# Why Taking This Course? Course Introduction, Descriptive Statistics and Data Visualization. Learning Goals. GENOME 560, Spring 2012

Save this PDF as:

Size: px
Start display at page:

Download "Why Taking This Course? Course Introduction, Descriptive Statistics and Data Visualization. Learning Goals. GENOME 560, Spring 2012"

## Transcription

1 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 of Data Data Statistics is fundamental in genomics because it is integral in the design, analysis and interpretation of experimental data What does this mean? Su In Lee, CSE & GS 1 2 Why Taking This Course? Data are interesting because they help us understand the world Genomics: Massive Amounts of Data Data Statistics is fundamental in genomics because it is integral in the design, analysis and interpretation of experimental data This course covers the key statistical concepts and methods necessary for extracting biological insights from experimental data Learning Goals 5 weeks is too short to cover every specific topic that might arise in the course of your research It is not a good strategy to treat what we learn in this course as recipes to follow Instead, we should focus on rigorous understanding of fundamental concepts that will provide you with the tools necessary to address routine statistical analyses foundation to understand and learn mode specific topics 3 4 1

2 Course Schedule Syllabus: Date May 1 May 3 May 8 May 10 May 15 May 17 May 22 May 24 May 29 May 31 Topic Descriptive Statistics and Data Visualization Random Variables and Probability Theories Probability Distributions Parameter Estimation Regression Methods Hypothesis testing I t test, confidence interval Hypothesis testing II ANOVA Hypothesis testing III Analysis of Categorical Data Bootstrapping, cross validation and permutation tests Assessing significance in high dimensional experiments Special topics that may be discussed in class include Bayesian networks, Expectation Maximization (EM) algorithm, principal component analysis Grading: 5 problem sets (20% each) 5 Books and Resources Course website No required text Good on line resources Some good books if you ever have some extra \$\$\$: Probability and Statistics for Engineering and the Scientists 6th Ed. Jay L. Devore (2004). Duxbury press, Thompson Brooks/Cole. Statistical Inference. Casella, G. and Berger, R. L. (1990). Wadsworth, Belmont, CA. Probabilistic Graphical Models: Principles and Techniques. Koller, D. and Friedman, N. (2009). MIT Press. 6 Class Meetings What is R? Class meets twice a week Tue/Thu 9 Foege S110 Each class will last for 80 minutes and be primarily lecture based The R statistical programming language is a free open source package based on the S language developed by Bell Labs May statistical functions are already built in Other forms of learning and interactions will be included Contributed packages expand the functionality to cutting edge research We will often interrupt lectures to work on problems in small groups as well as work through statistical analyses using R (please bring a laptop with R installed!) Amazing graphics Widely used in genetics, genomics, computational biology 7 8 2

3 R Resources Windows, Mac and Linux binaries available at project.org Lecture 1: Descriptive Statistics and Data Visualization Extensive resources at the above web site, in particular see: project.org/other docs.html 9 10 Outline What is descriptive statistics and exploratory data analysis? Why Descriptive/Graphical Summary? Before making inferences from data, it is essential to examine all your variables Basic numeral summaries of data Why? Basic graphical summaries of data Basic operations in R (If time permits) How to use R for calculating descriptive statistics and making graphs 11 To listen to the data: to catch mistakes to see patterns in the data to find violations of statistical assumptions to generate hypotheses and because if you don t, you will have trouble later 12 3

4 Types of Data Categorical Binary: 2 categories Nominal: more categories Ordinal: order matters E.g. gender, ethnicity, disease state, genotypes, etc Continuous (or Quantitative) Numeric values that can be ordered sequentially, and that do not naturally fall into discrete ranges. E.g. weight, number of seconds it takes to perform a task, gene expression levels, etc Dimensionality of Data Sets Univariate: Measurement made on one variable per subject Bivariate: Measurement made on two variables per subject Multivariate: Measurement made on many variables per subject Numerical Summaries of Data Central tendency measures. They are computed to give a center around which the measurements in the data are distributed. Central Tendency Measures: Mean To calculate the mean of a set of observations, add their value and divide by the number of observations: Variation or variability measures. They describe data spread or how far away the measurements are from the center. Relative standing measures. They describe the relative position of specific measurements in the data

5 Central Tendency Measures: Median Median: the exact middle value Calculation: If there are an odd number of observations, find the middle value If there are an even number of observations, find the middle two values and average them Which Measure Is Best? Mean is best for symmetric distributions without outliers Median is useful for skewed distributions or data with outliers Example: Some data: Age of participants: Median = (22+23)/2 = Scale: Variance Average of squared deviation of values from the mean Why Squared Deviations? Squares eliminate the negatives Absolute values do not have nice mathematical properties Result: Increasing contribution to the variance as you go farther from the mean

6 Why Divide By (n 1), not n? Why Divide By (n 1), not n? Empirical mean True mean You compute the difference between each observation and the mean of all n observations. You don t know the true mean of the population; all you know is the mean of your samples (empirical mean) Except for the rare cases where the sample mean happens to equal the population mean, the data will be closer to the sample mean than it will be to the true population mean. So the numerator will probably be a bit smaller (and can t be larger) than what it would be if you used the true mean. Biased estimator of the population variance 21 Empirical mean True mean To make up for this divide by (n 1) rather than n. Unbiased estimator of the population variance If you knew the sample mean, and all but one of the values, you could calculate what that last value must be. Statisticians say there are n 1 degrees of freedom. 22 Scale: Standard Deviation Variance is somewhat arbitrary What does it mean to have a variance of 10.8? Or 2.2? Or ? Or ? Scale: Standard Deviation Most commonly used measure of variation Shows variation about the mean Has the same units as the original data Nothing. But if you could standardize that value, you could talk about any variance (i.e. deviation) in equivalent terms Standard deviations are simply the square root of the variance

7 Interesting Theoretical Result Regardless of how the data are distributed, a certain percentage of values must fall within k standard deviations from the mean Often We Can Do Better For many lists of observations, especially if their histogram is bell shaped Roughly 68% of the observations in the list lie within 1 σ (standard deviation) of the average 95% of the observations lie within 2σ of the average Scale: Quartiles and IQR Percentiles (aka Quantiles) In general the n th percentile is a value such that n% of the observations fall at or below of it The first quartile, Q 1, is the value for which 25% of the observations are smaller and 75% are larger Q 2 is the same as the median (50% are smaller, 50% are larger) Only 25% of the observations are greater than the Q 3 27 Q 1 = 25 th percentile Median = 50 th percentile Q 2 = 75 th percentile 28 7

8 Graphical Summaries of Data Dimensionality of data matters Univariate: Measurement made on one variable per subject Multivariate: Measurement made on many variables per subject Univariate Data Histograms and bar plots What is the difference between a histogram and bar plot? Bar plot: Used for categorical variables to show frequency or proportion in each category Translate the data from frequency tables into a pictorial presentation Histogram: Used to visualize distribution (shape, center, range, variation) of continuous variables Bin size is important Effect of Bin Size on Histogram Simulated 1,000 N(0,1) and 500 N(1,1) More on Histograms What s the difference between a frequency histogram and a density histogram?

9 Box Plots Multivariate Data Clustering Organize variables into clusters Descriptive, not inferential Many approaches Clusters always produced Data reduction approaches Reduce n dimensional dataset into much smaller number Finds a new (smaller) set of variables that retains most of the information in the total sample Effective way to visualize multivariate data How to Make a Bad Graph Example 1 The aim of good data graphics: Display data accurately and clearly Some rules for displaying data badly: Display as little information as possible Obscure what you do show (with chart junk) Use pseudo 3d and color gratuitously Make a pie chart (preferably in color and 3d) Use a poorly chosen scale

10 Example 2 Example Example 4 Goals of Our R Tutorial Today Installing R Using R as a fancy calculator Data structures: scalars, vectors, data frames, matrices Reading in data from a file Subsetting and extracting data Writing and executing simple R scripts

11 Probabilities Probabilities Event Variable XXP(S)P(S) P(S)loglog Probability Statistical independence Joint probability 41 Probabilities of mutually independent events are summed Pr(adie comesup2or 3) = Pr(comes up 2) + Pr(comes up 3) = 1/ 6 + 1/ 6 = 1/ 3 Probabilities of independent events are multiplied to get the joint probability Pr(one die comesup2and theother one comesup 3) = Pr(first one comesup 2) + Pr(secondone comesup 3) = 1/ 6 + 1/ 6 = 1/ 3 Conditional probabilities are the joint probability divided by the probability of the event that they are conditioned on: P ( D S) = P( D S ) P( S) d 42 Goals of Our R Tutorial Today Installing R Using R as a fancy calculator P ( D S) P( D S, ) P( S) d Data structures: scalars, vectors, data frames, matrices Reading in data from a file Subsetting and extracting data Writing and executing simple R scripts

12 Some Jargon Units: the basic objects on which the experiment is done Variable: a measured characteristic of a unit Treatment: any specific experimental condition applied to the units. A treatment can be a combination of specific values (called levels) of each experimental factor 45 12

### Lecture 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

### BNG 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

### STATS8: 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

### Exploratory Data Analysis

Exploratory Data Analysis Johannes Schauer johannes.schauer@tugraz.at Institute of Statistics Graz University of Technology Steyrergasse 17/IV, 8010 Graz www.statistics.tugraz.at February 12, 2008 Introduction

### Mathematics. 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

### Dr. 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

### Describe what is meant by a placebo Contrast the double-blind procedure with the single-blind 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

### 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

### Lecture 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

### BASIC STATISTICAL METHODS FOR GENOMIC DATA ANALYSIS

BASIC STATISTICAL METHODS FOR GENOMIC DATA ANALYSIS SEEMA JAGGI Indian Agricultural Statistics Research Institute Library Avenue, New Delhi-110 012 seema@iasri.res.in Genomics A genome is an organism s

### Exploratory 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,

### 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

### Business 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, McGraw-Hill/Irwin, 2008, ISBN: 978-0-07-331988-9. Required Computing

### Statistics 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 1.1-1.6) Objectives

### Research 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.

### Variables. 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

### A Correlation of. to the. South Carolina Data Analysis and Probability Standards

A Correlation of to the South Carolina Data Analysis and Probability Standards INTRODUCTION This document demonstrates how Stats in Your World 2012 meets the indicators of the South Carolina Academic Standards

### Fairfield 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

### Northumberland 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

### Data 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

### Exercise 1.12 (Pg. 22-23)

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.

### Descriptive 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),

### 10-3 Measures of Central Tendency and Variation

10-3 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.

### Course 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, McGraw-Hill/Irwin, 2010, ISBN: 9780077384470 [This

### II. 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,

### Week 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

### Chapter 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,

### Quantitative Methods for Finance

Quantitative Methods for Finance Module 1: The Time Value of Money 1 Learning how to interpret interest rates as required rates of return, discount rates, or opportunity costs. 2 Learning how to explain

### Introduction 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

### Exploratory Data Analysis. Psychology 3256

Exploratory Data Analysis Psychology 3256 1 Introduction If you are going to find out anything about a data set you must first understand the data Basically getting a feel for you numbers Easier to find

### 3: Summary Statistics

3: Summary Statistics Notation Let s start by introducing some notation. Consider the following small data set: 4 5 30 50 8 7 4 5 The symbol n represents the sample size (n = 0). The capital letter X denotes

### 1.3 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

### Chapter 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

### Numerical 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

### Statistics 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

### Probability 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

### The 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

### 4.1 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

### The 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

### 430 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

### Introduction 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.................

### Geostatistics Exploratory Analysis

Instituto Superior de Estatística e Gestão de Informação Universidade Nova de Lisboa Master of Science in Geospatial Technologies Geostatistics Exploratory Analysis Carlos Alberto Felgueiras cfelgueiras@isegi.unl.pt

### Curriculum Map Statistics and Probability Honors (348) Saugus High School Saugus Public Schools 2009-2010

Curriculum Map Statistics and Probability Honors (348) Saugus High School Saugus Public Schools 2009-2010 Week 1 Week 2 14.0 Students organize and describe distributions of data by using a number of different

### EXPLORING 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

### We will use the following data sets to illustrate measures of center. DATA SET 1 The following are test scores from a class of 20 students:

MODE The mode of the sample is the value of the variable having the greatest frequency. Example: Obtain the mode for Data Set 1 77 For a grouped frequency distribution, the modal class is the class having

### Section Format Day Begin End Building Rm# Instructor. 001 Lecture Tue 6:45 PM 8:40 PM Silver 401 Ballerini

NEW YORK UNIVERSITY ROBERT F. WAGNER GRADUATE SCHOOL OF PUBLIC SERVICE Course Syllabus Spring 2016 Statistical Methods for Public, Nonprofit, and Health Management Section Format Day Begin End Building

### Chapter 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

### Data, Measurements, Features

Data, Measurements, Features Middle East Technical University Dep. of Computer Engineering 2009 compiled by V. Atalay What do you think of when someone says Data? We might abstract the idea that data are

### Lecture 2. Summarizing the Sample

Lecture 2 Summarizing the Sample WARNING: Today s lecture may bore some of you It s (sort of) not my fault I m required to teach you about what we re going to cover today. I ll try to make it as exciting

### 4. Introduction to Statistics

Statistics for Engineers 4-1 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

### Data 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

EC151.02 Statistics for Business and Economics (MWF 8:00-8:50) Instructor: Chiu Yu Ko Office: 462D, 21 Campenalla Way Phone: 2-6093 Email: kocb@bc.edu Office Hours: by appointment Description This course

### List 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.

### Describing 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

### What is Data Analysis. Kerala School of MathematicsCourse in Statistics for Scientis. Introduction to Data Analysis. Steps in a Statistical Study

Kerala School of Mathematics Course in Statistics for Scientists Introduction to Data Analysis T.Krishnan Strand Life Sciences, Bangalore What is Data Analysis Statistics is a body of methods how to use

### Module 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

### 1 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

### Organizing 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

### GCSE Statistics Revision notes

GCSE Statistics Revision notes Collecting data Sample This is when data is collected from part of the population. There are different methods for sampling Random sampling, Stratified sampling, Systematic

### MTH 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

### Diagrams 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

### MAT 12O ELEMENTARY STATISTICS I

LAGUARDIA COMMUNITY COLLEGE CITY UNIVERSITY OF NEW YORK DEPARTMENT OF MATHEMATICS, ENGINEERING, AND COMPUTER SCIENCE MAT 12O ELEMENTARY STATISTICS I 3 Lecture Hours, 1 Lab Hour, 3 Credits Pre-Requisite:

### Statistical Foundations: Measures of Location and Central Tendency and Summation and Expectation

Statistical Foundations: and Central Tendency and and Lecture 4 September 5, 2006 Psychology 790 Lecture #4-9/05/2006 Slide 1 of 26 Today s Lecture Today s Lecture Where this Fits central tendency/location

### Variables 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

### The 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,

### Foundation 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

### Numerical Measures of Central Tendency

Numerical Measures of Central Tendency Often, it is useful to have special numbers which summarize characteristics of a data set These numbers are called descriptive statistics or summary statistics. A

### business 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

### Visualizing 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

### MINITAB ASSISTANT WHITE PAPER

MINITAB ASSISTANT WHITE PAPER This paper explains the research conducted by Minitab statisticians to develop the methods and data checks used in the Assistant in Minitab 17 Statistical Software. One-Way

### Institute 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

### AP Statistics: Syllabus 1

AP Statistics: Syllabus 1 Scoring Components SC1 The course provides instruction in exploring data. 4 SC2 The course provides instruction in sampling. 5 SC3 The course provides instruction in experimentation.

### STA-201-TE. 5. Measures of relationship: correlation (5%) Correlation coefficient; Pearson r; correlation and causation; proportion of common variance

Principles of Statistics STA-201-TE This TECEP is an introduction to descriptive and inferential statistics. Topics include: measures of central tendency, variability, correlation, regression, hypothesis

### Summarizing 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

### Quantitative Data Analysis

Quantitative Data Analysis Text durch Klicken hinzufügen Definition http://www.deutsche-apothekerzeitung.de/uploads/tx_crondaz/t agesnews-image/umfragebogen_-_cirquedesprit Fotolia.jpg https:/ / tatics/

### What 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

### Chapter 7. One-way ANOVA

Chapter 7 One-way ANOVA One-way ANOVA examines equality of population means for a quantitative outcome and a single categorical explanatory variable with any number of levels. The t-test of Chapter 6 looks

### Data Mining: Exploring Data. Lecture Notes for Chapter 3. Slides by Tan, Steinbach, Kumar adapted by Michael Hahsler

Data Mining: Exploring Data Lecture Notes for Chapter 3 Slides by Tan, Steinbach, Kumar adapted by Michael Hahsler Topics Exploratory Data Analysis Summary Statistics Visualization What is data exploration?

### Descriptive Statistics

Descriptive Statistics Primer Descriptive statistics Central tendency Variation Relative position Relationships Calculating descriptive statistics Descriptive Statistics Purpose to describe or summarize

### Service courses for graduate students in degree programs other than the MS or PhD programs in Biostatistics.

Course Catalog In order to be assured that all prerequisites are met, students must acquire a permission number from the education coordinator prior to enrolling in any Biostatistics course. Courses are

### Multivariate Analysis of Ecological Data

Multivariate Analysis of Ecological Data MICHAEL GREENACRE Professor of Statistics at the Pompeu Fabra University in Barcelona, Spain RAUL PRIMICERIO Associate Professor of Ecology, Evolutionary Biology

### Biostatistics: Types of Data Analysis

Biostatistics: Types of Data Analysis Theresa A Scott, MS Vanderbilt University Department of Biostatistics theresa.scott@vanderbilt.edu http://biostat.mc.vanderbilt.edu/theresascott Theresa A Scott, MS

### Descriptive 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

### Tutor/(or Student) Guide to: Tutor-led Tutorials

Tutor/(or Student) Guide to: Tutor-led Tutorials (Module Code: Stat10050) Tutor Name: Module Co-ordinator: Dr. Patrick Murphy Description of Tutorials Introduction to Statistical Modelling Tutorials: Aim

Statistics Graduate Courses STAT 7002--Topics in Statistics-Biological/Physical/Mathematics (cr.arr.).organized study of selected topics. Subjects and earnable credit may vary from semester to semester.

### STAT355 - Probability & Statistics

STAT355 - Probability & Statistics Instructor: Kofi Placid Adragni Fall 2011 Chap 1 - Overview and Descriptive Statistics 1.1 Populations, Samples, and Processes 1.2 Pictorial and Tabular Methods in Descriptive

### COMMON CORE STATE STANDARDS FOR

COMMON CORE STATE STANDARDS FOR Mathematics (CCSSM) High School Statistics and Probability Mathematics High School Statistics and Probability Decisions or predictions are often based on data numbers in

### Descriptive 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

### Introduction to Regression and Data Analysis

Statlab Workshop Introduction to Regression and Data Analysis with Dan Campbell and Sherlock Campbell October 28, 2008 I. The basics A. Types of variables Your variables may take several forms, and it

### Chapter 7 Section 7.1: Inference for the Mean of a Population

Chapter 7 Section 7.1: Inference for the Mean of a Population Now let s look at a similar situation Take an SRS of size n Normal Population : N(, ). Both and are unknown parameters. Unlike what we used

### Chapter 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)

### South Carolina College- and Career-Ready (SCCCR) Probability and Statistics

South Carolina College- and Career-Ready (SCCCR) Probability and Statistics South Carolina College- and Career-Ready Mathematical Process Standards The South Carolina College- and Career-Ready (SCCCR)

### WEEK #22: PDFs and CDFs, Measures of Center and Spread

WEEK #22: PDFs and CDFs, Measures of Center and Spread Goals: Explore the effect of independent events in probability calculations. Present a number of ways to represent probability distributions. Textbook

### Interpreting Data in Normal Distributions

Interpreting Data in Normal Distributions This curve is kind of a big deal. It shows the distribution of a set of test scores, the results of rolling a die a million times, the heights of people on Earth,

### 2.0 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

### DESCRIPTIVE 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

### Introduction 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.

### Implications 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