Power of a test.

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

Power of a test. power The power of a test (against a specific alternative value) Is the probability that the test will reject the null hypothesis when.

 When we perform a hypothesis test, we make a decision to either Reject the Null Hypothesis or Fail to Reject the Null Hypothesis.  There is always the.

Decision Errors and Power

+ Chapter 10 Section 10.4 Part 2 – Inference as Decision.

AP Statistics – Chapter 9 Test Review

Hypothesis Testing: Type II Error and Power.

Statistics 201 – Lecture 23. Confidence Intervals Re-cap 1.Estimate the population mean with sample mean Know sample mean is unbiased estimator for 

Power of a test. power The power of a test (against a specific alternative value) Is the probability that the test will reject the null hypothesis when.

Chapter 9 Hypothesis Testing.

Business Statistics - QBM117 Testing hypotheses about a population mean.

Power of a Test Notes: P 183 and on your own paper.

© 2002 Thomson / South-Western Slide 9-1 Chapter 9 Hypothesis Testing with Single Samples.

Hypothesis Testing.

1 BA 275 Quantitative Business Methods Hypothesis Testing Elements of a Test Concept behind a Test Examples Agenda.

The Probability of a Type II Error and the Power of the Test

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.

 When we perform a hypothesis test, we make a decision to either Reject the Null Hypothesis or Fail to Reject the Null Hypothesis.  There is always the.

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

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.

Copyright © 2013 Pearson Education, Inc. Publishing as Prentice Hall Statistics for Business and Economics 8 th Edition Chapter 9 Hypothesis Testing: Single.

Power of a Hypothesis test. H 0 True H 0 False Reject Fail to reject Type I Correct Type II Power   Suppose H 0 is true – what if we decide to fail.

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.

+ The Practice of Statistics, 4 th edition – For AP* STARNES, YATES, MOORE Unit 5: Hypothesis Testing.

Goals… Define what is meant by a Type I error. Define what is meant by a Type II error. Define what is meant by the power of a test. Identify the relationship.

Introduction to Hypothesis Testing

Inference as Design Target Goal: I can calculate and interpret a type I and type II error. 9.1c h.w: pg 547: 15, 19, 21.

Type I and Type II Errors. For type I and type II errors, we must know the null and alternate hypotheses. H 0 : µ = 40 The mean of the population is 40.

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.

Power of a test. power The power of a test (against a specific alternative value) Is In practice, we carry out the test in hope of showing that the null.

Hypothesis Testing Steps for the Rejection Region Method State H 1 and State H 0 State the Test Statistic and its sampling distribution (normal or t) Determine.

Power of a Test. Remember: Type I error – Reject the H 0 when you shouldn’t have. Type II error - Fail to reject the H o when you should have.

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

Chapter 10 Lesson 10.2 Hypotheses and Test Procedures 10.2: Errors in Hypothesis Testing.

Tests of hypothesis Statistical hypothesis definition: A statistical hypothesis is an assertion or conjecture on or more population.

+ Homework 9.1:1-8, 21 & 22 Reading Guide 9.2 Section 9.1 Significance Tests: The Basics.

Introduction to Inference Tests of Significance Proof

Warm Up Check your understanding p. 563

Type I & Type II Errors And Power

Section Testing a Proportion

Power of a test.

Example: Propellant Burn Rate

Power of a test.

Hypothesis Testing: Hypotheses

CONCEPTS OF HYPOTHESIS TESTING

P-value Approach for Test Conclusion

AP Statistics: Chapter 21

Chapter Nine Part 1 (Sections 9.1 & 9.2) Hypothesis Testing

Chapter 9: Hypothesis Tests Based on a Single Sample

Introduction to Inference

Power of a Test.

Section 10.3 Making Sense of Statistical Significance

Introduction to Inference

Power Section 9.7.

Power of a test.

Power of a test.

Chapter 7: Statistical Issues in Research planning and Evaluation

Power of a Hypothesis Test

Power of a test.

Hypothesis Testing and Confidence Intervals (Part 2): Cohen’s d, Logic of Testing, and Confidence Intervals Lecture 9 Justin Kern April 9, 2018.

Chapter 9: Testing a Claim

Homework: pg. 727 & ) A. Ho: p=0.75, Ha:p>0.75

Power of a test.

The POWER of a hypothesis test

Power Problems.

Inference as Decision Section 10.4.

Power and Error What is it?.

The z-test for the Mean of a Normal Population

Statistical Power.

Presentation transcript:

Power of a test

The power of a test (against a specific alternative value) Is the probability that the test will reject the null hypothesis when the alternative is true In practice, we carry out the test in hope of showing that the null hypothesis is false, so high power is important

H0 True H0 False Reject Fail to reject Suppose H0 is false – what if we decide to reject it? Suppose H0 is false – what if we decide to fail to reject it? We correctly reject a false H0! H0 True H0 False Reject Fail to reject Suppose H0 is true – what if we decide to fail to reject it? Type I Correct a Power Suppose H0 is true – what if we decide to reject it? Correct Type II b

What is the probability of committing a Type I error? A researcher selects a random sample of size 49 from a population with standard deviation s = 35 in order to test at the 1% significance level the hypothesis: H0: m = 680 Ha: m > 680 What is the probability of committing a Type I error? a = .01

H0: m = 680 Ha: m > 680 For what values of the sample mean would you reject the null hypothesis? Invnorm(.99,680,5) =691.63

What is the power of the test? H0: m = 680 Ha: m > 680 If H0 is rejected, suppose that ma is 700. What is the probability of committing a Type II error? What is the power of the test? Normalcdf(-10^99,691.63,700,5) =.0471 Power = 1 - .0471 = .9529

What is the power of the test? H0: m = 680 Ha: m > 680 If H0 is rejected, suppose that ma is 695. What is the probability of committing a Type II error? What is the power of the test? Normalcdf(-10^99,691.63,695,5) =.2502 Power = 1 - .2502 = .7498

Fail to Reject H0 Reject H0 a ma m0 Power = 1 - b b

What happens to a, b, & power when the sample size is increased? Fail to Reject H0 Reject H0 a m0 b ma

Facts: The researcher is free to determine the value of a. The experimenter cannot control b, since it is dependent on the alternate value. The ideal situation is to have a as small as possible and power close to 1. (Power > .8) As a increases, power increases. (But also the chance of a type I error has increased!) Best way to increase power, without increasing a, is to increase the sample size

Identify the decision: A water quality control board reports that water is unsafe for drinking if the mean nitrate concentration exceeds 30 ppm. Water specimens are taken from a well. Identify the decision: a) You decide that the water is not safe to drink when in fact it is safe. Type I Error

Identify the decision: A water quality control board reports that water is unsafe for drinking if the mean nitrate concentration exceeds 30 ppm. Water specimens are taken from a well. Identify the decision: b) You decide that the water is not safe to drink when in fact it is not safe. Correct – Power!!

Bottles of a popular cola are suppose to contain 300 ml of cola Bottles of a popular cola are suppose to contain 300 ml of cola. A consumer group believes the company is under-filling the bottles. (Assume s = 50 with n = 30) Find the power of this test against the alternative m = 296 ml.