The Language of Statistical Decision Making Lecture 2 Section 1.3 Mon, Sep 5, 2005.

Slides:

Advertisements

Similar presentations

Power of a test. power The power of a test (against a specific alternative value) Is a tests ability to detect a false hypothesis Is the probability that.

Advertisements

Introduction to Hypothesis Testing

CHAPTER 21 More About Tests: “What Can Go Wrong?”.

Our goal is to assess the evidence provided by the data in favor of some claim about the population. Section 6.2Tests of Significance.

Section 9.2: What is a Test of Significance?. Remember… H o is the Null Hypothesis ▫When you are using a mathematical statement, the null hypothesis uses.

Hypothesis Testing Steps of a Statistical Significance Test. 1. Assumptions Type of data, form of population, method of sampling, sample size.

Power and Effect Size.

State the null and alternative hypotheses.

Determining Statistical Significance

Hypothesis testing is used to make decisions concerning the value of a parameter.

Hypothesis Testing.

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

1 Virtual COMSATS Inferential Statistics Lecture-17 Ossam Chohan Assistant Professor CIIT Abbottabad.

Errors in Hypothesis Tests. When you perform a hypothesis test you make a decision: When you make one of these decisions, there is a possibility that.

1 Power and Sample Size in Testing One Mean. 2 Type I & Type II Error Type I Error: reject the null hypothesis when it is true. The probability of a Type.

Hypothesis testing Chapter 9. Introduction to Statistical Tests.

STA Statistical Inference

Unit 8 Section : z Test for a Mean  Many hypotheses are tested using the generalized statistical formula: Test value = (Observed Value)-(expected.

AP STATS: PROJECT Take 5-10 minutes to brainstorm ideas for your final project. Proposals will be due on Friday (rough drafts will be peer edited on Thursday).

Lecture 16 Dustin Lueker.  Charlie claims that the average commute of his coworkers is 15 miles. Stu believes it is greater than that so he decides to.

What’s in the Bag? Lecture 4 Section Wed, Sep 7, 2005.

Hypothesis Testing – A Primer. Null and Alternative Hypotheses in Inferential Statistics Null hypothesis: The default position that there is no relationship.

Inferential Statistics Body of statistical computations relevant to making inferences from findings based on sample observations to some larger population.

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

Errors in Hypothesis Tests. When you perform a hypothesis test you make a decision: When you make one of these decisions, there is a possibility that.

Correct decisions –The null hypothesis is true and it is accepted –The null hypothesis is false and it is rejected Incorrect decisions –Type I Error The.

Errors in Hypothesis Tests Notes: P When you perform a hypothesis test you make a decision: When you make one of these decisions, there is a possibility.

Errors in Hypothesis Tests. When you perform a hypothesis test you make a decision: When you make one of these decisions, there is a possibility that.

CHAPTER 9 Testing a Claim

Unit 8 Section 8-3 – Day : P-Value Method for Hypothesis Testing  Instead of giving an α value, some statistical situations might alternatively.

What’s in the Bag? Lecture 4 Section Wed, Jan 25, 2006.

© 2001 Prentice-Hall, Inc.Chap 9-1 BA 201 Lecture 14 Fundamentals of Hypothesis Testing.

Introduction to hypothesis testing Hypothesis testing is about making decisions Is a hypothesis true or false? Ex. Are women paid less, on average, than.

Introduction to Hypothesis Testing

Statistical Techniques

1.  What inferential statistics does best is allow decisions to be made about populations based on the information about samples.  One of the most useful.

Sampling Distributions Statistics Introduction Let’s assume that the IQ in the population has a mean (  ) of 100 and a standard deviation (  )

Major Steps. 1.State the hypotheses.  Be sure to state both the null hypothesis and the alternative hypothesis, and identify which is the claim. H0H0.

Today: Hypothesis testing. Example: Am I Cheating? If each of you pick a card from the four, and I make a guess of the card that you picked. What proportion.

Chapter Ten McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. One-Sample Tests of Hypothesis.

Chapter 9: Hypothesis Tests for One Population Mean 9.2 Terms, Errors, and Hypotheses.

The Language of Statistical Decision Making Lecture 1 Section 1.3 Fri, Jan 20, 2006.

Significance Tests: The Basics Textbook Section 9.1.

Statistical Inference for the Mean Objectives: (Chapter 8&9, DeCoursey) -To understand the terms variance and standard error of a sample mean, Null Hypothesis,

AP Statistics Part IV – Inference: Conclusions with Confidence Chapter 10: Introduction to Inference 10.1Estimating with Confidence To make an inference.

The Language of Statistical Decision Making Lecture 2 Section 1.3 Mon, Sep 4, 2006.

Section Testing a Proportion

Power of a test.

The Language of Statistical Decision Making

CHAPTER 9 Testing a Claim

Hypothesis Testing: Hypotheses

A Closer Look at Testing

Chapter Review Problems

Statistical Tests - Power

P-value Approach for Test Conclusion

Chapter 9: Hypothesis Testing

The Language of Statistical Decision Making

Lecture 2 Hypothesis Test

Chapter 9: Hypothesis Tests Based on a Single Sample

The Language of Statistical Decision Making

Lecture 4 Section Wed, Sep 6, 2006

The Language of Statistical Decision Making

Section 10.3 Making Sense of Statistical Significance

Lecture 4 Section Wed, Jan 19, 2005

More About Tests Notes from

Power of a test.

Power of a test.

Lecture 3 Section – Mon, Aug 30, 2004

Inference as Decision Section 10.4.

AP STATISTICS LESSON 10 – 4 (DAY 2)

Presentation transcript:

The Language of Statistical Decision Making Lecture 2 Section 1.3 Mon, Sep 5, 2005

Statistical Significance Statistically significant – The difference between the claim of the null hypothesis and the data is large enough that it cannot reasonably be attributed to chance. Statistically significant – The difference between the claim of the null hypothesis and the data is large enough that it cannot reasonably be attributed to chance.

Possible Errors We might reject H 0 when it is true. We might reject H 0 when it is true. This is a Type I error. This is a Type I error. We might accept H 0 when it is false. We might accept H 0 when it is false. This is a Type II error. This is a Type II error. See Making Intelligent Errors, by Walter Williams. See Making Intelligent Errors, by Walter Williams.Making Intelligent ErrorsMaking Intelligent Errors

Decisions and Errors Correct Type I Error Correct Type II Error State of Nature H 0 trueH 0 false Accept H 0 Reject H 0 Decision

Example Consider the hypotheses: Consider the hypotheses: H 0 : A category 5 hurricane will not hit New Orleans in the next 25 years. H 0 : A category 5 hurricane will not hit New Orleans in the next 25 years. H 1 : A category 5 hurricane will hit New Orleans in the next 25 years. H 1 : A category 5 hurricane will hit New Orleans in the next 25 years. What are the negative consequences of each type of error? What are the negative consequences of each type of error? Which type of error is more serious? Which type of error is more serious? Which should get the benefit of the doubt? Which should get the benefit of the doubt?

Example We should probably reverse the roles: We should probably reverse the roles: H 0 : A category 5 hurricane will hit New Orleans in the next 25 years. H 0 : A category 5 hurricane will hit New Orleans in the next 25 years. H 1 : A category 5 hurricane will not hit New Orleans in the next 25 years. H 1 : A category 5 hurricane will not hit New Orleans in the next 25 years.

Example Consider the hypotheses: Consider the hypotheses: H 0 : An asteroid will not hit New Orleans in the next 25 years. H 0 : An asteroid will not hit New Orleans in the next 25 years. H 1 : An asteroid will hit New Orleans in the next 25 years. H 1 : An asteroid will hit New Orleans in the next 25 years. What are the negative consequences of each type of error? What are the negative consequences of each type of error? Which type of error is more serious? Which type of error is more serious? Which should get the benefit of the doubt? Which should get the benefit of the doubt?

Example These are fine the way they are: These are fine the way they are: H 0 : An asteroid will not hit New Orleans in the next 25 years. H 0 : An asteroid will not hit New Orleans in the next 25 years. H 1 : An asteroid will hit New Orleans in the next 25 years. H 1 : An asteroid will hit New Orleans in the next 25 years.

Significance Level Significance Level – The likelihood of rejecting H 0 when it is true, i.e., the likelihood of committing a Type I error. Significance Level – The likelihood of rejecting H 0 when it is true, i.e., the likelihood of committing a Type I error.  – The likelihood of a Type I error.  – The likelihood of a Type I error.  – The likelihood of a Type II error.  – The likelihood of a Type II error. That is,  is the significance level. That is,  is the significance level. The quantity 1 –  is called the power of the test. The quantity 1 –  is called the power of the test.

Significance Level The value of  is determined by our criteria for rejecting the null hypothesis (which we haven’t talked about yet). The value of  is determined by our criteria for rejecting the null hypothesis (which we haven’t talked about yet). If we demand overwhelming evidence against H 0 before rejecting it, then  will be small. If we demand overwhelming evidence against H 0 before rejecting it, then  will be small. If we demand little evidence against it, then  will be large. If we demand little evidence against it, then  will be large.

Significance Level Generally speaking, as  increases,  decreases. Generally speaking, as  increases,  decreases. That is, if we demand overwhelming evidence against H 0 (i.e., for H 1 ) before rejecting it, then  will be large. That is, if we demand overwhelming evidence against H 0 (i.e., for H 1 ) before rejecting it, then  will be large. If we demand little evidence against H 0, then  will be small. If we demand little evidence against H 0, then  will be small.

Let’s Do It! Let’s do it! 1.5, p. 13 – Which Error is Worse? Let’s do it! 1.5, p. 13 – Which Error is Worse? Let’s do it! 1.6, p. 14 – Testing a New Drug. Let’s do it! 1.6, p. 14 – Testing a New Drug. Porn can make you blind. Porn can make you blind. Porn can make you blind. Porn can make you blind.