Wednesday, April 22, Chi Squared Test
|
|
- May Holt
- 7 years ago
- Views:
Transcription
1 Chi Squared Test
2 Why Chi Squared? To test to see if, when we collect data, is the variation we see due to chance or due to something else?
3 This is the Chi Squared Test Formula Greek letter X is Chi Don t get confused- X 2 is the name of the whole variable- you don t have to ever take the square root of it or solve for X.
4 Coin Flipping Example If you flip a coin 100 times and get this data: 62 Heads 38 Tails The question we wonder about this data: Is this due to chance? Or... Is this not due to chance? For example: Perhaps there is something wrong with the coin? Perhaps there is something wrong with the way I am flipping the coin, etc.? Chi Squared test lets us answer this!!
5 Null Hypothesis The Chi Squared Test begins with the Null Hypothesis The Null Hypothesis says: There is no significant statistical difference between the observed and expected frequencies (i.e. the differences we see are simply due to chance). For a coin flipping experiment: The expected values are 50 heads, 50 tails. The observed values are 62 heads, 38 tails. Question we are trying to answer: are the observed values due to chance or... not due to chance?
6 Degrees of Freedom and Critical Values We need to define and understand these terms before we can use the Chi Squared test. The whole point of a Chi Squared test is to either reject or fail to reject the Null Hypothesis. Key is to exceed or not exceed your critical value. But first we have to figure out which number it is in this chart.
7 Degrees of Freedom Because we are comparing outcomes, we need at least two outcomes in our experiment. We are flipping coins so we have two outcomes- heads or tails. To get degrees of freedom we simply subtract one from the two possible outcomes. 2-1= 1 Therefore, in this experiment we have 1 degree of freedom
8 Critical Values Next thing you are looking for is a critical value. We will always use p = 0.05 value. This means we are 95% sure we are either failing to reject the Null Hypothesis or rejecting our Null Hypothesis. Critical Values can vary. If we want a higher degree of certainty that our results are true, we can use p= 0.01 value and then we would have 99% certainty, but 95% certainty is used by most scientists. For 1 degree of freedom at p=.05 the critical value = 3.84.
9 Null Hypothesis says: Null Hypothesis There is no significant statistical difference between the observed and expected frequencies (i.e. the differences we see are simply due to chance). We either reject or fail to reject the null hypothesis. Reject the Null Hypothesis: This means there is a statistical difference between the observed and expected frequencies Fail to Reject the Null Hypothesis: This means there is no statistical difference between the observed and expected frequencies In this case the critical value is If your Chi Squared is greater than you reject the Null Hypothesis Therefore, there is something aside from chance that is causing us to get more heads than tails. If your Chi Squared is less than you fail to reject the Null Hypothesis. This is usually what happens unless you have something that is impacting your results
10 50 tosses Practice- Coin Toss Expected: Heads: 25 Tails: 25 Observed: Heads: 28 Tails: 22 Do it for heads Do it for tails What is our Critical Value? 2-1 = If our Chi Squared is greater than the critical value we reject our Null Hypothesis If our Chi Squared is less than the critical value we fail to reject our Null Hypothesis This means there is no statistical significance between what we observed & what we expected. What we got is due to chance- nothing s weird about the coins or the way we tossed them.
11 Practice- Dice If you have throw 36 dice at once what would you expect? Expected: 6 of each dice (6 ones, 6 tw0s, 6 threes, 6 fours, etc. ) What did we get? Observed: See photo and count! Do a Chi Square analysis.
12 Chi Squared Degrees of Freedom 6-1=5 Critical Value: Fail to reject the Null Hypothesis No difference between obs and exp What we see is due to chance! Practice- Dice
13
AP: LAB 8: THE CHI-SQUARE TEST. Probability, Random Chance, and Genetics
Ms. Foglia Date AP: LAB 8: THE CHI-SQUARE TEST Probability, Random Chance, and Genetics Why do we study random chance and probability at the beginning of a unit on genetics? Genetics is the study of inheritance,
More informationLAB : THE CHI-SQUARE TEST. Probability, Random Chance, and Genetics
Period Date LAB : THE CHI-SQUARE TEST Probability, Random Chance, and Genetics Why do we study random chance and probability at the beginning of a unit on genetics? Genetics is the study of inheritance,
More informationIntroduction to Hypothesis Testing
I. Terms, Concepts. Introduction to Hypothesis Testing A. In general, we do not know the true value of population parameters - they must be estimated. However, we do have hypotheses about what the true
More informationOdds ratio, Odds ratio test for independence, chi-squared statistic.
Odds ratio, Odds ratio test for independence, chi-squared statistic. Announcements: Assignment 5 is live on webpage. Due Wed Aug 1 at 4:30pm. (9 days, 1 hour, 58.5 minutes ) Final exam is Aug 9. Review
More informationHaving a coin come up heads or tails is a variable on a nominal scale. Heads is a different category from tails.
Chi-square Goodness of Fit Test The chi-square test is designed to test differences whether one frequency is different from another frequency. The chi-square test is designed for use with data on a nominal
More informationUnderstand the role that hypothesis testing plays in an improvement project. Know how to perform a two sample hypothesis test.
HYPOTHESIS TESTING Learning Objectives Understand the role that hypothesis testing plays in an improvement project. Know how to perform a two sample hypothesis test. Know how to perform a hypothesis test
More informationStat 20: Intro to Probability and Statistics
Stat 20: Intro to Probability and Statistics Lecture 16: More Box Models Tessa L. Childers-Day UC Berkeley 22 July 2014 By the end of this lecture... You will be able to: Determine what we expect the sum
More informationTesting Research and Statistical Hypotheses
Testing Research and Statistical Hypotheses Introduction In the last lab we analyzed metric artifact attributes such as thickness or width/thickness ratio. Those were continuous variables, which as you
More informationUsing Excel for inferential statistics
FACT SHEET Using Excel for inferential statistics Introduction When you collect data, you expect a certain amount of variation, just caused by chance. A wide variety of statistical tests can be applied
More informationHypothesis testing - Steps
Hypothesis testing - Steps Steps to do a two-tailed test of the hypothesis that β 1 0: 1. Set up the hypotheses: H 0 : β 1 = 0 H a : β 1 0. 2. Compute the test statistic: t = b 1 0 Std. error of b 1 =
More informationClass 19: Two Way Tables, Conditional Distributions, Chi-Square (Text: Sections 2.5; 9.1)
Spring 204 Class 9: Two Way Tables, Conditional Distributions, Chi-Square (Text: Sections 2.5; 9.) Big Picture: More than Two Samples In Chapter 7: We looked at quantitative variables and compared the
More information6th Grade Lesson Plan: Probably Probability
6th Grade Lesson Plan: Probably Probability Overview This series of lessons was designed to meet the needs of gifted children for extension beyond the standard curriculum with the greatest ease of use
More informationp-values and significance levels (false positive or false alarm rates)
p-values and significance levels (false positive or false alarm rates) Let's say 123 people in the class toss a coin. Call it "Coin A." There are 65 heads. Then they toss another coin. Call it "Coin B."
More informationRecommend Continued CPS Monitoring. 63 (a) 17 (b) 10 (c) 90. 35 (d) 20 (e) 25 (f) 80. Totals/Marginal 98 37 35 170
Work Sheet 2: Calculating a Chi Square Table 1: Substance Abuse Level by ation Total/Marginal 63 (a) 17 (b) 10 (c) 90 35 (d) 20 (e) 25 (f) 80 Totals/Marginal 98 37 35 170 Step 1: Label Your Table. Label
More informationMATH 140 Lab 4: Probability and the Standard Normal Distribution
MATH 140 Lab 4: Probability and the Standard Normal Distribution Problem 1. Flipping a Coin Problem In this problem, we want to simualte the process of flipping a fair coin 1000 times. Note that the outcomes
More information2 GENETIC DATA ANALYSIS
2.1 Strategies for learning genetics 2 GENETIC DATA ANALYSIS We will begin this lecture by discussing some strategies for learning genetics. Genetics is different from most other biology courses you have
More informationExpected Value and the Game of Craps
Expected Value and the Game of Craps Blake Thornton Craps is a gambling game found in most casinos based on rolling two six sided dice. Most players who walk into a casino and try to play craps for the
More informationIndependent samples t-test. Dr. Tom Pierce Radford University
Independent samples t-test Dr. Tom Pierce Radford University The logic behind drawing causal conclusions from experiments The sampling distribution of the difference between means The standard error of
More informationStudy Guide for the Final Exam
Study Guide for the Final Exam When studying, remember that the computational portion of the exam will only involve new material (covered after the second midterm), that material from Exam 1 will make
More informationTABLE OF CONTENTS. About Chi Squares... 1. What is a CHI SQUARE?... 1. Chi Squares... 1. Hypothesis Testing with Chi Squares... 2
About Chi Squares TABLE OF CONTENTS About Chi Squares... 1 What is a CHI SQUARE?... 1 Chi Squares... 1 Goodness of fit test (One-way χ 2 )... 1 Test of Independence (Two-way χ 2 )... 2 Hypothesis Testing
More informationMath 58. Rumbos Fall 2008 1. Solutions to Review Problems for Exam 2
Math 58. Rumbos Fall 2008 1 Solutions to Review Problems for Exam 2 1. For each of the following scenarios, determine whether the binomial distribution is the appropriate distribution for the random variable
More informationLikelihood: Frequentist vs Bayesian Reasoning
"PRINCIPLES OF PHYLOGENETICS: ECOLOGY AND EVOLUTION" Integrative Biology 200B University of California, Berkeley Spring 2009 N Hallinan Likelihood: Frequentist vs Bayesian Reasoning Stochastic odels and
More informationLesson 1. Basics of Probability. Principles of Mathematics 12: Explained! www.math12.com 314
Lesson 1 Basics of Probability www.math12.com 314 Sample Spaces: Probability Lesson 1 Part I: Basic Elements of Probability Consider the following situation: A six sided die is rolled The sample space
More informationProjects Involving Statistics (& SPSS)
Projects Involving Statistics (& SPSS) Academic Skills Advice Starting a project which involves using statistics can feel confusing as there seems to be many different things you can do (charts, graphs,
More informationThat s Not Fair! ASSESSMENT #HSMA20. Benchmark Grades: 9-12
That s Not Fair! ASSESSMENT # Benchmark Grades: 9-12 Summary: Students consider the difference between fair and unfair games, using probability to analyze games. The probability will be used to find ways
More information6.3 Conditional Probability and Independence
222 CHAPTER 6. PROBABILITY 6.3 Conditional Probability and Independence Conditional Probability Two cubical dice each have a triangle painted on one side, a circle painted on two sides and a square painted
More informationHYPOTHESIS TESTING: POWER OF THE TEST
HYPOTHESIS TESTING: POWER OF THE TEST The first 6 steps of the 9-step test of hypothesis are called "the test". These steps are not dependent on the observed data values. When planning a research project,
More informationhp calculators HP 17bII+ Net Present Value and Internal Rate of Return Cash Flow Zero A Series of Cash Flows What Net Present Value Is
HP 17bII+ Net Present Value and Internal Rate of Return Cash Flow Zero A Series of Cash Flows What Net Present Value Is Present Value and Net Present Value Getting the Present Value And Now For the Internal
More informationContingency Tables and the Chi Square Statistic. Interpreting Computer Printouts and Constructing Tables
Contingency Tables and the Chi Square Statistic Interpreting Computer Printouts and Constructing Tables Contingency Tables/Chi Square Statistics What are they? A contingency table is a table that shows
More informationCrosstabulation & Chi Square
Crosstabulation & Chi Square Robert S Michael Chi-square as an Index of Association After examining the distribution of each of the variables, the researcher s next task is to look for relationships among
More informationChapter 26: Tests of Significance
Chapter 26: Tests of Significance Procedure: 1. State the null and alternative in words and in terms of a box model. 2. Find the test statistic: z = observed EV. SE 3. Calculate the P-value: The area under
More informationPEARSON R CORRELATION COEFFICIENT
PEARSON R CORRELATION COEFFICIENT Introduction: Sometimes in scientific data, it appears that two variables are connected in such a way that when one variable changes, the other variable changes also.
More informationLesson 1: Comparison of Population Means Part c: Comparison of Two- Means
Lesson : Comparison of Population Means Part c: Comparison of Two- Means Welcome to lesson c. This third lesson of lesson will discuss hypothesis testing for two independent means. Steps in Hypothesis
More informationQuestion: What is the probability that a five-card poker hand contains a flush, that is, five cards of the same suit?
ECS20 Discrete Mathematics Quarter: Spring 2007 Instructor: John Steinberger Assistant: Sophie Engle (prepared by Sophie Engle) Homework 8 Hints Due Wednesday June 6 th 2007 Section 6.1 #16 What is the
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 informationPeople have thought about, and defined, probability in different ways. important to note the consequences of the definition:
PROBABILITY AND LIKELIHOOD, A BRIEF INTRODUCTION IN SUPPORT OF A COURSE ON MOLECULAR EVOLUTION (BIOL 3046) Probability The subject of PROBABILITY is a branch of mathematics dedicated to building models
More informationHypothesis Testing for Beginners
Hypothesis Testing for Beginners Michele Piffer LSE August, 2011 Michele Piffer (LSE) Hypothesis Testing for Beginners August, 2011 1 / 53 One year ago a friend asked me to put down some easy-to-read notes
More informationSIMPLE LINEAR CORRELATION. r can range from -1 to 1, and is independent of units of measurement. Correlation can be done on two dependent variables.
SIMPLE LINEAR CORRELATION Simple linear correlation is a measure of the degree to which two variables vary together, or a measure of the intensity of the association between two variables. Correlation
More information" Y. Notation and Equations for Regression Lecture 11/4. Notation:
Notation: Notation and Equations for Regression Lecture 11/4 m: The number of predictor variables in a regression Xi: One of multiple predictor variables. The subscript i represents any number from 1 through
More informationstatistics Chi-square tests and nonparametric Summary sheet from last time: Hypothesis testing Summary sheet from last time: Confidence intervals
Summary sheet from last time: Confidence intervals Confidence intervals take on the usual form: parameter = statistic ± t crit SE(statistic) parameter SE a s e sqrt(1/n + m x 2 /ss xx ) b s e /sqrt(ss
More informationWeek 4: Standard Error and Confidence Intervals
Health Sciences M.Sc. Programme Applied Biostatistics Week 4: Standard Error and Confidence Intervals Sampling Most research data come from subjects we think of as samples drawn from a larger population.
More informationFirst-year Statistics for Psychology Students Through Worked Examples
First-year Statistics for Psychology Students Through Worked Examples 1. THE CHI-SQUARE TEST A test of association between categorical variables by Charles McCreery, D.Phil Formerly Lecturer in Experimental
More informationDistribution is a χ 2 value on the χ 2 axis that is the vertical boundary separating the area in one tail of the graph from the remaining area.
Section 8 4B Finding Critical Values for a Chi Square Distribution The entire area that is to be used in the tail(s) denoted by. The entire area denoted by can placed in the left tail and produce a Critical
More informationMathematical goals. Starting points. Materials required. Time needed
Level S2 of challenge: B/C S2 Mathematical goals Starting points Materials required Time needed Evaluating probability statements To help learners to: discuss and clarify some common misconceptions about
More informationSimple Regression Theory II 2010 Samuel L. Baker
SIMPLE REGRESSION THEORY II 1 Simple Regression Theory II 2010 Samuel L. Baker Assessing how good the regression equation is likely to be Assignment 1A gets into drawing inferences about how close the
More informationCoin Flip Questions. Suppose you flip a coin five times and write down the sequence of results, like HHHHH or HTTHT.
Coin Flip Questions Suppose you flip a coin five times and write down the sequence of results, like HHHHH or HTTHT. 1 How many ways can you get exactly 1 head? 2 How many ways can you get exactly 2 heads?
More informationMONT 107N Understanding Randomness Solutions For Final Examination May 11, 2010
MONT 07N Understanding Randomness Solutions For Final Examination May, 00 Short Answer (a) (0) How are the EV and SE for the sum of n draws with replacement from a box computed? Solution: The EV is n times
More information1.6 The Order of Operations
1.6 The Order of Operations Contents: Operations Grouping Symbols The Order of Operations Exponents and Negative Numbers Negative Square Roots Square Root of a Negative Number Order of Operations and Negative
More informationCalculating P-Values. Parkland College. Isela Guerra Parkland College. Recommended Citation
Parkland College A with Honors Projects Honors Program 2014 Calculating P-Values Isela Guerra Parkland College Recommended Citation Guerra, Isela, "Calculating P-Values" (2014). A with Honors Projects.
More informationPROBABILITY SECOND EDITION
PROBABILITY SECOND EDITION Table of Contents How to Use This Series........................................... v Foreword..................................................... vi Basics 1. Probability All
More informationDecision Making under Uncertainty
6.825 Techniques in Artificial Intelligence Decision Making under Uncertainty How to make one decision in the face of uncertainty Lecture 19 1 In the next two lectures, we ll look at the question of how
More informationProbability and Expected Value
Probability and Expected Value This handout provides an introduction to probability and expected value. Some of you may already be familiar with some of these topics. Probability and expected value are
More informationUniversity of Chicago Graduate School of Business. Business 41000: Business Statistics
Name: University of Chicago Graduate School of Business Business 41000: Business Statistics Special Notes: 1. This is a closed-book exam. You may use an 8 11 piece of paper for the formulas. 2. Throughout
More informationSCHOOL OF HEALTH AND HUMAN SCIENCES DON T FORGET TO RECODE YOUR MISSING VALUES
SCHOOL OF HEALTH AND HUMAN SCIENCES Using SPSS Topics addressed today: 1. Differences between groups 2. Graphing Use the s4data.sav file for the first part of this session. DON T FORGET TO RECODE YOUR
More informationTom wants to find two real numbers, a and b, that have a sum of 10 and have a product of 10. He makes this table.
Sum and Product This problem gives you the chance to: use arithmetic and algebra to represent and analyze a mathematical situation solve a quadratic equation by trial and improvement Tom wants to find
More informationGoal Setting. Your role as the coach is to develop and maintain an effective coaching plan with the client. You are there to
Goal Setting Your role as the coach is to develop and maintain an effective coaching plan with the client. You are there to Brainstorm with the client to define actions that will enable the client to demonstrate,
More informationThis chapter discusses some of the basic concepts in inferential statistics.
Research Skills for Psychology Majors: Everything You Need to Know to Get Started Inferential Statistics: Basic Concepts This chapter discusses some of the basic concepts in inferential statistics. Details
More informationElementary Statistics
lementary Statistics Chap10 Dr. Ghamsary Page 1 lementary Statistics M. Ghamsary, Ph.D. Chapter 10 Chi-square Test for Goodness of fit and Contingency tables lementary Statistics Chap10 Dr. Ghamsary Page
More informationBayesian Updating with Discrete Priors Class 11, 18.05, Spring 2014 Jeremy Orloff and Jonathan Bloom
1 Learning Goals Bayesian Updating with Discrete Priors Class 11, 18.05, Spring 2014 Jeremy Orloff and Jonathan Bloom 1. Be able to apply Bayes theorem to compute probabilities. 2. Be able to identify
More informationA Few Basics of Probability
A Few Basics of Probability Philosophy 57 Spring, 2004 1 Introduction This handout distinguishes between inductive and deductive logic, and then introduces probability, a concept essential to the study
More informationSolutions: Problems for Chapter 3. Solutions: Problems for Chapter 3
Problem A: You are dealt five cards from a standard deck. Are you more likely to be dealt two pairs or three of a kind? experiment: choose 5 cards at random from a standard deck Ω = {5-combinations of
More informationBivariate Statistics Session 2: Measuring Associations Chi-Square Test
Bivariate Statistics Session 2: Measuring Associations Chi-Square Test Features Of The Chi-Square Statistic The chi-square test is non-parametric. That is, it makes no assumptions about the distribution
More informationChapter 23. Two Categorical Variables: The Chi-Square Test
Chapter 23. Two Categorical Variables: The Chi-Square Test 1 Chapter 23. Two Categorical Variables: The Chi-Square Test Two-Way Tables Note. We quickly review two-way tables with an example. Example. Exercise
More informationAMS 5 CHANCE VARIABILITY
AMS 5 CHANCE VARIABILITY The Law of Averages When tossing a fair coin the chances of tails and heads are the same: 50% and 50%. So if the coin is tossed a large number of times, the number of heads and
More informationReady, Set, Go! Math Games for Serious Minds
Math Games with Cards and Dice presented at NAGC November, 2013 Ready, Set, Go! Math Games for Serious Minds Rande McCreight Lincoln Public Schools Lincoln, Nebraska Math Games with Cards Close to 20 -
More informationChapter 16: law of averages
Chapter 16: law of averages Context................................................................... 2 Law of averages 3 Coin tossing experiment......................................................
More informationDiscrete Mathematics and Probability Theory Fall 2009 Satish Rao, David Tse Note 10
CS 70 Discrete Mathematics and Probability Theory Fall 2009 Satish Rao, David Tse Note 10 Introduction to Discrete Probability Probability theory has its origins in gambling analyzing card games, dice,
More informationAim To help students prepare for the Academic Reading component of the IELTS exam.
IELTS Reading Test 1 Teacher s notes Written by Sam McCarter Aim To help students prepare for the Academic Reading component of the IELTS exam. Objectives To help students to: Practise doing an academic
More information1.5 Oneway Analysis of Variance
Statistics: Rosie Cornish. 200. 1.5 Oneway Analysis of Variance 1 Introduction Oneway analysis of variance (ANOVA) is used to compare several means. This method is often used in scientific or medical experiments
More informationATM 552 Notes: Review of Statistics Page 1
ATM 552 Notes: Review of Statistics Page 1 Class Notes: ATM 552 Objective Analysis 1. Review of Basic Statistics We will review a few features of statistics that come up frequently in objective analysis
More information2 Sample t-test (unequal sample sizes and unequal variances)
Variations of the t-test: Sample tail Sample t-test (unequal sample sizes and unequal variances) Like the last example, below we have ceramic sherd thickness measurements (in cm) of two samples representing
More informationSAMPLE SIZE CONSIDERATIONS
SAMPLE SIZE CONSIDERATIONS Learning Objectives Understand the critical role having the right sample size has on an analysis or study. Know how to determine the correct sample size for a specific study.
More informationYour logbook. Choosing a topic
This booklet contains information that will be used to complete a science fair project for the César Chávez science fair. It is designed to help participants to successfully complete a project. This booklet
More informationA Primer on Mathematical Statistics and Univariate Distributions; The Normal Distribution; The GLM with the Normal Distribution
A Primer on Mathematical Statistics and Univariate Distributions; The Normal Distribution; The GLM with the Normal Distribution PSYC 943 (930): Fundamentals of Multivariate Modeling Lecture 4: September
More informationMental Questions. Day 1. 1. What number is five cubed? 2. A circle has radius r. What is the formula for the area of the circle?
Mental Questions 1. What number is five cubed? KS3 MATHEMATICS 10 4 10 Level 8 Questions Day 1 2. A circle has radius r. What is the formula for the area of the circle? 3. Jenny and Mark share some money
More informationAssociation Between Variables
Contents 11 Association Between Variables 767 11.1 Introduction............................ 767 11.1.1 Measure of Association................. 768 11.1.2 Chapter Summary.................... 769 11.2 Chi
More informationIntroduction to Hypothesis Testing. Hypothesis Testing. Step 1: State the Hypotheses
Introduction to Hypothesis Testing 1 Hypothesis Testing A hypothesis test is a statistical procedure that uses sample data to evaluate a hypothesis about a population Hypothesis is stated in terms of the
More informationPlaying with Numbers
PLAYING WITH NUMBERS 249 Playing with Numbers CHAPTER 16 16.1 Introduction You have studied various types of numbers such as natural numbers, whole numbers, integers and rational numbers. You have also
More informationContent Sheet 7-1: Overview of Quality Control for Quantitative Tests
Content Sheet 7-1: Overview of Quality Control for Quantitative Tests Role in quality management system Quality Control (QC) is a component of process control, and is a major element of the quality management
More informationStats Review Chapters 9-10
Stats Review Chapters 9-10 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 informationRadiometric Dating Lab By Vicky Jordan
Science 8: The Deep Time Diaries Name Date Per Radiometric Dating Lab By Vicky Jordan Problem: How long will it take for 100 atoms of the radioactive parent Carbon-14 to completely decay to the stable
More informationThe mathematical branch of probability has its
ACTIVITIES for students Matthew A. Carlton and Mary V. Mortlock Teaching Probability and Statistics through Game Shows The mathematical branch of probability has its origins in games and gambling. And
More informationDESCRIPTIVE STATISTICS & DATA PRESENTATION*
Level 1 Level 2 Level 3 Level 4 0 0 0 0 evel 1 evel 2 evel 3 Level 4 DESCRIPTIVE STATISTICS & DATA PRESENTATION* Created for Psychology 41, Research Methods by Barbara Sommer, PhD Psychology Department
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 informationMgmt 469. Regression Basics. You have all had some training in statistics and regression analysis. Still, it is useful to review
Mgmt 469 Regression Basics You have all had some training in statistics and regression analysis. Still, it is useful to review some basic stuff. In this note I cover the following material: What is a regression
More informationSolving Rational Equations
Lesson M Lesson : Student Outcomes Students solve rational equations, monitoring for the creation of extraneous solutions. Lesson Notes In the preceding lessons, students learned to add, subtract, multiply,
More informationConcepts of Probability
Concepts of Probability Trial question: we are given a die. How can we determine the probability that any given throw results in a six? Try doing many tosses: Plot cumulative proportion of sixes Also look
More informationVieta s Formulas and the Identity Theorem
Vieta s Formulas and the Identity Theorem This worksheet will work through the material from our class on 3/21/2013 with some examples that should help you with the homework The topic of our discussion
More informationPermutation & Non-Parametric Tests
Permutation & Non-Parametric Tests Statistical tests Gather data to assess some hypothesis (e.g., does this treatment have an effect on this outcome?) Form a test statistic for which large values indicate
More informationBayesian Tutorial (Sheet Updated 20 March)
Bayesian Tutorial (Sheet Updated 20 March) Practice Questions (for discussing in Class) Week starting 21 March 2016 1. What is the probability that the total of two dice will be greater than 8, given that
More informationObjective. Materials. TI-73 Calculator
0. Objective To explore subtraction of integers using a number line. Activity 2 To develop strategies for subtracting integers. Materials TI-73 Calculator Integer Subtraction What s the Difference? Teacher
More informationAppendix 2 Statistical Hypothesis Testing 1
BIL 151 Data Analysis, Statistics, and Probability By Dana Krempels, Ph.D. and Steven Green, Ph.D. Most biological measurements vary among members of a study population. These variations may occur for
More informationIMPLEMENTING BUSINESS CONTINUITY MANAGEMENT IN A DISTRIBUTED ORGANISATION: A CASE STUDY
IMPLEMENTING BUSINESS CONTINUITY MANAGEMENT IN A DISTRIBUTED ORGANISATION: A CASE STUDY AUTHORS: Patrick Roberts (left) and Mike Stephens (right). Patrick Roberts: Following early experience in the British
More informationNovember 08, 2010. 155S8.6_3 Testing a Claim About a Standard Deviation or Variance
Chapter 8 Hypothesis Testing 8 1 Review and Preview 8 2 Basics of Hypothesis Testing 8 3 Testing a Claim about a Proportion 8 4 Testing a Claim About a Mean: σ Known 8 5 Testing a Claim About a Mean: σ
More informationRockefeller College University at Albany
Rockefeller College University at Albany PAD 705 Handout: Hypothesis Testing on Multiple Parameters In many cases we may wish to know whether two or more variables are jointly significant in a regression.
More informationThe overall size of these chance errors is measured by their RMS HALF THE NUMBER OF TOSSES NUMBER OF HEADS MINUS 0 400 800 1200 1600 NUMBER OF TOSSES
INTRODUCTION TO CHANCE VARIABILITY WHAT DOES THE LAW OF AVERAGES SAY? 4 coins were tossed 1600 times each, and the chance error number of heads half the number of tosses was plotted against the number
More informationLab 11. Simulations. The Concept
Lab 11 Simulations In this lab you ll learn how to create simulations to provide approximate answers to probability questions. We ll make use of a particular kind of structure, called a box model, that
More informationBinomial Probability Distribution
Binomial Probability Distribution In a binomial setting, we can compute probabilities of certain outcomes. This used to be done with tables, but with graphing calculator technology, these problems are
More informationStatistiek I. Proportions aka Sign Tests. John Nerbonne. CLCG, Rijksuniversiteit Groningen. http://www.let.rug.nl/nerbonne/teach/statistiek-i/
Statistiek I Proportions aka Sign Tests John Nerbonne CLCG, Rijksuniversiteit Groningen http://www.let.rug.nl/nerbonne/teach/statistiek-i/ John Nerbonne 1/34 Proportions aka Sign Test The relative frequency
More information2.5 Zeros of a Polynomial Functions
.5 Zeros of a Polynomial Functions Section.5 Notes Page 1 The first rule we will talk about is Descartes Rule of Signs, which can be used to determine the possible times a graph crosses the x-axis and
More information