Significance Tests: The Basics

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

Answers Proportions Day 1.

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

Section 7.1 Hypothesis Testing: Hypothesis: Null Hypothesis (H 0 ): Alternative Hypothesis (H 1 ): a statistical analysis used to decide which of two competing.

Testing a Claim I’m a great free-throw shooter!. Significance Tests A significance test is a formal procedure for comparing observed data with a claim.

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.

Using Inference to Make Decisions

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.

Warm-up Day of 8.1 and 8.2 Review. 8.2 P#20, 23 and 24 P#20 a. and b. c. Since the p-hat is along the line for reasonably likely events.

Errors & Power. 2 Results of Significant Test 1. P-value < alpha 2. P-value > alpha Reject H o & conclude H a in context Fail to reject H o & cannot conclude.

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.

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.

AP Statistics Section 11.4 B

Section 9.1(re-visited)  Making Sense of Statistical Significance  Inference as Decision.

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

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.

If we fail to reject the null when the null is false what type of error was made? Type II.

Lesson 2: Section 9.1 (part 2).  Interpret a Type I Error and a Type II Error in context, and give the consequences of each.  Understand the relationship.

Chapter 9 Testing A Claim 9.1 SIGNIFICANT TESTS: THE BASICS OUTCOME: I WILL STATE THE NULL AND ALTERNATIVE HYPOTHESES FOR A SIGNIFICANCE TEST ABOUT A POPULATION.

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

Making Sense of Statistical Significance Inference as Decision

Errors in Hypothesis Tests

Power of a test.

CHAPTER 9 Testing a Claim

Power of a test.

Power of a test.

CHAPTER 9 Testing a Claim

Chapter 9: Testing a Claim

Chapter 9: Testing a Claim

Errors in Hypothesis Tests

Errors in Hypothesis Tests

Statistical Tests - Power

Using Inference to Make Decisions

Section 9.1 Significance Tests: The Basics

Section 10.3 Making Sense of Statistical Significance

Errors in Hypothesis Tests

Chapter 9: Testing a Claim

Chapter 9: Testing a Claim

Chapter 9: Testing a Claim

Errors in Hypothesis Tests

Power of a test.

Power of a test.

Power of a test.

Chapter 9: Testing a Claim

CHAPTER 9 Testing a Claim

CHAPTER 9 Testing a Claim

Chapter 9: Testing a Claim

Chapter 9: Testing a Claim

Pick a card….

CHAPTER 9 Testing a Claim

Pull 2 samples of 20 pennies and record both averages (2 dots).

Chapter 9: Testing a Claim

Chapter 9: Testing a Claim

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

Power of a test.

Chapter 9: Testing a Claim

Chapter 9: Testing a Claim

CHAPTER 9 Testing a Claim

Chapter 9: Testing a Claim

Chapter 9: Testing a Claim

CHAPTER 9 Testing a Claim

Power Problems.

Chapter 9: Testing a Claim

Inference as Decision Section 10.4.

Chapter 9: Testing a Claim

Chapter 9: Testing a Claim

Chapter 9: Testing a Claim

Chapter 9: Testing a Claim

Presentation transcript:

Significance Tests: The Basics Section 9.1 again… Significance Tests: The Basics

Type I and Type II Errors If we reject 𝐻 0 when 𝐻 0 is true, we have committed a Type I error. If we fail to reject 𝐻 0 when 𝐻 0 is false, we have committed a Type II error.

Another way to look at it!

Examples If someone is on trial for murder: 𝐻 0 : 𝐻 𝑎 : Type I error – we reject that they are innocent when we shouldn’t have…meaning we convicted an innocent person. Type II error – we let a guilty person go free. Which is worse?

Examples If someone is on trial for stealing a candy bar: 𝐻 0 : 𝐻 𝑎 : Type I error – we reject that they are innocent when we shouldn’t have…meaning we convicted an innocent person. Type II error – we let a guilty person go free. Which is worse?

Put your notes on the floor. What is Type I error? What is Type II error?

Example The manager of Wendy’s wants to reduce the proportion of drive-through customers who have to wait more than two minutes on their order. Based on store records, the proportion is currently p=0.63. To reduce this proportion, the manager assigns an additional employee to assist with drive-through orders. During the next month, the manager will collect a random sample of drive-through times and test the hypotheses: 𝐻 0 :p=0.63 𝐻 0 :𝑝<0.63 Describe a Type I and Type II error in this setting and explain the consequences of each.

Significance and Type I Error The Significance level 𝛼 of any fixed level test is the probability of a Type 1 error. If given the chance, consider the consequences of a Type I error before choosing a significance level.

Example For a truckload of potatoes, we are testing the proportion that have blemishes. 𝐻 0 :𝑝=0.08 𝐻 0 :𝑝>0.08 Suppose that the potato-chip producer decides to carry out this test on a SRS of 500 potatoes using a 5% significant level.

Example

Power and Type II Error The power of a test against any alternative is one minus the probability of a Type II error for that alternative. 𝑃𝑜𝑤𝑒𝑟=1−𝛽 Power is NOT the compliment of Type I error! Beta is NOT the compliment of Type I error!

How are they related? 𝜶 𝜷 Power

Potatoes The potato-chip producer wonders whether the significance test of 𝐻 0 :𝑝= .08 vs. 𝐻 𝑎 :𝑝>.08 based on a random sample of 500 potatoes has enough power to detect a shipment of 11% blemished potatoes.

Homework Pg. 547 (19-25, 27-30)