8350: Lecture 2 Today s Class An introduction to matrix algebra
More informationChapter 3: Central Tendency
Chapter 3: Central Tendency Central Tendency In general terms, central tendency is a statistical measure that determines a single value that accurately describes the center of the distribution and represents
More informationA frequency distribution is a table used to describe a data set. A frequency table lists intervals or ranges of data values called data classes
A frequency distribution is a table used to describe a data set. A frequency table lists intervals or ranges of data values called data classes together with the number of data values from the set that
More informationEngineering Problem Solving and Excel. EGN 1006 Introduction to Engineering
Engineering Problem Solving and Excel EGN 1006 Introduction to Engineering Mathematical Solution Procedures Commonly Used in Engineering Analysis Data Analysis Techniques (Statistics) Curve Fitting techniques
More informationResearch Variables. Measurement. Scales of Measurement. Chapter 4: Data & the Nature of Measurement
Chapter 4: Data & the Nature of Graziano, Raulin. Research Methods, a Process of Inquiry Presented by Dustin Adams Research Variables Variable Any characteristic that can take more than one form or value.
More informationGCSE HIGHER Statistics Key Facts
GCSE HIGHER Statistics Key Facts Collecting Data When writing questions for questionnaires, always ensure that: 1. the question is worded so that it will allow the recipient to give you the information
More information( ) ( ) Central Tendency. Central Tendency
1 Central Tendency CENTRAL TENDENCY: A statistical measure that identifies a single score that is most typical or representative of the entire group Usually, a value that reflects the middle of the distribution
More informationPIXELLEVEL IMAGE FUSION USING BROVEY TRANSFORME AND WAVELET TRANSFORM
PIXELLEVEL IMAGE FUSION USING BROVEY TRANSFORME AND WAVELET TRANSFORM Rohan Ashok Mandhare 1, Pragati Upadhyay 2,Sudha Gupta 3 ME Student, K.J.SOMIYA College of Engineering, Vidyavihar, Mumbai, Maharashtra,
More informationIn this chapter, you will learn to use descriptive statistics to organize, summarize, analyze, and interpret data for contract pricing.
3.0  Chapter Introduction In this chapter, you will learn to use descriptive statistics to organize, summarize, analyze, and interpret data for contract pricing. Categories of Statistics. Statistics is
More information03 The full syllabus. 03 The full syllabus continued. For more information visit www.cimaglobal.com PAPER C03 FUNDAMENTALS OF BUSINESS MATHEMATICS
0 The full syllabus 0 The full syllabus continued PAPER C0 FUNDAMENTALS OF BUSINESS MATHEMATICS Syllabus overview This paper primarily deals with the tools and techniques to understand the mathematics
More informationInferential Statistics
Inferential Statistics Sampling and the normal distribution Zscores Confidence levels and intervals Hypothesis testing Commonly used statistical methods Inferential Statistics Descriptive statistics are
More informationMTH304: Honors Algebra II
MTH304: Honors Algebra II This course builds upon algebraic concepts covered in Algebra. Students extend their knowledge and understanding by solving openended problems and thinking critically. Topics
More informationRemote Sensing Image Processing
Remote Sensing Image Processing Preprocessing Geometric Correction Atmospheric correction Image enhancement Image classification Division of Spatial Information Science Graduate School Life and Environment
More informationStatTools Assignment #1, Winter 2007 This assignment has three parts.
StatTools Assignment #1, Winter 2007 This assignment has three parts. Before beginning this assignment, be sure to carefully read the General Instructions document that is located on the StatTools Assignments
More informationMathematics. Probability and Statistics Curriculum Guide. Revised 2010
Mathematics Probability and Statistics Curriculum Guide Revised 2010 This page is intentionally left blank. Introduction The Mathematics Curriculum Guide serves as a guide for teachers when planning instruction
More informationDescriptive Statistics
Y520 Robert S Michael Goal: Learn to calculate indicators and construct graphs that summarize and describe a large quantity of values. Using the textbook readings and other resources listed on the web
More informationDescribe what is meant by a placebo Contrast the doubleblind procedure with the singleblind procedure Review the structure for organizing a memo
Readings: Ha and Ha Textbook  Chapters 1 8 Appendix D & E (online) Plous  Chapters 10, 11, 12 and 14 Chapter 10: The Representativeness Heuristic Chapter 11: The Availability Heuristic Chapter 12: Probability
More informationSampling, frequency distribution, graphs, measures of central tendency, measures of dispersion
Statistics Basics Sampling, frequency distribution, graphs, measures of central tendency, measures of dispersion Part 1: Sampling, Frequency Distributions, and Graphs The method of collecting, organizing,
More informationFrequency distributions, central tendency & variability. Displaying data
Frequency distributions, central tendency & variability Displaying data Software SPSS Excel/Numbers/Google sheets Social Science Statistics website (socscistatistics.com) Creating and SPSS file Open the
More informationDimensionality Reduction: Principal Components Analysis
Dimensionality Reduction: Principal Components Analysis In data mining one often encounters situations where there are a large number of variables in the database. In such situations it is very likely
More informationbusiness statistics using Excel OXFORD UNIVERSITY PRESS Glyn Davis & Branko Pecar
business statistics using Excel Glyn Davis & Branko Pecar OXFORD UNIVERSITY PRESS Detailed contents Introduction to Microsoft Excel 2003 Overview Learning Objectives 1.1 Introduction to Microsoft Excel
More information13.2 Measures of Central Tendency
13.2 Measures of Central Tendency Measures of Central Tendency For a given set of numbers, it may be desirable to have a single number to serve as a kind of representative value around which all the numbers
More informationBracken County Schools Curriculum Guide Math
Unit 1: Expressions and Equations (Ch. 13) Suggested Length: Semester Course: 4 weeks Year Course: 8 weeks Program of Studies Core Content 1. How do you use basic skills and operands to create and solve
More informationSelecting the appropriate band combination for an RGB image using Landsat imagery
Selecting the appropriate band combination for an RGB image using Landsat imagery Ned Horning Version: 1.0 Creation Date: 20040101 Revision Date: 20040101 License: This document is licensed under a
More informationAn introduction to ValueatRisk Learning Curve September 2003
An introduction to ValueatRisk Learning Curve September 2003 ValueatRisk The introduction of ValueatRisk (VaR) as an accepted methodology for quantifying market risk is part of the evolution of risk
More informationBiostatistics: DESCRIPTIVE STATISTICS: 2, VARIABILITY
Biostatistics: DESCRIPTIVE STATISTICS: 2, VARIABILITY 1. Introduction Besides arriving at an appropriate expression of an average or consensus value for observations of a population, it is important to
More informationData Analysis: Describing Data  Descriptive Statistics
WHAT IT IS Return to Table of ontents Descriptive statistics include the numbers, tables, charts, and graphs used to describe, organize, summarize, and present raw data. Descriptive statistics are most
More informationUNDERSTANDING MULTIPLE REGRESSION
UNDERSTANDING Multiple regression analysis (MRA) is any of several related statistical methods for evaluating the effects of more than one independent (or predictor) variable on a dependent (or outcome)
More informationExercise 1.12 (Pg. 2223)
Individuals: The objects that are described by a set of data. They may be people, animals, things, etc. (Also referred to as Cases or Records) Variables: The characteristics recorded about each individual.
More informationNumerical Summarization of Data OPRE 6301
Numerical Summarization of Data OPRE 6301 Motivation... In the previous session, we used graphical techniques to describe data. For example: While this histogram provides useful insight, other interesting
More informationWATER BODY EXTRACTION FROM MULTI SPECTRAL IMAGE BY SPECTRAL PATTERN ANALYSIS
WATER BODY EXTRACTION FROM MULTI SPECTRAL IMAGE BY SPECTRAL PATTERN ANALYSIS Nguyen Dinh Duong Department of Environmental Information Study and Analysis, Institute of Geography, 18 Hoang Quoc Viet Rd.,
More informationTechnology StepbyStep Using StatCrunch
Technology StepbyStep Using StatCrunch Section 1.3 Simple Random Sampling 1. Select Data, highlight Simulate Data, then highlight Discrete Uniform. 2. Fill in the following window with the appropriate
More informationStatistical Concepts and Market Return
Statistical Concepts and Market Return 2014 Level I Quantitative Methods IFT Notes for the CFA exam Contents 1. Introduction... 2 2. Some Fundamental Concepts... 2 3. Summarizing Data Using Frequency Distributions...
More informationHigh School Algebra 1 Common Core Standards & Learning Targets
High School Algebra 1 Common Core Standards & Learning Targets Unit 1: Relationships between Quantities and Reasoning with Equations CCS Standards: Quantities NQ.1. Use units as a way to understand problems
More informationThe Role of SPOT Satellite Images in Mapping Air Pollution Caused by Cement Factories
The Role of SPOT Satellite Images in Mapping Air Pollution Caused by Cement Factories Dr. Farrag Ali FARRAG Assistant Prof. at Civil Engineering Dept. Faculty of Engineering Assiut University Assiut, Egypt.
More informationLecture 7 Cogsci 109. Thurs. Oct. 12, 2006
Lecture 7 Cogsci 109 Thurs. Oct. 12, 2006 Announcements Homework 2 is posted. Office hours Midterm is coming up somewhere in the next couple of weeks Anything lectured on, presented in section, in the
More informationChapter 3 Descriptive Statistics: Numerical Measures. Learning objectives
Chapter 3 Descriptive Statistics: Numerical Measures Slide 1 Learning objectives 1. Single variable Part I (Basic) 1.1. How to calculate and use the measures of location 1.. How to calculate and use the
More informationChapter 15 Multiple Choice Questions (The answers are provided after the last question.)
Chapter 15 Multiple Choice Questions (The answers are provided after the last question.) 1. What is the median of the following set of scores? 18, 6, 12, 10, 14? a. 10 b. 14 c. 18 d. 12 2. Approximately
More informationEnvironmental Remote Sensing GEOG 2021
Environmental Remote Sensing GEOG 2021 Lecture 4 Image classification 2 Purpose categorising data data abstraction / simplification data interpretation mapping for land cover mapping use land cover class
More information4.1 Exploratory Analysis: Once the data is collected and entered, the first question is: "What do the data look like?"
Data Analysis Plan The appropriate methods of data analysis are determined by your data types and variables of interest, the actual distribution of the variables, and the number of cases. Different analyses
More informationCHINHOYI UNIVERSITY OF TECHNOLOGY
CHINHOYI UNIVERSITY OF TECHNOLOGY SCHOOL OF NATURAL SCIENCES AND MATHEMATICS DEPARTMENT OF MATHEMATICS MEASURES OF CENTRAL TENDENCY AND DISPERSION INTRODUCTION From the previous unit, the Graphical displays
More informationHow Landsat Images are Made
How Landsat Images are Made Presentation by: NASA s Landsat Education and Public Outreach team June 2006 1 More than just a pretty picture Landsat makes pretty weird looking maps, and it isn t always easy
More informationINTRODUCTION REMOTE SENSING
INTRODUCTION REMOTE SENSING dr.ir. Jan Clevers Centre for GeoInformation Dept. Environmental Sciences Wageningen UR Remote Sensing > RS Sensor at a distance EARTH OBSERVATION EM energy Earth RS is a
More informationStats Review Chapters 34
Stats Review Chapters 34 Created by Teri Johnson Math Coordinator, Mary Stangler Center for Academic Success Examples are taken from Statistics 4 E by Michael Sullivan, III And the corresponding Test
More informationChapter 3: Data Description Numerical Methods
Chapter 3: Data Description Numerical Methods Learning Objectives Upon successful completion of Chapter 3, you will be able to: Summarize data using measures of central tendency, such as the mean, median,
More informationMBA 611 STATISTICS AND QUANTITATIVE METHODS
MBA 611 STATISTICS AND QUANTITATIVE METHODS Part I. Review of Basic Statistics (Chapters 111) A. Introduction (Chapter 1) Uncertainty: Decisions are often based on incomplete information from uncertain
More informationAlgebra I Vocabulary Cards
Algebra I Vocabulary Cards Table of Contents Expressions and Operations Natural Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers Absolute Value Order of Operations Expression
More informationDescriptive Statistics. Understanding Data: Categorical Variables. Descriptive Statistics. Dataset: Shellfish Contamination
Descriptive Statistics Understanding Data: Dataset: Shellfish Contamination Location Year Species Species2 Method Metals Cadmium (mg kg  ) Chromium (mg kg  ) Copper (mg kg  ) Lead (mg kg  ) Mercury
More informationHomework 3. Part 1. Name: Score: / null
Name: Score: / Homework 3 Part 1 null 1 For the following sample of scores, the standard deviation is. Scores: 7, 2, 4, 6, 4, 7, 3, 7 Answer Key: 2 2 For any set of data, the sum of the deviation scores
More informationF. Farrokhyar, MPhil, PhD, PDoc
Learning objectives Descriptive Statistics F. Farrokhyar, MPhil, PhD, PDoc To recognize different types of variables To learn how to appropriately explore your data How to display data using graphs How
More informationChapter 10. Key Ideas Correlation, Correlation Coefficient (r),
Chapter 0 Key Ideas Correlation, Correlation Coefficient (r), Section 0: Overview We have already explored the basics of describing single variable data sets. However, when two quantitative variables
More informationThis unit will lay the groundwork for later units where the students will extend this knowledge to quadratic and exponential functions.
Algebra I Overview View unit yearlong overview here Many of the concepts presented in Algebra I are progressions of concepts that were introduced in grades 6 through 8. The content presented in this course
More informationDATA INTERPRETATION AND STATISTICS
PholC60 September 001 DATA INTERPRETATION AND STATISTICS Books A easy and systematic introductory text is Essentials of Medical Statistics by Betty Kirkwood, published by Blackwell at about 14. DESCRIPTIVE
More informationTable 21. Sucrose concentration (% fresh wt.) of 100 sugar beet roots. Beet No. % Sucrose. Beet No.
Chapter 2. DATA EXPLORATION AND SUMMARIZATION 2.1 Frequency Distributions Commonly, people refer to a population as the number of individuals in a city or county, for example, all the people in California.
More informationFactor Analysis. Chapter 420. Introduction
Chapter 420 Introduction (FA) is an exploratory technique applied to a set of observed variables that seeks to find underlying factors (subsets of variables) from which the observed variables were generated.
More informationRemote Sensing of Global Climate Change
of Global Climate Change 2009 TECHNICAL STUFF... WHERE ON THE EARTH IS THAT??? Students should understand various geographic coordinate systems used to locate images, and how to translate these into distances
More informationAlgebra 2 Chapter 1 Vocabulary. identity  A statement that equates two equivalent expressions.
Chapter 1 Vocabulary identity  A statement that equates two equivalent expressions. verbal model A word equation that represents a reallife problem. algebraic expression  An expression with variables.
More informationLEARNING OBJECTIVES SCALES OF MEASUREMENT: A REVIEW SCALES OF MEASUREMENT: A REVIEW DESCRIBING RESULTS DESCRIBING RESULTS 8/14/2016
UNDERSTANDING RESEARCH RESULTS: DESCRIPTION AND CORRELATION LEARNING OBJECTIVES Contrast three ways of describing results: Comparing group percentages Correlating scores Comparing group means Describe
More informationIntroduction to Quantitative Methods
Introduction to Quantitative Methods October 15, 2009 Contents 1 Definition of Key Terms 2 2 Descriptive Statistics 3 2.1 Frequency Tables......................... 4 2.2 Measures of Central Tendencies.................
More informationLean Six Sigma Training/Certification Book: Volume 1
Lean Six Sigma Training/Certification Book: Volume 1 Six Sigma Quality: Concepts & Cases Volume I (Statistical Tools in Six Sigma DMAIC process with MINITAB Applications Chapter 1 Introduction to Six Sigma,
More informationNCSS Statistical Software Principal Components Regression. In ordinary least squares, the regression coefficients are estimated using the formula ( )
Chapter 340 Principal Components Regression Introduction is a technique for analyzing multiple regression data that suffer from multicollinearity. When multicollinearity occurs, least squares estimates
More informationCalculation of Minimum Distances. Minimum Distance to Means. Σi i = 1
Minimum Distance to Means Similar to Parallelepiped classifier, but instead of bounding areas, the user supplies spectral class means in ndimensional space and the algorithm calculates the distance between
More informationBig Ideas in Mathematics
Big Ideas in Mathematics which are important to all mathematics learning. (Adapted from the NCTM Curriculum Focal Points, 2006) The Mathematics Big Ideas are organized using the PA Mathematics Standards
More informationDescribing Data. We find the position of the central observation using the formula: position number =
HOSP 1207 (Business Stats) Learning Centre Describing Data This worksheet focuses on describing data through measuring its central tendency and variability. These measurements will give us an idea of what
More informationConcepts in Investments Risks and Returns (Relevant to PBE Paper II Management Accounting and Finance)
Concepts in Investments Risks and Returns (Relevant to PBE Paper II Management Accounting and Finance) Mr. Eric Y.W. Leung, CUHK Business School, The Chinese University of Hong Kong In PBE Paper II, students
More informationDigital image processing
746A27 Remote Sensing and GIS Lecture 4 Digital image processing Chandan Roy Guest Lecturer Department of Computer and Information Science Linköping University Digital Image Processing Most of the common
More informationModule 4: Data Exploration
Module 4: Data Exploration Now that you have your data downloaded from the Streams Project database, the detective work can begin! Before computing any advanced statistics, we will first use descriptive
More informationnot to be republished NCERT Measures of Central Tendency
You have learnt in previous chapter that organising and presenting data makes them comprehensible. It facilitates data processing. A number of statistical techniques are used to analyse the data. In this
More informationProceedings  AutoCarto Columbus, Ohio, USA  September 1618, Rajinder S. Nagi
Maintaining detail and color definition when integrating color and grayscale rasters using No Alteration of Grayscale or Intensity (NAGI) fusion method Rajinder S. Nagi ABSTRACT: Integrating color raster
More informationAn introduction to using Microsoft Excel for quantitative data analysis
Contents An introduction to using Microsoft Excel for quantitative data analysis 1 Introduction... 1 2 Why use Excel?... 2 3 Quantitative data analysis tools in Excel... 3 4 Entering your data... 6 5 Preparing
More informationEXPLORING SPATIAL PATTERNS IN YOUR DATA
EXPLORING SPATIAL PATTERNS IN YOUR DATA OBJECTIVES Learn how to examine your data using the Geostatistical Analysis tools in ArcMap. Learn how to use descriptive statistics in ArcMap and Geoda to analyze
More informationDescriptive statistics parameters: Measures of centrality
Descriptive statistics parameters: Measures of centrality Contents Definitions... 3 Classification of descriptive statistics parameters... 4 More about central tendency estimators... 5 Relationship between
More informationThe Big 50 Revision Guidelines for S1
The Big 50 Revision Guidelines for S1 If you can understand all of these you ll do very well 1. Know what is meant by a statistical model and the Modelling cycle of continuous refinement 2. Understand
More informationSummarizing and Displaying Categorical Data
Summarizing and Displaying Categorical Data Categorical data can be summarized in a frequency distribution which counts the number of cases, or frequency, that fall into each category, or a relative frequency
More informationDr. Peter Tröger Hasso Plattner Institute, University of Potsdam. Software Profiling Seminar, Statistics 101
Dr. Peter Tröger Hasso Plattner Institute, University of Potsdam Software Profiling Seminar, 2013 Statistics 101 Descriptive Statistics Population Object Object Object Sample numerical description Object
More informationAP STATISTICS REVIEW (YMS Chapters 18)
AP STATISTICS REVIEW (YMS Chapters 18) Exploring Data (Chapter 1) Categorical Data nominal scale, names e.g. male/female or eye color or breeds of dogs Quantitative Data rational scale (can +,,, with
More informationBusiness Statistics. Successful completion of Introductory and/or Intermediate Algebra courses is recommended before taking Business Statistics.
Business Course Text Bowerman, Bruce L., Richard T. O'Connell, J. B. Orris, and Dawn C. Porter. Essentials of Business, 2nd edition, McGrawHill/Irwin, 2008, ISBN: 9780073319889. Required Computing
More informationLecture 2: Descriptive Statistics and Exploratory Data Analysis
Lecture 2: Descriptive Statistics and Exploratory Data Analysis Further Thoughts on Experimental Design 16 Individuals (8 each from two populations) with replicates Pop 1 Pop 2 Randomly sample 4 individuals
More informationDescriptive Data Summarization
Descriptive Data Summarization (Understanding Data) First: Some data preprocessing problems... 1 Missing Values The approach of the problem of missing values adopted in SQL is based on nulls and threevalued
More informationMultiple regression  Matrices
Multiple regression  Matrices This handout will present various matrices which are substantively interesting and/or provide useful means of summarizing the data for analytical purposes. As we will see,
More information2. Simple Linear Regression
Research methods  II 3 2. Simple Linear Regression Simple linear regression is a technique in parametric statistics that is commonly used for analyzing mean response of a variable Y which changes according
More informationData Mining: Exploring Data. Lecture Notes for Chapter 3. Introduction to Data Mining
Data Mining: Exploring Data Lecture Notes for Chapter 3 Introduction to Data Mining by Tan, Steinbach, Kumar What is data exploration? A preliminary exploration of the data to better understand its characteristics.
More informationDiagrams and Graphs of Statistical Data
Diagrams and Graphs of Statistical Data One of the most effective and interesting alternative way in which a statistical data may be presented is through diagrams and graphs. There are several ways in
More informationGRADES 7, 8, AND 9 BIG IDEAS
Table 1: Strand A: BIG IDEAS: MATH: NUMBER Introduce perfect squares, square roots, and all applications Introduce rational numbers (positive and negative) Introduce the meaning of negative exponents for
More informationWhy Taking This Course? Course Introduction, Descriptive Statistics and Data Visualization. Learning Goals. GENOME 560, Spring 2012
Why Taking This Course? Course Introduction, Descriptive Statistics and Data Visualization GENOME 560, Spring 2012 Data are interesting because they help us understand the world Genomics: Massive Amounts
More informationCHAPTER THREE COMMON DESCRIPTIVE STATISTICS COMMON DESCRIPTIVE STATISTICS / 13
COMMON DESCRIPTIVE STATISTICS / 13 CHAPTER THREE COMMON DESCRIPTIVE STATISTICS The analysis of data begins with descriptive statistics such as the mean, median, mode, range, standard deviation, variance,
More informationProbability and Statistics Vocabulary List (Definitions for Middle School Teachers)
Probability and Statistics Vocabulary List (Definitions for Middle School Teachers) B Bar graph a diagram representing the frequency distribution for nominal or discrete data. It consists of a sequence
More information, then the form of the model is given by: which comprises a deterministic component involving the three regression coefficients (
Multiple regression Introduction Multiple regression is a logical extension of the principles of simple linear regression to situations in which there are several predictor variables. For instance if we
More information