# Scientific Method & Statistical Reasoning

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 Scientific Method & Statistical Reasoning Paul Gribble Winter, 2016

2 MD Chapters 1 & 2 The idea of pure science Philosophical stances on science Historical review Gets you thinking about the logic of science and experimentation

3 Assumptions Lawfulness of nature Regularities exist, can be discovered, and are understandable Nature is uniform Causality events have causes; if we reconstruct the causes, the event should occur again can we ever prove causality? Reductionism Can we ever prove anything? What is proof?

4 Assumptions Finite Causation causes are finite in number and discoverable generality of some sort is possible We don t have to replicate an infinite # of elements to replicate an effect Bias toward simplicity (parsimony) seek simplicity and distrust it start with simplest model: try to refute it; when it fails, add complexity (slowly)

5 Philosophy of Science Logical Positivism Karl Popper & deductive reasoning progress occurs by falsifying theories

6 Logical Fallacy Fallacy of inductive reasoning (affirming the consequent) Predict: If theory T, then data will follow pattern P Observe: data indeed follows pattern P Conclude: therefore theory T is true example A sore throat is one of the symptoms of influenza (the flu) I have a sore throat Therefore, I have the flu Of course other things besides influenza can cause a sort throat. For example the common cold. Or yelling a lot. Or cancer.

7 Falsification is better Falsification Predict: If theory T is true, then data will follow pattern P Observe: data do not follow pattern P Conclude: theory T cannot be true We cannot prove a theory to be true. We can only prove a theory to be false.

8 Karl Popper Theories must have concrete predictions constructs (measures) must be valid empirical methodology must be valid

9 Basis of Interpreting Data the Fisher tradition statistics is not mathematics statistics is not arithmetic or calculation statistics is a logical framework for: making decisions about theories based on data defending your arguments Fisher ( ) was a central figure in modern approaches to statistics The F-test is named after him

10 The Fundamental Idea THE critical ingredient in an inferential statistical test (in the frequentist approach): determining the probability, assuming the null hypothesis is true, of obtaining the observed data

11 The Fundamental Idea Calculation of probability is typically based on probability distributions continuous (e.g. z, t, F) discrete (e.g. binomial) We can also compute this probability without having to assume a theoretical distribution Use resampling techniques e.g. bootstrapping

12 Basis of Interpreting Data design experiments so that inferences drawn are fully justified and logically compelled by the data theoretical explanation is different from the statistical conclusion Fisher s key insight: randomization assures no uncontrolled factor will bias results of statistical tests

13 A Discrete Probability Example I Last fall in my lab we were making espresso, and I claimed that I could taste the difference between Illy beans (which are expensive) and Lavazza beans (which are less expensive). I Let s think about how to design a test to determine whether or not I actually have this ability

14 Testing Mr. EspressoHead Many factors might affect his judgment temperature of the espresso temperature of the milk use of sugar precise ratio of milk to espresso Prior to Fisher you must experimentally control for everything every latte must be identical except for the independent variable of interest

15 Testing Mr. EspressoHead How to design your experiment? a single judgment? he might get it right just by guessing this is the null hypothesis! H 0 is he does not have the claimed ability H 0 is that he is guessing

16 Testing Mr. EspressoHead How many cups are required for a sufficient test? how about 8 cups (4 Illy, 4 Lavazza) present in random order tell subject that they have to separate the 8 cups into 2 groups: 4 Illy and 4 Lavazza is this a sufficient # of judgments? how do we decide how many is sufficient?

17 Testing Mr. EspressoHead Key Idea consider the possible results of the experiment, and the probability of each, given the null hypothesis that he is guessing there are many ways of dividing a set of 8 cups into Illy and Lavazza Pr(correct by chance) = (# exactly correct divisions) / (total # possible divisions)

18 Testing Mr. EspressoHead only one division exactly matches the correct discrimination therefore numerator = 1 what about the denominator? how many ways are there to classify 8 cups into 2 groups of 4? equals # ways of choosing 4 Illy cups out of 8 (since the other 4 Lavazza are then determined)

19 Testing Mr. EspressoHead 8 possible choices for first of 4 Illy cups for each of these 8 there are 7 remaining cups from which to choose the second Illy cup for each of these 7 there are 6 remaining cups from which to choose the third Illy cup for each of these 6 there are 5 remaining cups from which to choose the fourth and final Illy cup total # choices = 8 x 7 x 6 x 5 = 1680

20 Testing Mr. EspressoHead total # choices = 1680 does order of choices matter? (no) any set of 4 things can be ordered 24 different ways (4 x 3 x 2 x1 ) each set of 4 Illy cups would thus appear 24 times in a listing of the 1680 orderings so total # of distinct sets (where order doesn t matter) = (1680 / 24) = 70 unique sets of 4 Illy cups

21 Testing Mr. EspressoHead we can calculate this more directly using the formula for # of combinations of n things taken k at a time 8 choose 4 nck = (n!) / (k! (n-k)! ) = 8! / (4! (8-4)! ) = (8x7x6x5x4x3x2x1) / (4x3x2x1)x(4x3x2x1) = (8x7x6x5) / (4x3x2x1) = 70

22 Testing Mr. EspressoHead we have now formulated a statistical test for our null hypothesis the probability of me choosing the correct 4 Illy cups by guessing is (1 / 70) = = 1.4 % so if I do pick the correct 4 Illy cups, then it is much more likely (98.6 %) that I was not guessing you cannot prove I wasn t guessing you can only say that the probability of the observed outcome, if I was guessing, is low (1.4 %)

23 Testing Mr. EspressoHead from the Chapter Pr(perfect or 3/4 correct) = (1+16)/70 = 24 % nearly 1/4 of the time, just by guessing! so observed performance of 3/4 correct may not be sufficient to convince us of my claim

24 Logic of Statistical Tests review to design a scientific test of Mr. EspressoHead s claim, we designed an experiment where the chances of him guessing correctly 4/4 were low so if he did get 4/4 correct then what can we conclude? we could choose to reject the null hypothesis that he was guessing, because we calculated that the chances of this happening, are low

25 How low should you go? how low is low enough to reject the null hypothesis? 5 % (1 in 20) p<.05 2 % (1 in 50) p<.02 1 % (1 in 100) p< % (1 in 1,000,000) p< answer: it is arbitrary, YOU must decide but consider convention in: your lab / journal / field

26 How low should you go? what is the relative cost of making a wrong conclusion? concluding YES he has the ability when in fact he doesn t (type-i error) concluding NO he doesn t have the ability when in fact he does (type-ii error) costs may be different depending on the situation drug trial for a new, but very expensive (but potentially beneficial) cancer drug your thesis experiment, which appears to contradict a major accepted theory in neuroscience your thesis experiment, which appears to contradict your own previous study

27 Tests based on Distributional Assumptions Instead of counting or calculating possible outcomes we typically rely on statistical tables give probabilities based on theoretical distributions of test statistics typically based on the assumption that the dependent variables are normally distributed allows generalization to population, not just a particular sample e.g. the t-test (next week) We can however proceed without assuming particular theoretical distributions non-parametric statistical tests resampling techniques

28 for next week catch up on readings MD 1 & 2 (today s class) Start in on readings for Hypothesis Testing (MC3, MC7, MCt, N14)

### Lecture 20 Popper s Deductive Method

Lecture 20 Popper s Deductive Method Patrick Maher Philosophy 270 Spring 2010 Karl Popper 1902: Born in Vienna. 1935: Logic of Scientific Discovery (in German). 1937 1945: Lecturer at Canterbury, New Zealand.

### Scientific Reasoning: A Solution to the Problem of Induction

International Journal of Basic & Applied Sciences IJBAS-IJENS Vol:10 No:03 49 Scientific Reasoning: A Solution to the Problem of Induction Wilayat Khan and Habib Ullah COMSATS Institute of Information

### Topic #6: Hypothesis. Usage

Topic #6: Hypothesis A hypothesis is a suggested explanation of a phenomenon or reasoned proposal suggesting a possible correlation between multiple phenomena. The term derives from the ancient Greek,

### Research Methods in Mathematical Sciences. mathematics, science and the scientific method

Research Methods in Mathematical Sciences mathematics, science and the scientific method What is science? What is science? Encyclopedia Britannica says Any system of knowledge that is concerned with the

### One natural response would be to cite evidence of past mornings, and give something like the following argument:

Hume on induction Suppose you were asked to give your reasons for believing that the sun will come up tomorrow, in the form of an argument for the claim that the sun will come up tomorrow. One natural

### 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

### IS HUME S ACCOUNT SCEPTICAL?

Michael Lacewing Hume on knowledge HUME S FORK Empiricism denies that we can know anything about how the world outside our own minds is without relying on sense experience. In IV, Hume argues that we can

### Cosmological Arguments for the Existence of God S. Clarke

Cosmological Arguments for the Existence of God S. Clarke [Modified Fall 2009] 1. Large class of arguments. Sometimes they get very complex, as in Clarke s argument, but the basic idea is simple. Lets

Section 5.1 Climbing an Infinite Ladder Suppose we have an infinite ladder and the following capabilities: 1. We can reach the first rung of the ladder. 2. If we can reach a particular rung of the ladder,

### Develop hypothesis and then research to find out if it is true. Derived from theory or primary question/research questions

Chapter 12 Hypothesis Testing Learning Objectives Examine the process of hypothesis testing Evaluate research and null hypothesis Determine one- or two-tailed tests Understand obtained values, significance,

### Descartes Fourth Meditation On human error

Descartes Fourth Meditation On human error Descartes begins the fourth Meditation with a review of what he has learned so far. He began his search for certainty by questioning the veracity of his own senses.

### We have already discussed hypothesis testing in study unit 13. In this

14 study unit fourteen hypothesis tests applied to means: two related samples We have already discussed hypothesis testing in study unit 13. In this study unit we shall test a hypothesis empirically in

### Direct Proofs. CS 19: Discrete Mathematics. Direct Proof: Example. Indirect Proof: Example. Proofs by Contradiction and by Mathematical Induction

Direct Proofs CS 19: Discrete Mathematics Amit Chakrabarti Proofs by Contradiction and by Mathematical Induction At this point, we have seen a few examples of mathematical proofs. These have the following

### Experimental Research Strategy Experimental Research (Platt)

Experimental Research Outline: Strategy of experimental research (Platt) What are experiments and how to do experimental research, Different kinds of experimental designs. Experimental Research Strategy

### The Cosmological Argument

A quick overview An a posteriori argument Everything that exists in the universe exists because it was caused by something else. That something was caused by something else It is necessary for something

### Chapter 1 Introduction to the Scientific Method Can Science Cure the Common Cold?

Chapter 1 Introduction to the Scientific Method Can Science Cure the Common Cold? 1.1 The Process of Science Science is a body of knowledge and the process used to obtain the knowledge As knowledge, science

### Lecture 3. Mathematical Induction

Lecture 3 Mathematical Induction Induction is a fundamental reasoning process in which general conclusion is based on particular cases It contrasts with deduction, the reasoning process in which conclusion

### Oh Yeah? Well, Prove It.

Oh Yeah? Well, Prove It. MT 43A - Abstract Algebra Fall 009 A large part of mathematics consists of building up a theoretical framework that allows us to solve problems. This theoretical framework is built

### Comparison of frequentist and Bayesian inference. Class 20, 18.05, Spring 2014 Jeremy Orloff and Jonathan Bloom

Comparison of frequentist and Bayesian inference. Class 20, 18.05, Spring 2014 Jeremy Orloff and Jonathan Bloom 1 Learning Goals 1. Be able to explain the difference between the p-value and a posterior

### TRANSCRIPT: In this lecture, we will talk about both theoretical and applied concepts related to hypothesis testing.

This is Dr. Chumney. The focus of this lecture is hypothesis testing both what it is, how hypothesis tests are used, and how to conduct hypothesis tests. 1 In this lecture, we will talk about both theoretical

### PROOF AND PROBABILITY(teaching notes)

PROOF AND PROBABILITY(teaching notes) In arguing for God s existence, it is important to distinguish between proof and probability. Different rules of reasoning apply depending on whether we are testing

### Inferential Statistics. Probability. From Samples to Populations. Katie Rommel-Esham Education 504

Inferential Statistics Katie Rommel-Esham Education 504 Probability Probability is the scientific way of stating the degree of confidence we have in predicting something Tossing coins and rolling dice

### NGSS Science & Engineering Practices Grades K-2

ACTIVITY 8: SCIENCE AND ENGINEERING SELF-ASSESSMENTS NGSS Science & Engineering Practices Grades K-2 1 = Little Understanding; 4 = Expert Understanding Practice / Indicator 1 2 3 4 NOTES Asking questions

### Inferential Statistics

Inferential Statistics Sampling and the normal distribution Z-scores Confidence levels and intervals Hypothesis testing Commonly used statistical methods Inferential Statistics Descriptive statistics are

### Appendix I The Scientific Method

Appendix I The Scientific Method The study of science is different from other disciplines in many ways. Perhaps the most important aspect of science is its adherence to the principle of what is usually

### Logic, Sets, and Proofs

Logic, Sets, and Proofs David A. Cox and Catherine C. McGeoch Amherst College 1 Logic Logical Statements. A logical statement is a mathematical statement that is either true or false. Here we denote logical

### Hypothesis testing. c 2014, Jeffrey S. Simonoff 1

Hypothesis testing So far, we ve talked about inference from the point of estimation. We ve tried to answer questions like What is a good estimate for a typical value? or How much variability is there

### The Philosophical Importance of Mathematical Logic Bertrand Russell

The Philosophical Importance of Mathematical Logic Bertrand Russell IN SPEAKING OF "Mathematical logic", I use this word in a very broad sense. By it I understand the works of Cantor on transfinite numbers

### Chapter 4. Descartes, Third Meditation. 4.1 Homework

Chapter 4 Descartes, Third Meditation 4.1 Homework Readings : - Descartes, Meditation III - Objections and Replies: a) Third O and R: CSM II, 132; 127-8. b) Fifth O and R: CSM II, 195-97, 251. c) First

### Basic Principles of Experimental Design. Basic Principles. Control. Theory and Scientific Judgment. Positivism. Not Identifying the Real Cause

1 Basic Principles of Experimental Design Basic Principles Cause and Effect: the cause must precede the effect in time. X Y (Sufficient) Z X Y We must control Z or include it. X Y (Necessary) Treatment

### Introduction to. Hypothesis Testing CHAPTER LEARNING OBJECTIVES. 1 Identify the four steps of hypothesis testing.

Introduction to Hypothesis Testing CHAPTER 8 LEARNING OBJECTIVES After reading this chapter, you should be able to: 1 Identify the four steps of hypothesis testing. 2 Define null hypothesis, alternative

### 11. Logic of Hypothesis Testing

11. Logic of Hypothesis Testing A. Introduction B. Significance Testing C. Type I and Type II Errors D. One- and Two-Tailed Tests E. Interpreting Significant Results F. Interpreting Non-Significant Results

### This 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

### 1. R In this and the next section we are going to study the properties of sequences of real numbers.

+a 1. R In this and the next section we are going to study the properties of sequences of real numbers. Definition 1.1. (Sequence) A sequence is a function with domain N. Example 1.2. A sequence of real

### Ad hominem: An argument directed at an opponent in a disagreement, not at the topic under discussion.

Glossary of Key Terms Ad hominem: An argument directed at an opponent in a disagreement, not at the topic under discussion. Agent: One who acts and is held responsible for those actions. Analytic judgment:

About Hypothesis Testing TABLE OF CONTENTS About Hypothesis Testing... 1 What is a HYPOTHESIS TEST?... 1 Hypothesis Testing... 1 Hypothesis Testing... 1 Steps in Hypothesis Testing... 2 Steps in Hypothesis

### 1. The Scientific Method

1 1. The Scientific Method The distinctive characteristic of science is its methodology. Science is not just a body of knowledge, but knowledge assembled by the application of the scientific methodology.

### Answer Key for California State Standards: Algebra I

Algebra I: Symbolic reasoning and calculations with symbols are central in algebra. Through the study of algebra, a student develops an understanding of the symbolic language of mathematics and the sciences.

### Mathematical Induction

Mathematical Induction MAT30 Discrete Mathematics Fall 016 MAT30 (Discrete Math) Mathematical Induction Fall 016 1 / 19 Outline 1 Mathematical Induction Strong Mathematical Induction MAT30 (Discrete Math)

### Science and Scientific Reasoning. Critical Thinking

Science and Scientific Reasoning Critical Thinking Some Common Myths About Science Science: What it is and what it is not Science and Technology Science is not the same as technology The goal of science

### Descriptive Statistics

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

### Reality in the Eyes of Descartes and Berkeley. By: Nada Shokry 5/21/2013 AUC - Philosophy

Reality in the Eyes of Descartes and Berkeley By: Nada Shokry 5/21/2013 AUC - Philosophy Shokry, 2 One person's craziness is another person's reality. Tim Burton This quote best describes what one finds

### MATH 10: Elementary Statistics and Probability Chapter 9: Hypothesis Testing with One Sample

MATH 10: Elementary Statistics and Probability Chapter 9: Hypothesis Testing with One Sample Tony Pourmohamad Department of Mathematics De Anza College Spring 2015 Objectives By the end of this set of

### Philosophical argument

Michael Lacewing Philosophical argument At the heart of philosophy is philosophical argument. Arguments are different from assertions. Assertions are simply stated; arguments always involve giving reasons.

### Hypothesis: the essential tool for research Source: Singh (2006), Kothari (1985) and Dawson (2002)

Hypothesis: the essential tool for research Source: Singh (2006), Kothari (1985) and Dawson (2002) As I mentioned it earlier that hypothesis is one of the fundamental tools for research in any kind of

### MULTIPLE REGRESSION AND ISSUES IN REGRESSION ANALYSIS

MULTIPLE REGRESSION AND ISSUES IN REGRESSION ANALYSIS MSR = Mean Regression Sum of Squares MSE = Mean Squared Error RSS = Regression Sum of Squares SSE = Sum of Squared Errors/Residuals α = Level of Significance

### DEVELOPING HYPOTHESIS AND

Shalini Prasad Ajith Rao Eeshoo Rehani DEVELOPING 500 METHODS SEPTEMBER 18 TH 2001 DEVELOPING HYPOTHESIS AND Introduction Processes involved before formulating the hypotheses. Definition Nature of Hypothesis

### General Procedures for Testing Hypotheses

Chapter 19 General Procedures for Testing Hypothesies 297 CHAPTER 19 General Procedures for Testing Hypotheses Introduction Skeleton Procedure for Testing Hypotheses An Example: Can the Bio-Engineer Increase

### The Scientific Method. An example. An example. An example. The Scientific Method. How would you define the scientific method? The Scientific Method

BES 301 Jan. 4, 2011 How would you define the scientific method? 1. Observation - collecting information (data) 2. Question formulating a question (often from the observation) 3. Hypothesis - forming a

### This section demonstrates some different techniques of proving some general statements.

Section 4. Number Theory 4.. Introduction This section demonstrates some different techniques of proving some general statements. Examples: Prove that the sum of any two odd numbers is even. Firstly you

### Hypothesis testing. c 2014, Jeffrey S. Simonoff 1

Hypothesis testing So far, we ve talked about inference from the point of estimation. We ve tried to answer questions like What is a good estimate for a typical value? or How much variability is there

### Aquinas on Essence, Existence, and Divine Simplicity Strange but Consistent. In the third question of the Summa Theologiae, Aquinas is concerned with

Aquinas on Essence, Existence, and Divine Simplicity Strange but Consistent In the third question of the Summa Theologiae, Aquinas is concerned with divine simplicity. This is important for him both theologically

### 0 : square root of zero. 1 : square root of one. 2 : square root of two. 3 : square root of three. 4 : square root of four. 5 : square root of five.

Instructor: Math 05 TOPICS IN MATHEMATICS REVIEW OF LECTURES XIII February 8 (Wed), 205 Yasuyuki Kachi Line #: 52920. 3. Square roots. Today we learn square-root/square-rooting. First, notation and pronunciation:

### 8.7 Mathematical Induction

8.7. MATHEMATICAL INDUCTION 8-135 8.7 Mathematical Induction Objective Prove a statement by mathematical induction Many mathematical facts are established by first observing a pattern, then making a conjecture

### The argument over p-values and the Null Hypothesis Significance Testing (NHST) paradigm. Matt Homer

The argument over p-values and the Null Hypothesis Significance Testing (NHST) paradigm Matt Homer m.s.homer@leeds.ac.uk http://www.education.leeds.ac.uk/people/staff/academic/homer This talk What prompted

### MS&E 226: Small Data. Lecture 17: Additional topics in inference (v1) Ramesh Johari

MS&E 226: Small Data Lecture 17: Additional topics in inference (v1) Ramesh Johari ramesh.johari@stanford.edu 1 / 34 Warnings 2 / 34 Modeling assumptions: Regression Remember that most of the inference

### Validity and Reliability. Edgar Degas: Portraits in a New Orleans Cotton Office, 1873

Validity and Reliability Edgar Degas: Portraits in a New Orleans Cotton Office, 1873 Validity and Reliability A more complete explanation of validity and reliability is provided at the accompanying web

### Statistical Foundations:

Statistical Foundations: Hypothesis Testing Psychology 790 Lecture #9 9/19/2006 Today sclass Hypothesis Testing. General terms and philosophy. Specific Examples Hypothesis Testing Rules of the NHST Game

### INTRODUCTION TO PROOFS: HOMEWORK SOLUTIONS

INTRODUCTION TO PROOFS: HOMEWORK SOLUTIONS STEVEN HEILMAN Contents 1. Homework 1 1 2. Homework 2 6 3. Homework 3 10 4. Homework 4 16 5. Homework 5 19 6. Homework 6 21 7. Homework 7 25 8. Homework 8 28

### Paradigm Shift in Social Science Research A Significance Testing and Effect Size Estimation Rapprochement?

PsycCRITIQUES 2004 by the American Psychological Association October 12, 2004 Vol. 49, Supplement 3. Paradigm Shift in Social Science Research A Significance Testing and Effect Size Estimation Rapprochement?

### Checklists and Examples for Registering Statistical Analyses

Checklists and Examples for Registering Statistical Analyses For well-designed confirmatory research, all analysis decisions that could affect the confirmatory results should be planned and registered

### Study 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

### Practical Research. Paul D. Leedy Jeanne Ellis Ormrod. Planning and Design. Tenth Edition

Practical Research Planning and Design Tenth Edition Paul D. Leedy Jeanne Ellis Ormrod 2013, 2010, 2005, 2001, 1997 Pearson Education, Inc. All rights reserved. Chapter 1 The Nature and Tools of Research

### Confidence intervals and hypothesis tests

Patrick Breheny January 19 Patrick Breheny STA 580: Biostatistics I 1/46 Recap In our last lecture, we discussed at some length the Public Health Service study of the polio vaccine We discussed the careful

### Chapter 8. Professor Tim Busken. April 20, Chapter 8. Tim Busken. 8.2 Basics of. Hypothesis Testing. Works Cited

Chapter 8 Professor April 20, 2014 In Chapter 8, we continue our study of inferential statistics. Concept: Inferential Statistics The two major activities of inferential statistics are 1 to use sample

### Science & Engineering Practices in Next Generation Science Standards

Science & Engineering Practices in Next Generation Science Standards Asking Questions and Defining Problems: A practice of science is to ask and refine questions that lead to descriptions and explanations

### 6.3 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

### Outline. The problem. The problem. data collection and causal inference. The problem. Role of Data Collection in Statistical Inference 12 April 2011

Eat less salt, drink more wine, dump the cell-phone, eat more salt, and live longer: teaching students to understand the role of data collection in statistical inference Outline 1) The problem. 2) Why

### Rudy Hirschheim. E.J. Ourso College of Business Louisiana State University

Scientific Knowledge Creation Rudy Hirschheim E.J. Ourso College of Business Louisiana State University What is science Science is to develop laws and theories to explain, predict, understand and control

### CONTINGENCY TABLES ARE NOT ALL THE SAME David C. Howell University of Vermont

CONTINGENCY TABLES ARE NOT ALL THE SAME David C. Howell University of Vermont To most people studying statistics a contingency table is a contingency table. We tend to forget, if we ever knew, that contingency

### M2L1. Random Events and Probability Concept

M2L1 Random Events and Probability Concept 1. Introduction In this lecture, discussion on various basic properties of random variables and definitions of different terms used in probability theory and

### The Way of G-d Class #6

The Way of G-d Class #6 A world that is getting older has to have a starting point. by Rabbi Moshe Zeldman 2007 JewishPathways.com 1 So far in our investigation of the logical basis for an infinite existence,

### On the Representation Theorems. of Neoclassical Utility Theory: A Comment

On the Representation Theorems of Neoclassical Utility Theory: A Comment Daniel Mahoney, PhD Atlanta, GA I would like to thank Robert P. Murphy for many helpful discussions on these issues. This is in

### MCQ TESTING OF HYPOTHESIS

MCQ TESTING OF HYPOTHESIS MCQ 13.1 A statement about a population developed for the purpose of testing is called: (a) Hypothesis (b) Hypothesis testing (c) Level of significance (d) Test-statistic MCQ

### Lecture #9 Tuesday, September 20, 2016 Textbook: Section 4.3, 5.1, 5.2, 5.3

STATISTICS 200 Lecture #9 Tuesday, September 20, 2016 Textbook: Section 4.3, 5.1, 5.2, 5.3 Objectives: Understand Simpson s paradox: What causes it, why it s surprising Contrast statistical significance

### Exact Nonparametric Tests for Comparing Means - A Personal Summary

Exact Nonparametric Tests for Comparing Means - A Personal Summary Karl H. Schlag European University Institute 1 December 14, 2006 1 Economics Department, European University Institute. Via della Piazzuola

### Practice of Thesis Projects

Practice of Thesis Projects Goal of a thesis Ba thesis: a report written individually in which: A clear research question is formulated based on a problem definition and a given objective; The student

### WRITING PROOFS. Christopher Heil Georgia Institute of Technology

WRITING PROOFS Christopher Heil Georgia Institute of Technology A theorem is just a statement of fact A proof of the theorem is a logical explanation of why the theorem is true Many theorems have this

### Hypothesis testing. Hypothesis testing asks how unusual it is to get data that differ from the null hypothesis.

Hypothesis testing Hypothesis testing asks how unusual it is to get data that differ from the null hypothesis. If the data would be quite unlikely under H 0, we reject H 0. So we need to know how good

### 15.0 More Hypothesis Testing

15.0 More Hypothesis Testing 1 Answer Questions Type I and Type II Error Power Calculation Bayesian Hypothesis Testing 15.1 Type I and Type II Error In the philosophy of hypothesis testing, the null hypothesis

### On Cuneo s defence of the parity premise

1 On Cuneo s defence of the parity premise G.J.E. Rutten 1. Introduction In his book The Normative Web Terence Cuneo provides a core argument for his moral realism of a paradigmatic sort. Paradigmatic

### Relative Risk, Odds, and Fisher s exact test

Relative Risk, Odds, and Fisher s exact test I) Relative Risk A) Simply, relative risk is the ratio of p 1 / p 2. For instance, suppose we wanted to take another look at our Seat belt safety data from

### ORDERS OF ELEMENTS IN A GROUP

ORDERS OF ELEMENTS IN A GROUP KEITH CONRAD 1. Introduction Let G be a group and g G. We say g has finite order if g n = e for some positive integer n. For example, 1 and i have finite order in C, since

### Conditional Probability, Hypothesis Testing, and the Monty Hall Problem

Conditional Probability, Hypothesis Testing, and the Monty Hall Problem Ernie Croot September 17, 2008 On more than one occasion I have heard the comment Probability does not exist in the real world, and

### NGSS Science and Engineering Practices* (March 2013 Draft)

Science and Engineering Practices Asking Questions and Defining Problems A practice of science is to ask and refine questions that lead to descriptions and explanations of how the natural and designed

### Hypothesis tests: the t-tests

Hypothesis tests: the t-tests Introduction Invariably investigators wish to ask whether their data answer certain questions that are germane to the purpose of the investigation. It is often the case that

### 13 Infinite Sets. 13.1 Injections, Surjections, and Bijections. mcs-ftl 2010/9/8 0:40 page 379 #385

mcs-ftl 2010/9/8 0:40 page 379 #385 13 Infinite Sets So you might be wondering how much is there to say about an infinite set other than, well, it has an infinite number of elements. Of course, an infinite

### Mathematical Induction. Part Three

Mathematical Induction Part Three Announcements Problem Set Two due Friday, October 4 at 2:5PM (just before class) Stop by office hours with questions! Email us at cs03@cs.stanford.edu with questions!

### Research Methods & Experimental Design

Research Methods & Experimental Design 16.422 Human Supervisory Control April 2004 Research Methods Qualitative vs. quantitative Understanding the relationship between objectives (research question) and

### Steps to Answering the Questions with Data

Hypothesis Testing Steps to Answering the Questions with Data How does science advance knowledge? How do we answer questions about the world using observations? Generally, science forms a question and

### Reading 7 : Program Correctness

CS/Math 240: Introduction to Discrete Mathematics Fall 2015 Instructors: Beck Hasti, Gautam Prakriya Reading 7 : Program Correctness 7.1 Program Correctness Showing that a program is correct means that

### Grade 7/8 Math Circles Sequences and Series

Faculty of Mathematics Waterloo, Ontario N2L 3G1 Centre for Education in Mathematics and Computing Grade 7/8 Math Circles Sequences and Series November 30, 2012 What are sequences? A sequence is an ordered

### Correlational Research

Correlational Research Chapter Fifteen Correlational Research Chapter Fifteen Bring folder of readings The Nature of Correlational Research Correlational Research is also known as Associational Research.

### Answer keys for Assignment 10: Measurement of study variables

Answer keys for Assignment 10: Measurement of study variables (The correct answer is underlined in bold text) 1. In a study, participants are asked to indicate the type of pet they have at home (ex: dog,

### Five High Order Thinking Skills

Five High Order Introduction The high technology like computers and calculators has profoundly changed the world of mathematics education. It is not only what aspects of mathematics are essential for learning,

### Attribute Gage R&R An Overview

Attribute Gage R&R An Overview Presented to ASQ Section 1302 August 18, 2011 by Jon Ridgway Overview What is an Attribute Gage R&R? Why is it worth the work? What are the caveats? How do I perform it?

### CHAPTER 3. Methods of Proofs. 1. Logical Arguments and Formal Proofs

CHAPTER 3 Methods of Proofs 1. Logical Arguments and Formal Proofs 1.1. Basic Terminology. An axiom is a statement that is given to be true. A rule of inference is a logical rule that is used to deduce