ChiSquare vs. z Section 25.9


 Lionel Manning
 1 years ago
 Views:
Transcription
1 ChiSquare vs. z Section 25.9 Lecture 49 Robb T. Koether HampdenSydney College Wed, Apr 20, 2016 Robb T. Koether (HampdenSydney College) ChiSquare vs. zsection 25.9 Wed, Apr 20, / 11
2 Outline 1 χ 2 Versus z Goodnessoffit Test, 2 Categories 2 2 Table 2 Assignment Robb T. Koether (HampdenSydney College) ChiSquare vs. zsection 25.9 Wed, Apr 20, / 11
3 Example There are two situations where the χ 2 test has 1 degree of freedom. A goodnessoffit test with only 2 categories. A twoway table with 2 rows and 2 columns. Robb T. Koether (HampdenSydney College) ChiSquare vs. zsection 25.9 Wed, Apr 20, / 11
4 Example There are two situations where the χ 2 test has 1 degree of freedom. A goodnessoffit test with only 2 categories. A twoway table with 2 rows and 2 columns. In these cases, the test could be performed as a ztest. Goodnessoffit test Test of one proportion. 2 2 table Comparing two proportions. Robb T. Koether (HampdenSydney College) ChiSquare vs. zsection 25.9 Wed, Apr 20, / 11
5 Outline 1 χ 2 Versus z Goodnessoffit Test, 2 Categories 2 2 Table 2 Assignment Robb T. Koether (HampdenSydney College) ChiSquare vs. zsection 25.9 Wed, Apr 20, / 11
6 Goodnessoffit Test, 2 Categories To test a coin for fairness, we toss it 1000 times and get 467 heads and 533 tails. Robb T. Koether (HampdenSydney College) ChiSquare vs. zsection 25.9 Wed, Apr 20, / 11
7 Goodnessoffit Test, 2 Categories To test a coin for fairness, we toss it 1000 times and get 467 heads and 533 tails. Using the ztest: Robb T. Koether (HampdenSydney College) ChiSquare vs. zsection 25.9 Wed, Apr 20, / 11
8 Goodnessoffit Test, 2 Categories To test a coin for fairness, we toss it 1000 times and get 467 heads and 533 tails. Using the ztest: The sample proportion is ˆp = Robb T. Koether (HampdenSydney College) ChiSquare vs. zsection 25.9 Wed, Apr 20, / 11
9 Goodnessoffit Test, 2 Categories To test a coin for fairness, we toss it 1000 times and get 467 heads and 533 tails. Using the ztest: The sample proportion is ˆp = The test statistic is z = (0.5)(0.5) 1000 = = Robb T. Koether (HampdenSydney College) ChiSquare vs. zsection 25.9 Wed, Apr 20, / 11
10 Goodnessoffit Test, 2 Categories Using the goodnessoffit test: Robb T. Koether (HampdenSydney College) ChiSquare vs. zsection 25.9 Wed, Apr 20, / 11
11 Goodnessoffit Test, 2 Categories Using the goodnessoffit test: The observed and expected counts: Heads Tails Total Obs Exp Robb T. Koether (HampdenSydney College) ChiSquare vs. zsection 25.9 Wed, Apr 20, / 11
12 Goodnessoffit Test, 2 Categories Using the goodnessoffit test: The observed and expected counts: The test statistic is Heads Tails Total Obs Exp χ 2 = ( ) ( )2 500 = = Robb T. Koether (HampdenSydney College) ChiSquare vs. zsection 25.9 Wed, Apr 20, / 11
13 Outline 1 χ 2 Versus z Goodnessoffit Test, 2 Categories 2 2 Table 2 Assignment Robb T. Koether (HampdenSydney College) ChiSquare vs. zsection 25.9 Wed, Apr 20, / 11
14 2 2 Table To test two coins to see whether they land heads equally often, we toss each coin 1000 times. Robb T. Koether (HampdenSydney College) ChiSquare vs. zsection 25.9 Wed, Apr 20, / 11
15 2 2 Table To test two coins to see whether they land heads equally often, we toss each coin 1000 times. The first coin lands heads 600 times; the second coin lands heads 550 times. Robb T. Koether (HampdenSydney College) ChiSquare vs. zsection 25.9 Wed, Apr 20, / 11
16 2 2 Table To test two coins to see whether they land heads equally often, we toss each coin 1000 times. The first coin lands heads 600 times; the second coin lands heads 550 times. Using the ztest: Robb T. Koether (HampdenSydney College) ChiSquare vs. zsection 25.9 Wed, Apr 20, / 11
17 2 2 Table To test two coins to see whether they land heads equally often, we toss each coin 1000 times. The first coin lands heads 600 times; the second coin lands heads 550 times. Using the ztest: The sample proportions are ˆp 1 = and ˆp 2 = Robb T. Koether (HampdenSydney College) ChiSquare vs. zsection 25.9 Wed, Apr 20, / 11
18 2 2 Table To test two coins to see whether they land heads equally often, we toss each coin 1000 times. The first coin lands heads 600 times; the second coin lands heads 550 times. Using the ztest: The sample proportions are ˆp 1 = and ˆp 2 = The pooled estimate is ˆp = = = Robb T. Koether (HampdenSydney College) ChiSquare vs. zsection 25.9 Wed, Apr 20, / 11
19 2 2 Table To test two coins to see whether they land heads equally often, we toss each coin 1000 times. The first coin lands heads 600 times; the second coin lands heads 550 times. Using the ztest: The sample proportions are ˆp 1 = and ˆp 2 = The pooled estimate is ˆp = = = The test statistic is z = (0.575)( ) ( ) = = Robb T. Koether (HampdenSydney College) ChiSquare vs. zsection 25.9 Wed, Apr 20, / 11
20 2 2 Table Using the goodnessoffit test: Robb T. Koether (HampdenSydney College) ChiSquare vs. zsection 25.9 Wed, Apr 20, / 11
21 2 2 Table Using the goodnessoffit test: The 2 2 table is Heads Tails Total Coin Coin Robb T. Koether (HampdenSydney College) ChiSquare vs. zsection 25.9 Wed, Apr 20, / 11
22 2 2 Table Using the goodnessoffit test: The 2 2 table is Heads Tails Total Coin Coin Robb T. Koether (HampdenSydney College) ChiSquare vs. zsection 25.9 Wed, Apr 20, / 11
23 2 2 Table Using the goodnessoffit test: The 2 2 table is The test statistic is Heads Tails Total Coin Coin χ 2 = ( ) ( ) ( ) ( )2 425 = = Robb T. Koether (HampdenSydney College) ChiSquare vs. zsection 25.9 Wed, Apr 20, / 11
24 Outline 1 χ 2 Versus z Goodnessoffit Test, 2 Categories 2 2 Table 2 Assignment Robb T. Koether (HampdenSydney College) ChiSquare vs. zsection 25.9 Wed, Apr 20, / 11
25 Assignment Assignment Read Sections Robb T. Koether (HampdenSydney College) ChiSquare vs. zsection 25.9 Wed, Apr 20, / 11
The GoodnessofFit Test
The GoodnessofFit Test Lecture 49 Section 14.3 Robb T. Koether HampdenSydney College Tue, Apr 24, 2012 Robb T. Koether (HampdenSydney College) The GoodnessofFit Test Tue, Apr 24, 2012 1 / 15 Outline
More informationLecture 42 Section 14.3. Tue, Apr 8, 2008
the Lecture 42 Section 14.3 HampdenSydney College Tue, Apr 8, 2008 Outline the 1 2 the 3 4 5 the The will compute χ 2 areas, but not χ 2 percentiles. (That s ok.) After performing the χ 2 test by hand,
More informationChi Square (χ 2 ) Statistical Instructions EXP 3082L Jay Gould s Elaboration on Christensen and Evans (1980)
Chi Square (χ 2 ) Statistical Instructions EXP 3082L Jay Gould s Elaboration on Christensen and Evans (1980) For the Driver Behavior Study, the Chi Square Analysis II is the appropriate analysis below.
More informationThe GoodnessofFit Test
on the Lecture 49 Section 14.3 HampdenSydney College Tue, Apr 21, 2009 Outline 1 on the 2 3 on the 4 5 Hypotheses on the (Steps 1 and 2) (1) H 0 : H 1 : H 0 is false. (2) α = 0.05. p 1 = 0.24 p 2 = 0.20
More informationClass 19: Two Way Tables, Conditional Distributions, ChiSquare (Text: Sections 2.5; 9.1)
Spring 204 Class 9: Two Way Tables, Conditional Distributions, ChiSquare (Text: Sections 2.5; 9.) Big Picture: More than Two Samples In Chapter 7: We looked at quantitative variables and compared the
More informationAP STATISTICS 2010 SCORING GUIDELINES (Form B)
AP STATISTICS 2010 SCORING GUIDELINES (Form B) Question 5 Intent of Question The primary goals of this question were to assess students ability to (1) calculate appropriate probabilities, including conditional
More informationPASS Sample Size Software
Chapter 250 Introduction The Chisquare test is often used to test whether sets of frequencies or proportions follow certain patterns. The two most common instances are tests of goodness of fit using multinomial
More informationAP: LAB 8: THE CHISQUARE TEST. Probability, Random Chance, and Genetics
Ms. Foglia Date AP: LAB 8: THE CHISQUARE 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 informationIs it statistically significant? The chisquare test
UAS Conference Series 2013/14 Is it statistically significant? The chisquare test Dr Gosia Turner Student Data Management and Analysis 14 September 2010 Page 1 Why chisquare? Tests whether two categorical
More information112 Goodness of Fit Test
112 Goodness of Fit Test In This section we consider sample data consisting of observed frequency counts arranged in a single row or column (called a oneway frequency table). We will use a hypothesis
More informationOdds ratio, Odds ratio test for independence, chisquared statistic.
Odds ratio, Odds ratio test for independence, chisquared 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 informationLAB : THE CHISQUARE TEST. Probability, Random Chance, and Genetics
Period Date LAB : THE CHISQUARE 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 informationComparing Multiple Proportions, Test of Independence and Goodness of Fit
Comparing Multiple Proportions, Test of Independence and Goodness of Fit Content Testing the Equality of Population Proportions for Three or More Populations Test of Independence Goodness of Fit Test 2
More informationChapter 23. Two Categorical Variables: The ChiSquare Test
Chapter 23. Two Categorical Variables: The ChiSquare Test 1 Chapter 23. Two Categorical Variables: The ChiSquare Test TwoWay Tables Note. We quickly review twoway tables with an example. Example. Exercise
More informationChapter 11. Chapter 11 Overview. Chapter 11 Objectives 11/24/2015. Other ChiSquare Tests
11/4/015 Chapter 11 Overview Chapter 11 Introduction 111 Test for Goodness of Fit 11 Tests Using Contingency Tables Other ChiSquare Tests McGrawHill, Bluman, 7th ed., Chapter 11 1 Bluman, Chapter 11
More informationSPSS Tests for Versions 9 to 13
SPSS Tests for Versions 9 to 13 Chapter 2 Descriptive Statistic (including median) Choose Analyze Descriptive statistics Frequencies... Click on variable(s) then press to move to into Variable(s): list
More informationChi Square Goodness of Fit & Twoway Tables (Create) MATH NSPIRED
Overview In this activity, you will look at a setting that involves categorical data and determine which is the appropriate chisquare test to use. You will input data into a list or matrix and conduct
More informationLesson 8: The Difference Between Theoretical Probabilities and Estimated Probabilities
The Difference Between Theoretical Probabilities and Estimated Probabilities Student Outcomes Given theoretical probabilities based on a chance experiment, students describe what they expect to see when
More information+ Section 6.2 and 6.3
Section 6.2 and 6.3 Learning Objectives After this section, you should be able to DEFINE and APPLY basic rules of probability CONSTRUCT Venn diagrams and DETERMINE probabilities DETERMINE probabilities
More informationChisquare (χ 2 ) Tests
Math 442  Mathematical Statistics II May 5, 2008 Common Uses of the χ 2 test. 1. Testing Goodnessoffit. Chisquare (χ 2 ) Tests 2. Testing Equality of Several Proportions. 3. Homogeneity Test. 4. Testing
More informationstatistics Chisquare 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 informationUnit 29 ChiSquare GoodnessofFit Test
Unit 29 ChiSquare GoodnessofFit Test Objectives: To perform the chisquare hypothesis test concerning proportions corresponding to more than two categories of a qualitative variable To perform the Bonferroni
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 information1. A credit card company randomly generates temporary three digit pass codes for cardholders. The
Math 3201 Quiz Section 3.3 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. A credit card company randomly generates temporary three digit pass codes for
More informationProbability Calculator
Chapter 95 Introduction Most statisticians have a set of probability tables that they refer to in doing their statistical wor. This procedure provides you with a set of electronic statistical tables that
More informationLecture 9 Maher on Inductive Probability
Lecture 9 Maher on Inductive Probability Patrick Maher Scientific Thought II Spring 2010 Two concepts of probability Example You know that a coin is either twoheaded or twotailed but you have no information
More informationMind on Statistics. Chapter 15
Mind on Statistics Chapter 15 Section 15.1 1. A student survey was done to study the relationship between class standing (freshman, sophomore, junior, or senior) and major subject (English, Biology, French,
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 informationCATEGORICAL DATA ChiSquare Tests for Univariate Data
CATEGORICAL DATA ChiSquare Tests For Univariate Data 1 CATEGORICAL DATA ChiSquare Tests for Univariate Data Recall that a categorical variable is one in which the possible values are categories or groupings.
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 informationHypothesis Testing for a Proportion
Math 122 Intro to Stats Chapter 6 Semester II, 201516 Inference for Categorical Data Hypothesis Testing for a Proportion In a survey, 1864 out of 2246 randomly selected adults said texting while driving
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 informationSTAT 35A HW2 Solutions
STAT 35A HW2 Solutions http://www.stat.ucla.edu/~dinov/courses_students.dir/09/spring/stat35.dir 1. A computer consulting firm presently has bids out on three projects. Let A i = { awarded project i },
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 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 informationIntroduction to Game Theory IIIii. Payoffs: Probability and Expected Utility
Introduction to Game Theory IIIii Payoffs: Probability and Expected Utility Lecture Summary 1. Introduction 2. Probability Theory 3. Expected Values and Expected Utility. 1. Introduction We continue further
More informationChapter 16: law of averages
Chapter 16: law of averages Context................................................................... 2 Law of averages 3 Coin tossing experiment......................................................
More informationElementary probability
Elementary probability Many of the principal applications of calculus are to questions of probability and statistics. We shall include here an introduction to elementary probability, and eventually some
More informationElementary Statistics
lementary Statistics Chap10 Dr. Ghamsary Page 1 lementary Statistics M. Ghamsary, Ph.D. Chapter 10 Chisquare Test for Goodness of fit and Contingency tables lementary Statistics Chap10 Dr. Ghamsary Page
More informationModule 9: Nonparametric Tests. The Applied Research Center
Module 9: Nonparametric Tests The Applied Research Center Module 9 Overview } Nonparametric Tests } Parametric vs. Nonparametric Tests } Restrictions of Nonparametric Tests } OneSample ChiSquare Test
More informationREPEATED TRIALS. The probability of winning those k chosen times and losing the other times is then p k q n k.
REPEATED TRIALS Suppose you toss a fair coin one time. Let E be the event that the coin lands heads. We know from basic counting that p(e) = 1 since n(e) = 1 and 2 n(s) = 2. Now suppose we play a game
More informationLecture 8. Confidence intervals and the central limit theorem
Lecture 8. Confidence intervals and the central limit theorem Mathematical Statistics and Discrete Mathematics November 25th, 2015 1 / 15 Central limit theorem Let X 1, X 2,... X n be a random sample of
More informationTests for Two Proportions
Chapter 200 Tests for Two Proportions Introduction This module computes power and sample size for hypothesis tests of the difference, ratio, or odds ratio of two independent proportions. The test statistics
More informationAnalysis of categorical data: Course quiz instructions for SPSS
Analysis of categorical data: Course quiz instructions for SPSS The dataset Please download the Online sales dataset from the Download pod in the Course quiz resources screen. The filename is smr_bus_acd_clo_quiz_online_250.xls.
More information1. The sample space S is the set of all possible outcomes. 2. An event is a set of one or more outcomes for an experiment. It is a sub set of S.
1 Probability Theory 1.1 Experiment, Outcomes, Sample Space Example 1 n psychologist examined the response of people standing in line at a copying machines. Student volunteers approached the person first
More informationChi Squared and Fisher's Exact Tests. Observed vs Expected Distributions
BMS 617 Statistical Techniques for the Biomedical Sciences Lecture 11: ChiSquared and Fisher's Exact Tests Chi Squared and Fisher's Exact Tests This lecture presents two similarly structured tests, Chisquared
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 informationCLASSROOM PERFORMANCE GENERAL EDUCATION A RESEARCH BRIEF
CLASSROOM PERFORMANCE GENERAL EDUCATION A RESEARCH BRIEF Research Briefs The dissemination of relevant information is a critical component of the performance improvement process. Research briefs are one
More informationSolutions to Homework 10 Statistics 302 Professor Larget
s to Homework 10 Statistics 302 Professor Larget Textbook Exercises 7.14 RockPaperScissors (Graded for Accurateness) In Data 6.1 on page 367 we see a table, reproduced in the table below that shows the
More informationProbability and Statistics Lecture 9: 1 and 2Sample Estimation
Probability and Statistics Lecture 9: 1 and Sample Estimation to accompany Probability and Statistics for Engineers and Scientists Fatih Cavdur Introduction A statistic θ is said to be an unbiased estimator
More informationThe NeymanPearson lemma. The NeymanPearson lemma
The NeymanPearson lemma In practical hypothesis testing situations, there are typically many tests possible with significance level α for a null hypothesis versus alternative hypothesis. This leads to
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 informationUse of the ChiSquare Statistic. Marie DienerWest, PhD Johns Hopkins University
This work is licensed under a Creative Commons AttributionNonCommercialShareAlike License. Your use of this material constitutes acceptance of that license and the conditions of use of materials on this
More informationPermutation Tests with SAS
Permutation Tests with SAS /* testmultest1.sas */ options linesize=79 noovp formdlim='_'; title 'Permutation test example from lecture: Onesided p = 0.10'; data scramble; input group Y; datalines; 1 1.3
More informationChapter 16. Law of averages. Chance. Example 1: rolling two dice Sum of draws. Setting up a. Example 2: American roulette. Summary.
Overview Box Part V Variability The Averages Box We will look at various chance : Tossing coins, rolling, playing Sampling voters We will use something called s to analyze these. Box s help to translate
More informationChapter 3 RANDOM VARIATE GENERATION
Chapter 3 RANDOM VARIATE GENERATION In order to do a Monte Carlo simulation either by hand or by computer, techniques must be developed for generating values of random variables having known distributions.
More informationHypothesis Testing. Barrow, Statistics for Economics, Accounting and Business Studies, 4 th edition Pearson Education Limited 2006
Hypothesis Testing Lecture 4 Hypothesis Testing Hypothesis testing is about making decisions Is a hypothesis true or false? Are women paid less, on average, than men? Principles of Hypothesis Testing The
More informationLecture 13  χ 2 Tests
Lecture 13  χ 2 Tests Statistics 102 Colin Rundel March 6, 2013 Weldon s dice Weldon s dice Walter Frank Raphael Weldon (18601906), was an English evolutionary biologist and a founder of biometry. He
More informationComputer Lab 3 Thursday, 24 February, 2011 DMS 106 4:00 5:15PM
Statistics: Continuous Methods STAT452/652, Spring 2011 Computer Lab 3 Thursday, 24 February, 2011 DMS 106 4:00 5:15PM Goodness of Fit tests: Chisquare, KolmogorovSmirnov, AndersonDarling, ShapiroWilk
More informationStaff Senate Nominations and Elections Frequently Asked Questions
1. Why would I be interested in running for Staff Senate? If you are interested in promoting the general welfare of the university, providing input on issues impacting staff and encouraging communication
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 informationNonParametric Tests in SPSS (withinsubjects) Dr Daniel Boduszek
NonParametric Tests in SPSS (withinsubjects) Dr Daniel Boduszek d.boduszek@hud.ac.uk Outline Wilcoxon Signedrank test SPSS procedure Interpretation of SPSS output Reporting Fridman s test SPSS procedure
More informationStatistical Inference. Prof. Kate Calder. If the coin is fair (chance of heads = chance of tails) then
Probability Statistical Inference Question: How often would this method give the correct answer if I used it many times? Answer: Use laws of probability. 1 Example: Tossing a coin If the coin is fair (chance
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question
Stats: Test Review Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question Provide an appropriate response. ) Given H0: p 0% and Ha: p < 0%, determine
More informationAn interval estimate (confidence interval) is an interval, or range of values, used to estimate a population parameter. For example 0.476<p<0.
Lecture #7 Chapter 7: Estimates and sample sizes In this chapter, we will learn an important technique of statistical inference to use sample statistics to estimate the value of an unknown population parameter.
More informationPROBABILITIES AND PROBABILITY DISTRIBUTIONS
Published in "Random Walks in Biology", 1983, Princeton University Press PROBABILITIES AND PROBABILITY DISTRIBUTIONS Howard C. Berg Table of Contents PROBABILITIES PROBABILITY DISTRIBUTIONS THE BINOMIAL
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 informationProbabilities and Proportions
CHAPTER 4 Probabilities and Proportions Chapter Overview While the graphic and numeric methods of Chapters 2 and 3 provide us with tools for summarizing data, probability theory, the subject of this chapter,
More informationMendelian Genetics. I. Background
Mendelian Genetics Objectives 1. To understand the Principles of Segregation and Independent Assortment. 2. To understand how Mendel s principles can explain transmission of characters from one generation
More informationHypothesis Testing Level I Quantitative Methods. IFT Notes for the CFA exam
Hypothesis Testing 2014 Level I Quantitative Methods IFT Notes for the CFA exam Contents 1. Introduction... 3 2. Hypothesis Testing... 3 3. Hypothesis Tests Concerning the Mean... 10 4. Hypothesis Tests
More informationAlgebra 2 C Chapter 12 Probability and Statistics
Algebra 2 C Chapter 12 Probability and Statistics Section 3 Probability fraction Probability is the ratio that measures the chances of the event occurring For example a coin toss only has 2 equally likely
More informationHaving a coin come up heads or tails is a variable on a nominal scale. Heads is a different category from tails.
Chisquare Goodness of Fit Test The chisquare test is designed to test differences whether one frequency is different from another frequency. The chisquare test is designed for use with data on a nominal
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 informationChapter 7 Probability. Example of a random circumstance. Random Circumstance. What does probability mean?? Goals in this chapter
Homework (due Wed, Oct 27) Chapter 7: #17, 27, 28 Announcements: Midterm exams keys on web. (For a few hours the answer to MC#1 was incorrect on Version A.) No grade disputes now. Will have a chance to
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 informationProbability: Terminology and Examples Class 2, 18.05, Spring 2014 Jeremy Orloff and Jonathan Bloom
Probability: Terminology and Examples Class 2, 18.05, Spring 2014 Jeremy Orloff and Jonathan Bloom 1 Learning Goals 1. Know the definitions of sample space, event and probability function. 2. Be able to
More informationExamination 110 Probability and Statistics Examination
Examination 0 Probability and Statistics Examination Sample Examination Questions The Probability and Statistics Examination consists of 5 multiplechoice test questions. The test is a threehour examination
More informationGoodness of Fit Goodness of fit  2 classes
Goodness of Fit Goodness of fit  2 classes A B 78 22 Do these data correspond reasonably to the proportions 3:1? We previously discussed options for testing p A =0.75! Exact pvalue Exact confidence interval
More informationChapter 14: 16, 9, 12; Chapter 15: 8 Solutions When is it appropriate to use the normal approximation to the binomial distribution?
Chapter 14: 16, 9, 1; Chapter 15: 8 Solutions 141 When is it appropriate to use the normal approximation to the binomial distribution? The usual recommendation is that the approximation is good if np
More informationJudi Kinney, Author Jo Reynolds, Illustrations and Graphic Design
Judi Kinney, Author Jo Reynolds, Illustrations and Graphic Design An Attainment Company Publication 2003 Attainment Company, Inc. All rights reserved. Printed in the United States of America ISBN 1578614791
More informationMAT 1000. Mathematics in Today's World
MAT 1000 Mathematics in Today's World We talked about Cryptography Last Time We will talk about probability. Today There are four rules that govern probabilities. One good way to analyze simple probabilities
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 informationHypothesis Testing COMP 245 STATISTICS. Dr N A Heard. 1 Hypothesis Testing 2 1.1 Introduction... 2 1.2 Error Rates and Power of a Test...
Hypothesis Testing COMP 45 STATISTICS Dr N A Heard Contents 1 Hypothesis Testing 1.1 Introduction........................................ 1. Error Rates and Power of a Test.............................
More informationAdverse Impact Ratio for Females (0/ 1) = 0 (5/ 17) = 0.2941 Adverse impact as defined by the 4/5ths rule was not found in the above data.
1 of 9 12/8/2014 12:57 PM (an OnLine Internet based application) Instructions: Please fill out the information into the form below. Once you have entered your data below, you may select the types of analysis
More informationCHAPTER 11. GOODNESS OF FIT AND CONTINGENCY TABLES
CHAPTER 11. GOODNESS OF FIT AND CONTINGENCY TABLES The chisquare distribution was discussed in Chapter 4. We now turn to some applications of this distribution. As previously discussed, chisquare is
More informationStatistics. Onetwo sided test, Parametric and nonparametric test statistics: one group, two groups, and more than two groups samples
Statistics Onetwo sided test, Parametric and nonparametric test statistics: one group, two groups, and more than two groups samples February 3, 00 Jobayer Hossain, Ph.D. & Tim Bunnell, Ph.D. Nemours
More information5. Ordinal regression: cumulative categories proportional odds. 6. Ordinal regression: comparison to single reference generalized logits
Lecture 23 1. Logistic regression with binary response 2. Proc Logistic and its surprises 3. quadratic model 4. HosmerLemeshow test for lack of fit 5. Ordinal regression: cumulative categories proportional
More informationSTAT 145 (Notes) Al Nosedal anosedal@unm.edu Department of Mathematics and Statistics University of New Mexico. Fall 2013
STAT 145 (Notes) Al Nosedal anosedal@unm.edu Department of Mathematics and Statistics University of New Mexico Fall 2013 CHAPTER 18 INFERENCE ABOUT A POPULATION MEAN. Conditions for Inference about mean
More informationChapter 13. ChiSquare. Crosstabs and Nonparametric Tests. Specifically, we demonstrate procedures for running two separate
1 Chapter 13 ChiSquare This section covers the steps for running and interpreting chisquare analyses using the SPSS Crosstabs and Nonparametric Tests. Specifically, we demonstrate procedures for running
More informationGeneral Procedure for Hypothesis Test. Five types of statistical analysis. 1. Formulate H 1 and H 0. General Procedure for Hypothesis Test
Five types of statistical analysis General Procedure for Hypothesis Test Descriptive Inferential Differences Associative Predictive What are the characteristics of the respondents? What are the characteristics
More informationSession 8 Probability
Key Terms for This Session Session 8 Probability Previously Introduced frequency New in This Session binomial experiment binomial probability model experimental probability mathematical probability outcome
More informationInstructions for : TI83, 83Plus, 84Plus for STP classes, Ela Jackiewicz
Computing areas under normal curves: option 2 normalcdf(lower limit, upper limit, mean, standard deviation) will give are between lower and upper limits (mean=0 and St.dev=1 are default values) Ex1 To
More informationTI89, TI92, Voyage 200 List Editor Basics
TI89, TI92, Voyage 200 List Editor Basics What follows is a brief description of how to enter, retrieve, and manipulate data in the List Editor of the TI89, TI92, and Voyage 200. (The instructions
More informationStatistical Foundations:
Statistical Foundations: Hypothesis Testing Psychology 790 Lecture #10 9/26/2006 Today sclass Hypothesis Testing. An Example. Types of errors illustrated. Misconceptions about hypothesis testing. Upcoming
More informationAP Statistics 7!3! 6!
Lesson 64 Introduction to Binomial Distributions Factorials 3!= Definition: n! = n( n 1)( n 2)...(3)(2)(1), n 0 Note: 0! = 1 (by definition) Ex. #1 Evaluate: a) 5! b) 3!(4!) c) 7!3! 6! d) 22! 21! 20!
More informationChapter 4 Lecture Notes
Chapter 4 Lecture Notes Random Variables October 27, 2015 1 Section 4.1 Random Variables A random variable is typically a realvalued function defined on the sample space of some experiment. For instance,
More information6. Let X be a binomial random variable with distribution B(10, 0.6). What is the probability that X equals 8? A) (0.6) (0.4) B) 8! C) 45(0.6) (0.
Name: Date:. For each of the following scenarios, determine the appropriate distribution for the random variable X. A) A fair die is rolled seven times. Let X = the number of times we see an even number.
More informationHypothesis Testing. Bluman Chapter 8
CHAPTER 8 Learning Objectives C H A P T E R E I G H T Hypothesis Testing 1 Outline 81 Steps in Traditional Method 82 z Test for a Mean 83 t Test for a Mean 84 z Test for a Proportion 85 2 Test for
More informationTopic 8. Chi Square Tests
BE540W Chi Square Tests Page 1 of 5 Topic 8 Chi Square Tests Topics 1. Introduction to Contingency Tables. Introduction to the Contingency Table Hypothesis Test of No Association.. 3. The Chi Square Test
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 information