Statistical Analysis I


 Homer Collins
 1 years ago
 Views:
Transcription
1 CTSI BERD Research Methods Seminar Series Statistical Analysis I Lan Kong, PhD Associate Professor Department of Public Health Sciences December 22, 2014
2 Biostatistics, Epidemiology, Research Design(BERD) BERD Goals: Match the needs of investigators to the appropriate biostatisticians/epidemiologists/methodologists Provide BERD support to investigators Offer BERD education to students and investigators via inperson, videoconferenced, and online classes
3 BERD Seminar Series Date Title Presenter Sept. 8 Intro to Clinical Research Designs & Duanping Liao Crosssectional Study Sept. 22 Cohort Study Duanping Liao Oct. 6 Case Control Study Duanping Liao Oct. 20 Matched Case Control Study Duanping Liao Nov. 3 Clinical Trials Vern Chinchilli Nov. 17 Power and Sample Size Allen Kunselman Dec. 8 Data Management Rosanne Pogash Dec. 22 Statistical Analysis 1 (HY only) Lan Kong Jan. 5 Statistical Analysis 2 (HY only) Mosuk Chow Jan. 19 Putting it all together in a research Duanping Liao proposal/protocol Feb. 2 MetaAnalysis Vern Chinchilli
4 Statistics Encompasses Study design Selection of efficient design (cohort study/casecontrol study) Sample size Randomization Data collection Summarizing data Important first step in understanding the data collected Analyzing data to draw conclusions Communicating the results of analyses
5 Keys to Successful Collaboration Between Statistician and Investigator: A TwoWay Street Involve statistician at beginning of project (planning/design phase) Specific objectives Communication avoid jargon willingness to explain details
6 Keys to Successful Collaboration: A TwoWay Street Respect Knowledge Skills Experience Time Embrace statistician as a member of the research team Fund statistician on grant application for best collaboration Most statisticians are supported by grants, not by Institutional funds
7 Statistical Analysis Describing data Numeric or graphic Statistical Inference Estimation of parameters of interest Hypothesis testing Regression modeling Interpretation and presentation of the results
8 Describing data: Basic Terms Measurement assignment of a number to something Data collection of measurements Sample collected data Population all possible data Variable a property or characteristic of the population/sample e.g., gender, weight, blood pressure.
9 Example of data set/sample Data on albumin and bilirubin levels before and after treatment with a study drug ID DRUG BILI ALBUMIN BASE_BIL BASE_ALB
10 Describing Data Types of data Summary measures (numeric) Visually describing data (graphical)
11 Types of Variables Qualitative or Categorical Binary (or dichotomous) True/False, Yes/No Nominal no natural ordering Ethnicity Ordinal Categories have natural ranks Degree of agreement (strong, modest, weak) Size of tumor (small, medium, large) Quantitative Ratio  Ordered, constant scale, natural zero (age, weight) IntervalOrdered, constant scale, no natural zero Differences make sense, but ratios do not Temperature in Celsius (3020 =2010, but 20 /10 is not twice as hot)
12 Types of Measurements for Quantitative Variables Continuous: Weight, Height, Age Discrete: a countable number of values The number of births, Age in years Likert scale: agree, strongly agree, etc. Somewhere between ordinal and discrete Scales with <= 4 possibilities are usually considered to be ordinal. Scales with >=7 possibilities are usually considered to be discrete.
13 Descriptive Statistics Quantitative variable Measure(s) of central location/tendency Mean Median Mode Measure(s) of variability (dispersion) describe the spread of the distribution
14 Descriptive Statistics (cont.) Summary Measures of dispersion/variation Minimum and Maximum Range = Maximum Minimum Sample variances (abbreviated s 2 ) and standard deviation (s or SD) with denominator=n1
15 Other Measures of Variation Interquartile range (IQR): 75 th percentile 25 th percentile MAD: median absolute deviation CV: Coefficient of variation Ratio of SD over sample mean Measure relative variability Independent of measurement units Useful for comparing two or more sets of data
16 Describing data graphically Tell whole story of data, detect outliers Histogram Stem and Leaf Plot Box Plot
17 Histogram 113 men Each bar spans a width of 5 mmhg. The height represents the number of individuals in that range of SBP. Number of Men Systolic BP (mmhg) Divide range of data into intervals (bins) of equal width. Count the number of observations in each class.
18 Histogram of SBP Number of Men Number of Men Systolic BP (mmhg) Systolic BP (mmhg) Bin Width = 20 mmhg Bin Width = 1 mmhg
19 Stem and Leaf Plot Provides a good summary of data structure Easy to construct and much less prone to error than the tally method of finding a histogram stem : the first digit or digits of the number. leaf : the trailing digit.
20 Box Plot: SBP for 113 Males Boxplot of Systolic Blood Pressures Sample of 113 Men Largest Observation 75 th Percentile Sample Median Blood Pressure 25 th Percentile Smallest Observation
21 Descriptive Statistics (cont.) Categorical variable Frequency (counts) distribution Relative frequency (percentages) Pie chart Bar graph
22 Describe relationship between two variables One quantitative and one categorical Descriptive statistics within each category Side by side boxplots/histograms Both quantitative Scatter plot Both categorical Contingency table
23 Statistical Inference A process of making inference (an estimate, prediction, or decision) about a population (parameters) based on a sample (statistics) drawn from that population. Inference Sample Population Percentage Parameters (Fixed, unknown) Statistics (Vary from sample to sample) Number of Men Systolic BP (mmhg) Systolic BP (mmhg)
24 Statistical Inference Questions to ask in selecting appropriate methods Are observation units independent? How many variables are of interest? Type and distribution of variable(s)? Onesample or twosample problem? Are samples independent? Parameters of interest (mean, variance, proportion)? Sample size sufficient for the chosen method? (see decision making flow chart in the handout)
25 Estimation of population mean We don t know the population mean μ but would like to know it. We draw a sample from the population. We calculate the sample mean X. How close is X to μ? Statistical theory will tell us how close X is to μ. Statistical inference is the process of trying to draw conclusions about the population from the sample.
26 Key Statistical Concept Question: How close is the sample mean to the population mean? Statistical Inference for sample mean Sample mean will change from sample to sample We need a statistical model to quantify the distribution of sample means (Sampling distribution) Assume normal distribution for the population data
27 Normal Distribution Normal distribution, denoted by N(µ, σ 2 ), is characterized by two parameters µ: The mean is the center. σ: The standard deviation measures the spread (variability). Probability density function Standard Deviation Standard Deviation Mean Mean
28 Distribution of Blood Pressure in Men (population) % 95% 99.7% Y: Blood pressure Y~ N(µ, σ 2 ) Parameters: Mean, µ= 125 mmhg SD, σ = 14 mmhg The rule for normal distribution applied to the distribution of systolic blood pressure in men.
29 Sampling Distribution The sampling distribution refers to the distribution of the sample statistics (e.g. sample means) over all possible samples of size n that could have been selected from the study population. If the population data follow normal distribution N(µ, σ 2 ), then the sample means follow normal distribution N(µ, σ 2 /n). What if the population data do not come from normal distribution?
30 Central Limit Theorem (CLT) If the sample size is large, the distribution of sample means approximates a normal distribution. X ~ N(µ, σ 2 /n) The Central Limit Theorem works even when the population is not normally distributed (or even not continuous).http://onlinestatbook.com/stat_sim/sampling_dist/index.h tml For sample means, the standard rule is n > 60 for the Central Limit Theorem to kick in, depending on how abnormal the population distribution is. 60 is a worstcase scenario.
31 Sampling Distribution By CLT, about 95% of the time, the sample mean will be within two standard errors of the population mean. This tells us how close the sample statistic should be to the population parameter. Standard errors (SE) measure the precision of your sample statistic. A small SE means it is more precise. The SE is the standard deviation of the sampling distribution of the statistic.
32 Standard Error of Sample Mean The standard error of sample mean (SEM) is a measure of the precision of the sample mean. SEM = σ n σ: standard deviation (SD) of population distribution. The standard deviation is no the standard error of a statistic!
33 Example Measure systolic blood pressure on random sample of 100 students Sample size n = 100 Sample mean x = 125 mm Hg Sample SD s = 14.0 mm Hg SEM = 14 = mmhg Population SD (σ) can be replaced by sample SD for large sample
34 Confidence Interval for population mean An approximate 95% confidence interval for population mean µ is: X ± 2 SEM or precisely X is a random variable (vary from sample to sample), so confidence interval is random and it has 95% chance of covering µ before a sample is selected. Once a sample is taken, we observe X = x, then either µ is within the calculated interval or it is not. The confidence interval gives the range of plausible values for µ.
F. 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 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 informationExploratory data analysis (Chapter 2) Fall 2011
Exploratory data analysis (Chapter 2) Fall 2011 Data Examples Example 1: Survey Data 1 Data collected from a Stat 371 class in Fall 2005 2 They answered questions about their: gender, major, year in school,
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 informationStatistics I for QBIC. Contents and Objectives. Chapters 1 7. Revised: August 2013
Statistics I for QBIC Text Book: Biostatistics, 10 th edition, by Daniel & Cross Contents and Objectives Chapters 1 7 Revised: August 2013 Chapter 1: Nature of Statistics (sections 1.11.6) Objectives
More informationWhat is Statistics? Statistics is about Collecting data Organizing data Analyzing data Presenting data
Introduction What is Statistics? Statistics is about Collecting data Organizing data Analyzing data Presenting data What is Statistics? Statistics is divided into two areas: descriptive statistics and
More informationMTH 140 Statistics Videos
MTH 140 Statistics Videos Chapter 1 Picturing Distributions with Graphs Individuals and Variables Categorical Variables: Pie Charts and Bar Graphs Categorical Variables: Pie Charts and Bar Graphs Quantitative
More informationNorthumberland Knowledge
Northumberland Knowledge Know Guide How to Analyse Data  November 2012  This page has been left blank 2 About this guide The Know Guides are a suite of documents that provide useful information about
More information4. Introduction to Statistics
Statistics for Engineers 41 4. Introduction to Statistics Descriptive Statistics Types of data A variate or random variable is a quantity or attribute whose value may vary from one unit of investigation
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 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 informationCentral Tendency. n Measures of Central Tendency: n Mean. n Median. n Mode
Central Tendency Central Tendency n A single summary score that best describes the central location of an entire distribution of scores. n Measures of Central Tendency: n Mean n The sum of all scores divided
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 informationGraphical and Tabular. Summarization of Data OPRE 6301
Graphical and Tabular Summarization of Data OPRE 6301 Introduction and Recap... Descriptive statistics involves arranging, summarizing, and presenting a set of data in such a way that useful information
More informationDescriptive statistics Statistical inference statistical inference, statistical induction and inferential statistics
Descriptive statistics is the discipline of quantitatively describing the main features of a collection of data. Descriptive statistics are distinguished from inferential statistics (or inductive statistics),
More informationVariables. Exploratory Data Analysis
Exploratory Data Analysis Exploratory Data Analysis involves both graphical displays of data and numerical summaries of data. A common situation is for a data set to be represented as a matrix. There is
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 informationII. DISTRIBUTIONS distribution normal distribution. standard scores
Appendix D Basic Measurement And Statistics The following information was developed by Steven Rothke, PhD, Department of Psychology, Rehabilitation Institute of Chicago (RIC) and expanded by Mary F. Schmidt,
More informationHistogram. Graphs, and measures of central tendency and spread. Alternative: density (or relative frequency ) plot /13/2004
Graphs, and measures of central tendency and spread 9.07 9/13/004 Histogram If discrete or categorical, bars don t touch. If continuous, can touch, should if there are lots of bins. Sum of bin heights
More informationVariables and Data A variable contains data about anything we measure. For example; age or gender of the participants or their score on a test.
The Analysis of Research Data The design of any project will determine what sort of statistical tests you should perform on your data and how successful the data analysis will be. For example if you decide
More informationIntroductory Statistics Notes
Introductory Statistics Notes Jamie DeCoster Department of Psychology University of Alabama 348 Gordon Palmer Hall Box 870348 Tuscaloosa, AL 354870348 Phone: (205) 3484431 Fax: (205) 3488648 August
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 informationOutline of Topics. Statistical Methods I. Types of Data. Descriptive Statistics
Statistical Methods I Tamekia L. Jones, Ph.D. (tjones@cog.ufl.edu) Research Assistant Professor Children s Oncology Group Statistics & Data Center Department of Biostatistics Colleges of Medicine and Public
More informationSample Exam #1 Elementary Statistics
Sample Exam #1 Elementary Statistics Instructions. No books, notes, or calculators are allowed. 1. Some variables that were recorded while studying diets of sharks are given below. Which of the variables
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 informationChapter 1: Looking at Data Section 1.1: Displaying Distributions with Graphs
Types of Variables Chapter 1: Looking at Data Section 1.1: Displaying Distributions with Graphs Quantitative (numerical)variables: take numerical values for which arithmetic operations make sense (addition/averaging)
More information1.5 NUMERICAL REPRESENTATION OF DATA (Sample Statistics)
1.5 NUMERICAL REPRESENTATION OF DATA (Sample Statistics) As well as displaying data graphically we will often wish to summarise it numerically particularly if we wish to compare two or more data sets.
More information1 Measures for location and dispersion of a sample
Statistical Geophysics WS 2008/09 7..2008 Christian Heumann und Helmut Küchenhoff Measures for location and dispersion of a sample Measures for location and dispersion of a sample In the following: Variable
More informationGood luck! BUSINESS STATISTICS FINAL EXAM INSTRUCTIONS. Name:
Glo bal Leadership M BA BUSINESS STATISTICS FINAL EXAM Name: INSTRUCTIONS 1. Do not open this exam until instructed to do so. 2. Be sure to fill in your name before starting the exam. 3. You have two hours
More information2 Descriptive statistics with R
Biological data analysis, Tartu 2006/2007 1 2 Descriptive statistics with R Before starting with basic concepts of data analysis, one should be aware of different types of data and ways to organize data
More informationDongfeng Li. Autumn 2010
Autumn 2010 Chapter Contents Some statistics background; ; Comparing means and proportions; variance. Students should master the basic concepts, descriptive statistics measures and graphs, basic hypothesis
More information430 Statistics and Financial Mathematics for Business
Prescription: 430 Statistics and Financial Mathematics for Business Elective prescription Level 4 Credit 20 Version 2 Aim Students will be able to summarise, analyse, interpret and present data, make predictions
More informationData Types. 1. Continuous 2. Discrete quantitative 3. Ordinal 4. Nominal. Figure 1
Data Types By Tanya Hoskin, a statistician in the Mayo Clinic Department of Health Sciences Research who provides consultations through the Mayo Clinic CTSA BERD Resource. Don t let the title scare you.
More informationAP Statistics Chapter 1 Test  Multiple Choice
AP Statistics Chapter 1 Test  Multiple Choice Name: 1. The following bar graph gives the percent of owners of three brands of trucks who are satisfied with their truck. From this graph, we may conclude
More informationWeek 1. Exploratory Data Analysis
Week 1 Exploratory Data Analysis Practicalities This course ST903 has students from both the MSc in Financial Mathematics and the MSc in Statistics. Two lectures and one seminar/tutorial per week. Exam
More informationBasics and Beyond: Displaying Your Data. Mario Davidson, PhD Vanderbilt University School of Medicine Department of Biostatistics Instructor
Basics and Beyond: Displaying Your Data Mario Davidson, PhD Vanderbilt University School of Medicine Department of Biostatistics Instructor Objectives 1.Understand the types of data and levels of measurement
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 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 informationThe Big Picture. Describing Data: Categorical and Quantitative Variables Population. Descriptive Statistics. Community Coalitions (n = 175)
Describing Data: Categorical and Quantitative Variables Population The Big Picture Sampling Statistical Inference Sample Exploratory Data Analysis Descriptive Statistics In order to make sense of data,
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 informationUsing SPSS, Chapter 2: Descriptive Statistics
1 Using SPSS, Chapter 2: Descriptive Statistics Chapters 2.1 & 2.2 Descriptive Statistics 2 Mean, Standard Deviation, Variance, Range, Minimum, Maximum 2 Mean, Median, Mode, Standard Deviation, Variance,
More informationImplications of Big Data for Statistics Instruction 17 Nov 2013
Implications of Big Data for Statistics Instruction 17 Nov 2013 Implications of Big Data for Statistics Instruction Mark L. Berenson Montclair State University MSMESB Mini Conference DSI Baltimore November
More informationa. mean b. interquartile range c. range d. median
3. Since 4. The HOMEWORK 3 Due: Feb.3 1. A set of data are put in numerical order, and a statistic is calculated that divides the data set into two equal parts with one part below it and the other part
More informationThe right edge of the box is the third quartile, Q 3, which is the median of the data values above the median. Maximum Median
CONDENSED LESSON 2.1 Box Plots In this lesson you will create and interpret box plots for sets of data use the interquartile range (IQR) to identify potential outliers and graph them on a modified box
More informationStatistics Review PSY379
Statistics Review PSY379 Basic concepts Measurement scales Populations vs. samples Continuous vs. discrete variable Independent vs. dependent variable Descriptive vs. inferential stats Common analyses
More informationBNG 202 Biomechanics Lab. Descriptive statistics and probability distributions I
BNG 202 Biomechanics Lab Descriptive statistics and probability distributions I Overview The overall goal of this short course in statistics is to provide an introduction to descriptive and inferential
More informationLecture 1: Review and Exploratory Data Analysis (EDA)
Lecture 1: Review and Exploratory Data Analysis (EDA) Sandy Eckel seckel@jhsph.edu Department of Biostatistics, The Johns Hopkins University, Baltimore USA 21 April 2008 1 / 40 Course Information I Course
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 informationSPSS for Exploratory Data Analysis Data used in this guide: studentp.sav (http://people.ysu.edu/~gchang/stat/studentp.sav)
Data used in this guide: studentp.sav (http://people.ysu.edu/~gchang/stat/studentp.sav) Organize and Display One Quantitative Variable (Descriptive Statistics, Boxplot & Histogram) 1. Move the mouse pointer
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 informationMeans, standard deviations and. and standard errors
CHAPTER 4 Means, standard deviations and standard errors 4.1 Introduction Change of units 4.2 Mean, median and mode Coefficient of variation 4.3 Measures of variation 4.4 Calculating the mean and standard
More informationWhat are Data? The Research Question (Randomised Controlled Trials (RCTs)) The Research Question (Non RCTs)
What are Data? Quantitative Data o Sets of measurements of objective descriptions of physical and behavioural events; susceptible to statistical analysis Qualitative data o Descriptive, views, actions
More informationFairfield Public Schools
Mathematics Fairfield Public Schools AP Statistics AP Statistics BOE Approved 04/08/2014 1 AP STATISTICS Critical Areas of Focus AP Statistics is a rigorous course that offers advanced students an opportunity
More informationSTA201TE. 5. Measures of relationship: correlation (5%) Correlation coefficient; Pearson r; correlation and causation; proportion of common variance
Principles of Statistics STA201TE This TECEP is an introduction to descriptive and inferential statistics. Topics include: measures of central tendency, variability, correlation, regression, hypothesis
More informationList of Examples. Examples 319
Examples 319 List of Examples DiMaggio and Mantle. 6 Weed seeds. 6, 23, 37, 38 Vole reproduction. 7, 24, 37 Wooly bear caterpillar cocoons. 7 Homophone confusion and Alzheimer s disease. 8 Gear tooth strength.
More informationDESCRIPTIVE STATISTICS AND EXPLORATORY DATA ANALYSIS
DESCRIPTIVE STATISTICS AND EXPLORATORY DATA ANALYSIS SEEMA JAGGI Indian Agricultural Statistics Research Institute Library Avenue, New Delhi  110 012 seema@iasri.res.in 1. Descriptive Statistics Statistics
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 informationFoundation of Quantitative Data Analysis
Foundation of Quantitative Data Analysis Part 1: Data manipulation and descriptive statistics with SPSS/Excel HSRS #10  October 17, 2013 Reference : A. Aczel, Complete Business Statistics. Chapters 1
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 informationInstitute of Actuaries of India Subject CT3 Probability and Mathematical Statistics
Institute of Actuaries of India Subject CT3 Probability and Mathematical Statistics For 2015 Examinations Aim The aim of the Probability and Mathematical Statistics subject is to provide a grounding in
More informationTreatment and analysis of data Applied statistics Lecture 3: Sampling and descriptive statistics
Treatment and analysis of data Applied statistics Lecture 3: Sampling and descriptive statistics Topics covered: Parameters and statistics Sample mean and sample standard deviation Order statistics and
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 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 informationIntroduction to Statistics for Psychology. Quantitative Methods for Human Sciences
Introduction to Statistics for Psychology and Quantitative Methods for Human Sciences Jonathan Marchini Course Information There is website devoted to the course at http://www.stats.ox.ac.uk/ marchini/phs.html
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 informationVisualizing Data. Contents. 1 Visualizing Data. Anthony Tanbakuchi Department of Mathematics Pima Community College. Introductory Statistics Lectures
Introductory Statistics Lectures Visualizing Data Descriptive Statistics I Department of Mathematics Pima Community College Redistribution of this material is prohibited without written permission of the
More informationThe Ordered Array. Chapter Chapter Goals. Organizing and Presenting Data Graphically. Before you continue... Stem and Leaf Diagram
Chapter  Chapter Goals After completing this chapter, you should be able to: Construct a frequency distribution both manually and with Excel Construct and interpret a histogram Chapter Presenting Data
More informationStatistics and research
Statistics and research Usaneya Perngparn Chitlada Areesantichai Drug Dependence Research Center (WHOCC for Research and Training in Drug Dependence) College of Public Health Sciences Chulolongkorn University,
More informationCurriculum Map Statistics and Probability Honors (348) Saugus High School Saugus Public Schools 20092010
Curriculum Map Statistics and Probability Honors (348) Saugus High School Saugus Public Schools 20092010 Week 1 Week 2 14.0 Students organize and describe distributions of data by using a number of different
More information1.3 Measuring Center & Spread, The Five Number Summary & Boxplots. Describing Quantitative Data with Numbers
1.3 Measuring Center & Spread, The Five Number Summary & Boxplots Describing Quantitative Data with Numbers 1.3 I can n Calculate and interpret measures of center (mean, median) in context. n Calculate
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 informationDescribing, Exploring, and Comparing Data
24 Chapter 2. Describing, Exploring, and Comparing Data Chapter 2. Describing, Exploring, and Comparing Data There are many tools used in Statistics to visualize, summarize, and describe data. This chapter
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 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 informationDESCRIPTIVE STATISTICS  CHAPTERS 1 & 2 1
DESCRIPTIVE STATISTICS  CHAPTERS 1 & 2 1 OVERVIEW STATISTICS PANIK...THE THEORY AND METHODS OF COLLECTING, ORGANIZING, PRESENTING, ANALYZING, AND INTERPRETING DATA SETS SO AS TO DETERMINE THEIR ESSENTIAL
More informationDescriptive Statistics. Purpose of descriptive statistics Frequency distributions Measures of central tendency Measures of dispersion
Descriptive Statistics Purpose of descriptive statistics Frequency distributions Measures of central tendency Measures of dispersion Statistics as a Tool for LIS Research Importance of statistics in research
More informationBiostatistics: A QUICK GUIDE TO THE USE AND CHOICE OF GRAPHS AND CHARTS
Biostatistics: A QUICK GUIDE TO THE USE AND CHOICE OF GRAPHS AND CHARTS 1. Introduction, and choosing a graph or chart Graphs and charts provide a powerful way of summarising data and presenting them in
More informationChapter 2  Graphical Summaries of Data
Chapter 2  Graphical Summaries of Data Data recorded in the sequence in which they are collected and before they are processed or ranked are called raw data. Raw data is often difficult to make sense
More informationQuantitative or Qualitative?
2.1 Data: and Levels of Measurement 1 Quantitative or Qualitative?! Quantitative data consist of values representing counts or measurements " Variable: Year in school! Qualitative (or nonnumeric) data
More informationDescriptive Statistics and Measurement Scales
Descriptive Statistics 1 Descriptive Statistics and Measurement Scales Descriptive statistics are used to describe the basic features of the data in a study. They provide simple summaries about the sample
More informationData Mining Techniques Chapter 5: The Lure of Statistics: Data Mining Using Familiar Tools
Data Mining Techniques Chapter 5: The Lure of Statistics: Data Mining Using Familiar Tools Occam s razor.......................................................... 2 A look at data I.........................................................
More informationModule 2: Introduction to Quantitative Data Analysis
Module 2: Introduction to Quantitative Data Analysis Contents Antony Fielding 1 University of Birmingham & Centre for Multilevel Modelling Rebecca Pillinger Centre for Multilevel Modelling Introduction...
More informationGraphing Data Presentation of Data in Visual Forms
Graphing Data Presentation of Data in Visual Forms Purpose of Graphing Data Audience Appeal Provides a visually appealing and succinct representation of data and summary statistics Provides a visually
More informationCenter: Finding the Median. Median. Spread: Home on the Range. Center: Finding the Median (cont.)
Center: Finding the Median When we think of a typical value, we usually look for the center of the distribution. For a unimodal, symmetric distribution, it s easy to find the center it s just the center
More informationSampling Distribution of a Normal Variable
Ismor Fischer, 5/9/01 5.1 5. Formal Statement and Examples Comments: Sampling Distribution of a Normal Variable Given a random variable. Suppose that the population distribution of is known to be normal,
More informationCA200 Quantitative Analysis for Business Decisions. File name: CA200_Section_04A_StatisticsIntroduction
CA200 Quantitative Analysis for Business Decisions File name: CA200_Section_04A_StatisticsIntroduction Table of Contents 4. Introduction to Statistics... 1 4.1 Overview... 3 4.2 Discrete or continuous
More informationIntroduction to Statistics and Quantitative Research Methods
Introduction to Statistics and Quantitative Research Methods Purpose of Presentation To aid in the understanding of basic statistics, including terminology, common terms, and common statistical methods.
More informationCourse Text. Required Computing Software. Course Description. Course Objectives. StraighterLine. Business Statistics
Course Text Business Statistics Lind, Douglas A., Marchal, William A. and Samuel A. Wathen. Basic Statistics for Business and Economics, 7th edition, McGrawHill/Irwin, 2010, ISBN: 9780077384470 [This
More informationIntro to Statistics 8 Curriculum
Intro to Statistics 8 Curriculum Unit 1 Bar, Line and Circle Graphs Estimated time frame for unit Big Ideas 8 Days... Essential Question Concepts Competencies Lesson Plans and Suggested Resources Bar graphs
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 informationElementary Statistics
Elementary Statistics Chapter 1 Dr. Ghamsary Page 1 Elementary Statistics M. Ghamsary, Ph.D. Chap 01 1 Elementary Statistics Chapter 1 Dr. Ghamsary Page 2 Statistics: Statistics is the science of collecting,
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 informationMATH 103/GRACEY PRACTICE EXAM/CHAPTERS 23. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
MATH 3/GRACEY PRACTICE EXAM/CHAPTERS 23 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Provide an appropriate response. 1) The frequency distribution
More informationDescriptive Statistics and Exploratory Data Analysis
Descriptive Statistics and Exploratory Data Analysis Dean s s Faculty and Resident Development Series UT College of Medicine Chattanooga Probasco Auditorium at Erlanger January 14, 2008 Marc Loizeaux,
More informationChapter 2: Frequency Distributions and Graphs
Chapter 2: Frequency Distributions and Graphs Learning Objectives Upon completion of Chapter 2, you will be able to: Organize the data into a table or chart (called a frequency distribution) Construct
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 informationThere are some general common sense recommendations to follow when presenting
Presentation of Data The presentation of data in the form of tables, graphs and charts is an important part of the process of data analysis and report writing. Although results can be expressed within
More informationOrganizing Your Approach to a Data Analysis
Biost/Stat 578 B: Data Analysis Emerson, September 29, 2003 Handout #1 Organizing Your Approach to a Data Analysis The general theme should be to maximize thinking about the data analysis and to minimize
More informationPie Charts. proportion of icecream flavors sold annually by a given brand. AMS5: Statistics. Cherry. Cherry. Blueberry. Blueberry. Apple.
Graphical Representations of Data, Mean, Median and Standard Deviation In this class we will consider graphical representations of the distribution of a set of data. The goal is to identify the range of
More information2.0 Lesson Plan. Answer Questions. Summary Statistics. Histograms. The Normal Distribution. Using the Standard Normal Table
2.0 Lesson Plan Answer Questions 1 Summary Statistics Histograms The Normal Distribution Using the Standard Normal Table 2. Summary Statistics Given a collection of data, one needs to find representations
More information