Evaluating Hypotheses Chapter 9 Homework: 1-9. Descriptive vs. Inferential Statistics n Descriptive l quantitative descriptions of characteristics ~

Slides:



Advertisements
Similar presentations
Introduction to Hypothesis Testing
Advertisements

Anthony Greene1 Simple Hypothesis Testing Detecting Statistical Differences In The Simplest Case:  and  are both known I The Logic of Hypothesis Testing:
Statistical Techniques I EXST7005 Lets go Power and Types of Errors.
Hypothesis testing Week 10 Lecture 2.
Statistical Significance What is Statistical Significance? What is Statistical Significance? How Do We Know Whether a Result is Statistically Significant?
1. Estimation ESTIMATION.
Review: What influences confidence intervals?
HYPOTHESIS TESTING Four Steps Statistical Significance Outcomes Sampling Distributions.
Evaluating Hypotheses Chapter 9. Descriptive vs. Inferential Statistics n Descriptive l quantitative descriptions of characteristics.
Statistical Significance What is Statistical Significance? How Do We Know Whether a Result is Statistically Significant? How Do We Know Whether a Result.
Hypothesis testing & Inferential Statistics
Introduction to Hypothesis Testing CJ 526 Statistical Analysis in Criminal Justice.
Inferences About Means of Single Samples Chapter 10 Homework: 1-6.
Inferences About Means of Single Samples Chapter 10 Homework: 1-6.
C82MCP Diploma Statistics School of Psychology University of Nottingham 1 Overview of Lecture Independent and Dependent Variables Between and Within Designs.
Introduction to Hypothesis Testing CJ 526 Statistical Analysis in Criminal Justice.
PY 427 Statistics 1Fall 2006 Kin Ching Kong, Ph.D Lecture 6 Chicago School of Professional Psychology.
BCOR 1020 Business Statistics
Chapter 12 Inferring from the Data. Inferring from Data Estimation and Significance testing.
Probability Population:
Chapter 5For Explaining Psychological Statistics, 4th ed. by B. Cohen 1 Suppose we wish to know whether children who grow up in homes without access to.
Inferential Statistics
Testing Hypotheses.
Chapter Ten Introduction to Hypothesis Testing. Copyright © Houghton Mifflin Company. All rights reserved.Chapter New Statistical Notation The.
Statistics for the Social Sciences
Hypothesis Testing:.
Overview of Statistical Hypothesis Testing: The z-Test
Testing Hypotheses I Lesson 9. Descriptive vs. Inferential Statistics n Descriptive l quantitative descriptions of characteristics n Inferential Statistics.
Overview Definition Hypothesis
1 © Lecture note 3 Hypothesis Testing MAKE HYPOTHESIS ©
© 2008 McGraw-Hill Higher Education The Statistical Imagination Chapter 9. Hypothesis Testing I: The Six Steps of Statistical Inference.
Descriptive statistics Inferential statistics
Introduction to Hypothesis Testing for μ Research Problem: Infant Touch Intervention Designed to increase child growth/weight Weight at age 2: Known population:
Sections 8-1 and 8-2 Review and Preview and Basics of Hypothesis Testing.
Estimation and Hypothesis Testing Now the real fun begins.
Tuesday, September 10, 2013 Introduction to hypothesis testing.
Chapter 8 Introduction to Hypothesis Testing
Tests of significance & hypothesis testing Dr. Omar Al Jadaan Assistant Professor – Computer Science & Mathematics.
4-1 Statistical Inference The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population.
1 Today Null and alternative hypotheses 1- and 2-tailed tests Regions of rejection Sampling distributions The Central Limit Theorem Standard errors z-tests.
Overview Basics of Hypothesis Testing
1 Statistical Inference Greg C Elvers. 2 Why Use Statistical Inference Whenever we collect data, we want our results to be true for the entire population.
The Argument for Using Statistics Weighing the Evidence Statistical Inference: An Overview Applying Statistical Inference: An Example Going Beyond Testing.
Chapter 8 Introduction to Hypothesis Testing
S519: Evaluation of Information Systems Social Statistics Inferential Statistics Chapter 8: Significantly significant.
1 Lecture note 4 Hypothesis Testing Significant Difference ©
Inference and Inferential Statistics Methods of Educational Research EDU 660.
Lecture 16 Section 8.1 Objectives: Testing Statistical Hypotheses − Stating hypotheses statements − Type I and II errors − Conducting a hypothesis test.
1 Chapter 8 Introduction to Hypothesis Testing. 2 Name of the game… Hypothesis testing Statistical method that uses sample data to evaluate a hypothesis.
Statistical Inference for the Mean Objectives: (Chapter 9, DeCoursey) -To understand the terms: Null Hypothesis, Rejection Region, and Type I and II errors.
Review I A student researcher obtains a random sample of UMD students and finds that 55% report using an illegally obtained stimulant to study in the past.
© Copyright McGraw-Hill 2004
Inferential Statistics Inferential statistics allow us to infer the characteristic(s) of a population from sample data Slightly different terms and symbols.
Testing Hypotheses II Lesson 10. A Directional Hypothesis (1-tailed) n Does reading to young children increase IQ scores?  = 100,  = 15, n = 25 l sample.
Statistical Techniques
Statistical Inference Statistical inference is concerned with the use of sample data to make inferences about unknown population parameters. For example,
Education 793 Class Notes Inference and Hypothesis Testing Using the Normal Distribution 8 October 2003.
European Patients’ Academy on Therapeutic Innovation The Purpose and Fundamentals of Statistics in Clinical Trials.
Course Overview Collecting Data Exploring Data Probability Intro. Inference Comparing Variables Relationships between Variables Means/Variances Proportions.
Descriptive and Inferential Statistics Descriptive statistics The science of describing distributions of samples or populations Inferential statistics.
Statistical Inference for the Mean Objectives: (Chapter 8&9, DeCoursey) -To understand the terms variance and standard error of a sample mean, Null Hypothesis,
Two main tasks in inferential statistics: (revisited) 1)Estimation : Use data to infer population parameter  e.g., estimate victimization rate from NCVS.
Chapter 9 Introduction to the t Statistic
Hypothesis Testing I The One-sample Case
Review and Preview and Basics of Hypothesis Testing
Hypothesis Testing and Confidence Intervals (Part 1): Using the Standard Normal Lecture 8 Justin Kern October 10 and 12, 2017.
Chapter Review Problems
Testing Hypotheses I Lesson 9.
Type I and Type II Errors
Introduction To Hypothesis Testing
Presentation transcript:

Evaluating Hypotheses Chapter 9 Homework: 1-9

Descriptive vs. Inferential Statistics n Descriptive l quantitative descriptions of characteristics ~

Inferential Statistics n Making conclusions (inferences) about parameters e.g.,   X confidence intervals: infer  lies within interval l also quantitative ~

Hypothesis Testing n Most widely used inferential statistics n Hypothesis l testable assumption or inference about a parameter or distribution l should conclusion (inference) be accepted? l final result a decision: YES or NO l qualitative not quantitative ~

Hypothesis Testing n Example: IQ scores  = 100,  = 15 l Take random sample of students n = 10 n Hypothesis: sample is consistent with population with above parameters l sample is the same as population ~

Evaluating Hypotheses

Proving / Disproving Hypotheses n Logic of science built on disproving l easier than proving l but ultimately want to prove n State 2 mutually exclusive hypotheses l if one is true, other cannot be true ~

Hypothesis Evaluation n Null Hypothesis: H 0 l there is no difference between groups n Alternative Hypothesis: H 1 also called “experimental” hypothesis l there is a difference between groups ~

Steps in Hypothesis Evaluation 1. State null & alternative hypotheses H 0 and H 1 2. Set criterion for rejecting H 0 level of significance:  3. collect sample; compute sample statistic & test statistic 4. Interpret results is outcome statistically significant? ~

Hypothesis Evaluation n Example: IQ and electric fields l question: Does living near power lines affect IQ of children? n H 0 : there is no difference l Living near power lines does not alter IQ.  = 100 n H 1 : Living near power lines does alter IQ.   100 ~

Hypothesis Evaluation n Outcome of study l reject or “accept” null hypothesis n Reject H o l accept as H 1 true n “Accepting” null hypothesis l difficult or impossible to “prove” H o l actually: fail to reject H o l i.e., data are inconclusive ~

Evaluating H o and H 1 n Hypotheses about population parameters n Test statistic l especially designed to test H o n Procedure depends on… l particular test statistic used l directionality of hypotheses l level of significance ~

Directionality & Hypotheses n Directionality affects critical values used n Nondirectional l two-tailed test H o :  = 100; H 1 :   100 l change could be either direction l Do not know what effect will be may increase or decrease IQ ~

Directionality & Hypotheses n Directional l one tailed test l Have prior evidence that suggests direction of effect l predict that effect will be larger or smaller, but only 1 H o:  < 100 H 1 :  > 100 ~

Errors n “Accept” or reject H o l only probability we made correct decision l also probability made wrong decision n Type I error l incorrectly rejecting H o l e.g., may think a new antidepressant is effective, when it is NOT ~

Errors n Type II error l incorrectly “accepting” H o l e.g., may think a new antidepressant is not effective, when it really is n Do not know if we make error l because we do not know true population parameters ~

Actual state of nature H 0 is true H 0 is false Decision Accept H 0 Reject H 0 Correct Type I Error Type II Error Errors

Level of Significance (  ) n Probability of making Type I error l complement of level of confidence = 1  =.05 l conduct experiment 100 times l 5 times will make Type I error n Want probability of Type I error small ~

Statistical Significance n If reject H 0 n Outcome is “statistically significant” l difference between groups is... greater than expected by chance alone l due to sampling, etc. n Does NOT say it is meaningful ~

Statistical Power n Power l probability of correctly rejecting H 0  = probability of Type II error l complement of power *power = 1 -  ~

Practical Significance n Degree to which result is important l result can be statistically significant l but not important in real world n Effect size l measure of magnitude of result l difference between means of 2 groups l e.g., IQ: 1 point small effect, 15 large ~

Procedure for Evaluating Hypotheses n Experiment l Draw random sample l compute statistic l determine if reasonably comes from population If no, reject H 0 n Use test statistic to make decision n 3 important distributions variable, sample statistic, test statistic~

Test Statistic n distribution of test statistic l has known probabilities n General form test statistic = sample statistic - population parameter standard error of sample statistic difference actually obtained: X -  l divided by difference by chance alone ~

Steps in Hypothesis Evaluation 1. State null & alternative hypotheses H 0 and H 1 2. Set criterion for rejecting H 0 level of significance:  3. collect sample; compute sample statistic & test statistic 4. Interpret results u is outcome statistically significant? u *If so, is it practically significant? ~