1 Introduction to Randomization Tests 3/7/2011 Copyright © 2011 Dan Nettleton.

Slides:

Advertisements

Similar presentations

An Simple Introduction to Statistical Significance Julie Graves MST Conference June 2014.

Advertisements

1 Parametric Empirical Bayes Methods for Microarrays 3/7/2011 Copyright © 2011 Dan Nettleton.

Introduction to Basic Statistical Methodology. CHAPTER 1 ~ Introduction ~

1 Introduction to Experimental Design 1/26/2009 Copyright © 2009 Dan Nettleton.

Objectives (BPS chapter 15)

Topic 6: Introduction to Hypothesis Testing

Introduction to Hypothesis Testing

Introduction to Inference Estimating with Confidence Chapter 6.1.

Business Statistics for Managerial Decision

Statistical Treatment of Data Significant Figures : number of digits know with certainty + the first in doubt. Rounding off: use the same number of significant.

TESTING A HYPOTHESIS RELATING TO THE POPULATION MEAN 1 This sequence describes the testing of a hypothesis at the 5% and 1% significance levels. It also.

Introduction to the design (and analysis) of experiments James M. Curran Department of Statistics, University of Auckland

Introduction to Testing a Hypothesis Testing a treatment Descriptive statistics cannot determine if differences are due to chance. A sampling error occurs.

Tests of significance: The basics BPS chapter 15 © 2006 W.H. Freeman and Company.

Copyright (c) 2004 Brooks/Cole, a division of Thomson Learning, Inc. Chapter 8 Tests of Hypotheses Based on a Single Sample.

Testing Hypotheses about a Population Proportion Lecture 29 Sections 9.1 – 9.3 Tue, Oct 23, 2007.

Section 9.1 Introduction to Statistical Tests 9.1 / 1 Hypothesis testing is used to make decisions concerning the value of a parameter.

Tests of significance: The basics BPS chapter 15 © 2006 W.H. Freeman and Company.

Statistics 101 Chapter 10. Section 10-1 We want to infer from the sample data some conclusion about a wider population that the sample represents. Inferential.

{ Chapter 4: Designing Studies 4.3 Using Studies Wisely.

Copyright © Cengage Learning. All rights reserved. 10 Inferences Involving Two Populations.

AP Statistics Section 11.1 A Basics of Significance Tests

Hypothesis Testing Introduction to Statistics Chapter 8 Mar 2-4, 2010 Classes #13-14.

Introductions NAME HOME TOWN FIELD OF RESEARCH AND/OR MAJOR SOMETHING FUN THAT YOU DID THIS SUMMER.

Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide

Aim: How can we assign experimental units to treatments in a way that is fair to all of the treatments?

Lecture 16 Section 8.1 Objectives: Testing Statistical Hypotheses − Stating hypotheses statements − Type I and II errors − Conducting a hypothesis test.

The Practice of Statistics, 5th Edition Starnes, Tabor, Yates, Moore Bedford Freeman Worth Publishers CHAPTER 10 Comparing Two Populations or Groups 10.1.

The Practice of Statistics, 5th Edition Starnes, Tabor, Yates, Moore Bedford Freeman Worth Publishers CHAPTER 10 Comparing Two Populations or Groups 10.1.

Statistical Significance The power of ALPHA. “ Significant ” in the statistical sense does not mean “ important. ” It means simply “ not likely to happen.

CHAPTER 15: Tests of Significance The Basics ESSENTIAL STATISTICS Second Edition David S. Moore, William I. Notz, and Michael A. Fligner Lecture Presentation.

BPS - 3rd Ed. Chapter 141 Tests of significance: the basics.

Introduction to Hypothesis Testing: the z test. Testing a hypothesis about SAT Scores (p210) Standard error of the mean Normal curve Finding Boundaries.

Copyright © Cengage Learning. All rights reserved. 12 Analysis of Variance.

AP Statistics Section 11.1 B More on Significance Tests.

Introduction to inference Tests of significance IPS chapter 6.2 © 2006 W.H. Freeman and Company.

1 Estimation of Gene-Specific Variance 2/17/2011 Copyright © 2011 Dan Nettleton.

Hypothesis Testing Introduction to Statistics Chapter 8 Feb 24-26, 2009 Classes #12-13.

Introduction to Testing a Hypothesis Testing a treatment Descriptive statistics cannot determine if differences are due to chance. Sampling error means.

Tests of significance: The basics BPS chapter 14 © 2006 W.H. Freeman and Company.

Chapter 13: Part III AP Statistics.

4.3 Using Studies Wisely Objective SWBAT Describe the scope of inference that is appropriate in a statistical study.

Learning Objectives After this section, you should be able to: The Practice of Statistics, 5 th Edition1 DESCRIBE the shape, center, and spread of the.

A Quantitative Overview to Gene Expression Profiling in Animal Genetics Armidale Animal Breeding Summer Course, UNE, Feb Analysis of (cDNA) Microarray.

Producing Data 1.

Estimation of Gene-Specific Variance

CHAPTER 10 Comparing Two Populations or Groups

WARM – UP A local newspaper conducts a poll to predict the outcome of a Senate race. After conducting a random sample of 1200 voters, they find 52% support.

CHAPTER 10 Comparing Two Populations or Groups

Tests of significance: The basics

What does it mean to say that the results of an experiment are (or are not) statistically significant? The significance level,  (conventionally set to.

Incomplete Block Experimental Designs

Accel Precalculus Unit #1: Data Analysis Lesson #4: Introduction to Statistics.

Significance Tests: The Basics

Introduction to Randomization Tests

CHAPTER 10 Comparing Two Populations or Groups

Research Strategies: How Psychologists Ask and Answer Questions

Introduction to Basic Statistical Methodology

Incomplete Block Experimental Designs

Parametric Empirical Bayes Methods for Microarrays

Introduction to Experimental Design

CHAPTER 10 Comparing Two Populations or Groups

CHAPTER 10 Comparing Two Populations or Groups

CHAPTER 10 Comparing Two Populations or Groups

CHAPTER 10 Comparing Two Populations or Groups

Principles of Experimental Design

CHAPTER 10 Comparing Two Populations or Groups

CHAPTER 10 Comparing Two Populations or Groups

Principles of Experimental Design

CHAPTER 10 Comparing Two Populations or Groups

Presentation transcript:

1 Introduction to Randomization Tests 3/7/2011 Copyright © 2011 Dan Nettleton

2 An Example Suppose I have an instrument that measures the mRNA transcript abundance of a certain gene. I have developed a drug that I suspect will alter the expression of that gene when the drug is injected into a rat. I randomly divide a group of eight rats into two groups of four. Each rat in one group is injected with the drug. Each rat in the other group is injected with a control substance.

3 Hypothetical Data I use my instrument to measure the expression of the gene in each rat after treatment and obtain the following results: Control Drug Expression Average The difference in averages is 22-13=9. I wish to claim that this difference was caused by the drug.

4 Interpretation of the Results Clearly there is some natural variation in expression (not due to treatment) because the expression measures differ among rats within each treatment group. Maybe the observed difference (22-13=9) showed up simply because I happened to choose the rats with larger expression for injection with the drug. What is the chance of seeing such a large difference in treatment means if the drug has no effect?

5 Random Difference Assignment Control Drug in Averages

6 Difference in Treatment Means (Control – Drug) Number of Random Assignments Distribution of Difference between Treatment Means Assuming No Treatment Effect

7 Conclusions Only 2 of the 70 possible random assignments would have led to a difference between treatment means as large as 9. Thus, under the assumption of no drug effect, the chance of seeing a difference as large as we observed was 2/70 = Because is a small probability, we have reason to attribute the observed difference to the effect of the drug rather than a coincidence due to the way we assigned our experimental units to treatment groups.

8 Randomization Test This is an example of a randomization test. R.A. Fisher described such tests in the first half of the 20th century. Randomization tests are closely related to permutation tests (almost synonymous) which are popular for assessing statistical significance because they do not rely on specific distributional assumptions.