Statistical Foundations:
|
|
- Marjorie Merritt
- 7 years ago
- Views:
Transcription
1 Statistical Foundations: Hypothesis Testing Psychology 790 Lecture #10 9/26/2006
2 Today sclass Hypothesis Testing. An Example. Types of errors illustrated. Misconceptions about hypothesis testing.
3 Upcoming Schedule Today (9/26): Hypothesis Testing. Thursday 9/28: Confidence Intervals. Tuesday 10/3: t and two-sample tests. t Thursday 10/5: Midterm review Tuesday 10/10: Midterm (20 item multiple choice). Wednesday (10/11 national holiday for my wife s 30 th birthday) Thursday 10/12: Fall break. Tuesday 10/17: Correlation and Regression from Hays.
4 Hypothesis Testing Example
5 An Example of Hypothesis Testing Recall from last week we talked a bit about the Wechsler Adult Intelligence Scale. In the general population, the test has an average of 100 and a standard deviation of 15. Lets go and try a hypothesis test to see if KU students have a similar mean WAIS score. We will sample 100 KU students at random and administer the WAIS.
6 Buy the WAIS on ebay!!
7 Example Setup What is the null hypothesis? H 0 : μ KU = 100 What is the alternative hypothesis? H A : μ KU 100
8 Distributional Setup The key element in our example is to find out what the assumed distribution under H 0. In our case, we will be sampling 100 subjects and taking a sample mean. What does the sampling distribution of the mean look like for N=100? σ ( ) 15, = N 100, N ( 100,1.51 ) N = 100 μ N
9 Distribution of Test Statistic Under Ui Using R, Rthe plot ltto the right is a picture of the distribution of the test statistic ( x ) under the null hypothesis. Null Hypothesis
10 Step 1: Set the Type I Error Rate Before we collect our sample, we must first set the Type I error rate for our experiment. Recall the Type I error rate (or α) is the maximum probability we will allow for rejecting the null hypothesis when the null hypothesis is true. This sets up the decision rule for our test. From this, we can obtain a critical value to which we can compare our test statistic. Wh d? What rate do you want to set? Let s to α = 0.05, for tradition s sake.
11 Decision Rule Using α = 0.05, we can then assign a region of our null distribution where we will reject the null hypothesis. Because we have no idea which direction KU s sample mean will fall, we will split our region into two halfs: An upper tail and a lower tail. We then want to find the following points: α 2 = 0. = α 2 = 0. X ( ) = U such that P x X U 025 X such that P L X L Find these two points. ( x ) 025
12 Decision Rule Plot We will reject H 0 if our sample mean is in either of these two regions
13 Our Sample KU Students Laser
14 Our Sample Lucky for you, I have tweaked my laser pointer to now give me the WAIS score (up to 5 digits) for individuals when hit with the laser beam.
15 Test Statistic Our sample mean was The sample SD was Now, what do we decide about our hypothesis test? We reject H 0 because our sample mean of j 0 p falls into the rejection region (it is greater than ).
16 Errors in Hypothesis Testing
17 Inferential Errors and NHST Real World Null is true Null is false Con nclusion n of the te est lse Null is tr rue Null is fa Correct decision Type I error Type II error Correct decision
18 Errors and Our Example Knowing a bit about the truth (from simulated data), we can revisit our example for a better description of Type I and Type II errors with graphics. From the example, we knew that the null population sampling distribution of the mean was N(100,1.5). The KU student population sampling distribution for mean WAIS scores was N(105,1.5). We can overlay the two populations and draw regions representing Type II errors.
19 Type I Error Null Distribution ib ti Alternative Distribution ib ti
20 Type II Error Null Distribution ib ti Alternative Distribution ib ti
21 Power Null Distribution ib ti Alternative Distribution ib ti
22 Points of Interest The example we explored previously was an example of what is called a z-test of a sample mean. Significance tests have been developed for a number of statistics difference between two group means: t-test difference between two or more group means: ANOVA differences between proportions: chi-square
23 How do we control Type I errors? The Type I error rate is typically controlled by the researcher. It is called the alpha rate, and corresponds to the probability cut-off that one uses in a significance test. By convention, researchers often use an alpha rate of.05. In other words, they will only reject the null hypothesis when a statistic is likely to occur 5% of the time or less when the null hypothesis is true. In principle, any probability value could be chosen for making the accept/reject decision. 5% is used by convention.
24 Type I errors What does 5% mean in this context? It means that we will only make a decision error 5% of the time if the null hypothesis is true. If the null hypothesis is false, the Type I error rate is undefined.
25 How do we control Type II errors? Type II errors can also be controlled by the experimenter. The Type II error rate is sometimes called beta. How can the beta rate be controlled? The easiest way to control Type II errors is by increase the statistical power of a test.
26 Statistical Power Statistical power is defined as the probability of rejecting the null hypothesis when it is false a correct decision (1-beta). Power is strongly influenced by sample size. With a larger N, we are more likely l to reject the null hypothesis if it is truly false. (As N increases, the standard error shrinks. Sampling error becomes less problematic, and true differences are easier to detect.)
27 Power and correlation This graph shows how the power of the significance test for a correlation varies as a function of sample size. Notice that when N = 80, there is about an 80% chance of correctly rejecting the null hypothesis (beta =.20). When N = 45, we only have a 50% chance of making the correct decision a coin toss (beta =.50). POWER Population r = SAMPLE SIZE
28 Power and correlation Power also varies as a function of the size of the correlation. r =.80 r =.60 When the population correlation is large (e.g.,.80), it requires fewer subjects to correctly reject the null hypothesis that the population correlation is 0. When the population p correlation is smallish (e.g.,.20), it requires a large number of subjects to correctly reject the null hypothesis. POWER r =.40 r =.20 When the population correlation is 0, the probability of rejecting the null is constant at 5% (alpha). Here power is technically undefined because the null hypothesis is true SAMPLE SIZE r =.00
29 Low Power Studies Because correlations in the.2 to.4 range are typically observed in non-experimental research, one would be wise not to trust research based on sample sizes less than 60ish r =.80 r =.60 r =.40 Why? Because such research only stands a 50% chance of yielding the correct decision, if the null is false. It would be more efficient (and, importantly, just as accurate) to flip a coin to make the decision rather than collecting data and using a significance test. POWER r =.20 r = SAMPLE SIZE
30 A Sad Fact In 1962 Jacob Cohen surveyed all articles in the Journal of Abnormal and Social Psychology and determined that the typical power of research conducted in this area was 53%. An even sadder fact: In 1989, Sedlmeier and Gigerenzer surveyed studies in the same journal (now called the Journal of Abnormal Psychology) and found that the power had decreased slightly. Researchers, unfortunately, pay little attention to power. As a consequence, the Type II error rate of research in psychology is likely to be dangerously high maybe as high as 50%.
31 Power in Research Design Power is important to consider, and should be used to design research projects. Given an educated guess about what the population parameter might be (e.g., a correlation of.30, a mean difference of.5 SD), one can determine the number of subjects needed for a desired level of power. Cohen and others recommend that researchers try to obtain a power level of about 80%.
32 Power in Research Design Thus, if one used an alpha-level level of 5% and collected enough subjects to ensure a power of 80% for an assumed effect, one would know, before the study was done, what the theoretical error rates are for the statistical test. Although these error rates correspond to long-run outcomes, one could get a sense of whether the research design was a credible one whether it is likely to minimize the two kinds of errors that are possible in NHST and, correspondingly, maximize the likelihood of making a correct decision.
33 Misconceptions About Hypothesis Testing
34 Three Common Misinterpretations of Significance Tests and p-values 1. The p-value indicates the probability that the results are due to sampling error or chance. 2. A statistically significant result is a reliable result. 3. A statistically significant result is a powerful, important result.
35 Misinterpretation # 1 The p-value is a conditional probability. The probability of observing a specific range of sample statistics GIVEN (i.e., conditional upon) that the null hypothesis is true. P(D H o ). This is not equivalent to the probability bilit of the null hypothesis being true, given the data. P(H o D) P(D H o )
36 Misinterpretation # 2 Is a significant result a reliable, easily replicated result? Not necessarily. The p-value is a poor indicator of the replicability of a finding. Replicability (assuming a real effect exists, that is, that he null hypothesis is false), is primarily a function of statistical ttiti power.
37 Misinterpretation # 2 If a study had a statistical power equivalent to 80%, what is the probability of obtaining a significant result twice? The probability of two independent events both occurring is the simple product of the probability bilit of each of them occurring =.64 If power = 50%? =.25 Bottom line: The likelihood of replicating a result is determined by statistical power, not the p-value derived from a significance test. When power of the test is low, the likelihood lih of a long-run series of replications is even lower.
38 Misinterpretation # 3 Is a significant result a powerful, important result? Not necessarily. The importance of the result, of course, depends on the issue at hand, the theoretical context of the finding, etc.
39 Misinterpretation # 3 We can measure the practical or theoretical significance of an effect using an index of effect size. An effect size is a quantitative index of the strength of the relationship between two variables. Some common measures of effect size are correlations, regression weights, t-values, and R-squared.
40 Misinterpretation # 3 Importantly, the same effect size can have different p- values, depending on the sample size of the study. For example, a correlation of.30 would not statistically significant with a sample size of 30, but would be statistically ti ti significant ifi with a sample size of 130. Bottom line: The p-value is a poor way to evaluate the Bottom line: The p value is a poor way to evaluate the practical significance of a research result.
41 Wrapping Up Today was another fun lecture about the philosophy p of hypothesis testing. We do hypothesis testing all the time. That doesn tmakeit something without error, though.
42 Next Time Confidence Intervals and their association with hypothesis tests. Confidence Intervals (Ch ).
Experimental Design. Power and Sample Size Determination. Proportions. Proportions. Confidence Interval for p. The Binomial Test
Experimental Design Power and Sample Size Determination Bret Hanlon and Bret Larget Department of Statistics University of Wisconsin Madison November 3 8, 2011 To this point in the semester, we have largely
More informationStatistics 2014 Scoring Guidelines
AP Statistics 2014 Scoring Guidelines College Board, Advanced Placement Program, AP, AP Central, and the acorn logo are registered trademarks of the College Board. AP Central is the official online home
More informationIntroduction to. Hypothesis Testing CHAPTER LEARNING OBJECTIVES. 1 Identify the four steps of hypothesis testing.
Introduction to Hypothesis Testing CHAPTER 8 LEARNING OBJECTIVES After reading this chapter, you should be able to: 1 Identify the four steps of hypothesis testing. 2 Define null hypothesis, alternative
More informationMONT 107N Understanding Randomness Solutions For Final Examination May 11, 2010
MONT 07N Understanding Randomness Solutions For Final Examination May, 00 Short Answer (a) (0) How are the EV and SE for the sum of n draws with replacement from a box computed? Solution: The EV is n times
More informationIntroduction to Hypothesis Testing. Hypothesis Testing. Step 1: State the Hypotheses
Introduction to Hypothesis Testing 1 Hypothesis Testing A hypothesis test is a statistical procedure that uses sample data to evaluate a hypothesis about a population Hypothesis is stated in terms of the
More informationClass 19: Two Way Tables, Conditional Distributions, Chi-Square (Text: Sections 2.5; 9.1)
Spring 204 Class 9: Two Way Tables, Conditional Distributions, Chi-Square (Text: Sections 2.5; 9.) Big Picture: More than Two Samples In Chapter 7: We looked at quantitative variables and compared the
More informationII. DISTRIBUTIONS distribution normal distribution. standard scores
Appendix D Basic Measurement And Statistics The following information was developed by Steven Rothke, PhD, Department of Psychology, Rehabilitation Institute of Chicago (RIC) and expanded by Mary F. Schmidt,
More informationTwo-sample hypothesis testing, II 9.07 3/16/2004
Two-sample hypothesis testing, II 9.07 3/16/004 Small sample tests for the difference between two independent means For two-sample tests of the difference in mean, things get a little confusing, here,
More informationStudy Guide for the Final Exam
Study Guide for the Final Exam When studying, remember that the computational portion of the exam will only involve new material (covered after the second midterm), that material from Exam 1 will make
More informationPrinciples of Hypothesis Testing for Public Health
Principles of Hypothesis Testing for Public Health Laura Lee Johnson, Ph.D. Statistician National Center for Complementary and Alternative Medicine johnslau@mail.nih.gov Fall 2011 Answers to Questions
More informationSection 13, Part 1 ANOVA. Analysis Of Variance
Section 13, Part 1 ANOVA Analysis Of Variance Course Overview So far in this course we ve covered: Descriptive statistics Summary statistics Tables and Graphs Probability Probability Rules Probability
More informationresearch/scientific includes the following: statistical hypotheses: you have a null and alternative you accept one and reject the other
1 Hypothesis Testing Richard S. Balkin, Ph.D., LPC-S, NCC 2 Overview When we have questions about the effect of a treatment or intervention or wish to compare groups, we use hypothesis testing Parametric
More informationChapter 7 Notes - Inference for Single Samples. You know already for a large sample, you can invoke the CLT so:
Chapter 7 Notes - Inference for Single Samples You know already for a large sample, you can invoke the CLT so: X N(µ, ). Also for a large sample, you can replace an unknown σ by s. You know how to do a
More informationDescriptive Statistics
Descriptive Statistics Primer Descriptive statistics Central tendency Variation Relative position Relationships Calculating descriptive statistics Descriptive Statistics Purpose to describe or summarize
More informationOutline. Definitions Descriptive vs. Inferential Statistics The t-test - One-sample t-test
The t-test Outline Definitions Descriptive vs. Inferential Statistics The t-test - One-sample t-test - Dependent (related) groups t-test - Independent (unrelated) groups t-test Comparing means Correlation
More informationFairfield Public Schools
Mathematics Fairfield Public Schools AP Statistics AP Statistics BOE Approved 04/08/2014 1 AP STATISTICS Critical Areas of Focus AP Statistics is a rigorous course that offers advanced students an opportunity
More informationTutorial 5: Hypothesis Testing
Tutorial 5: Hypothesis Testing Rob Nicholls nicholls@mrc-lmb.cam.ac.uk MRC LMB Statistics Course 2014 Contents 1 Introduction................................ 1 2 Testing distributional assumptions....................
More informationUsing Excel for inferential statistics
FACT SHEET Using Excel for inferential statistics Introduction When you collect data, you expect a certain amount of variation, just caused by chance. A wide variety of statistical tests can be applied
More informationHYPOTHESIS TESTING: CONFIDENCE INTERVALS, T-TESTS, ANOVAS, AND REGRESSION
HYPOTHESIS TESTING: CONFIDENCE INTERVALS, T-TESTS, ANOVAS, AND REGRESSION HOD 2990 10 November 2010 Lecture Background This is a lightning speed summary of introductory statistical methods for senior undergraduate
More informationComparison of frequentist and Bayesian inference. Class 20, 18.05, Spring 2014 Jeremy Orloff and Jonathan Bloom
Comparison of frequentist and Bayesian inference. Class 20, 18.05, Spring 2014 Jeremy Orloff and Jonathan Bloom 1 Learning Goals 1. Be able to explain the difference between the p-value and a posterior
More informationSimple Linear Regression Inference
Simple Linear Regression Inference 1 Inference requirements The Normality assumption of the stochastic term e is needed for inference even if it is not a OLS requirement. Therefore we have: Interpretation
More informationLAB 4 INSTRUCTIONS CONFIDENCE INTERVALS AND HYPOTHESIS TESTING
LAB 4 INSTRUCTIONS CONFIDENCE INTERVALS AND HYPOTHESIS TESTING In this lab you will explore the concept of a confidence interval and hypothesis testing through a simulation problem in engineering setting.
More informationProjects Involving Statistics (& SPSS)
Projects Involving Statistics (& SPSS) Academic Skills Advice Starting a project which involves using statistics can feel confusing as there seems to be many different things you can do (charts, graphs,
More informationGeneral Method: Difference of Means. 3. Calculate df: either Welch-Satterthwaite formula or simpler df = min(n 1, n 2 ) 1.
General Method: Difference of Means 1. Calculate x 1, x 2, SE 1, SE 2. 2. Combined SE = SE1 2 + SE2 2. ASSUMES INDEPENDENT SAMPLES. 3. Calculate df: either Welch-Satterthwaite formula or simpler df = min(n
More informationThere are three kinds of people in the world those who are good at math and those who are not. PSY 511: Advanced Statistics for Psychological and Behavioral Research 1 Positive Views The record of a month
More informationConsider a study in which. How many subjects? The importance of sample size calculations. An insignificant effect: two possibilities.
Consider a study in which How many subjects? The importance of sample size calculations Office of Research Protections Brown Bag Series KB Boomer, Ph.D. Director, boomer@stat.psu.edu A researcher conducts
More informationA Statistical Analysis of Popular Lottery Winning Strategies
CS-BIGS 4(1): 66-72 2010 CS-BIGS http://www.bentley.edu/csbigs/vol4-1/chen.pdf A Statistical Analysis of Popular Lottery Winning Strategies Albert C. Chen Torrey Pines High School, USA Y. Helio Yang San
More informationTwo-Sample T-Tests Assuming Equal Variance (Enter Means)
Chapter 4 Two-Sample T-Tests Assuming Equal Variance (Enter Means) Introduction This procedure provides sample size and power calculations for one- or two-sided two-sample t-tests when the variances of
More informationChapter 8 Hypothesis Testing Chapter 8 Hypothesis Testing 8-1 Overview 8-2 Basics of Hypothesis Testing
Chapter 8 Hypothesis Testing 1 Chapter 8 Hypothesis Testing 8-1 Overview 8-2 Basics of Hypothesis Testing 8-3 Testing a Claim About a Proportion 8-5 Testing a Claim About a Mean: s Not Known 8-6 Testing
More informationTwo-sample inference: Continuous data
Two-sample inference: Continuous data Patrick Breheny April 5 Patrick Breheny STA 580: Biostatistics I 1/32 Introduction Our next two lectures will deal with two-sample inference for continuous data As
More informationPsychology 60 Fall 2013 Practice Exam Actual Exam: Next Monday. Good luck!
Psychology 60 Fall 2013 Practice Exam Actual Exam: Next Monday. Good luck! Name: 1. The basic idea behind hypothesis testing: A. is important only if you want to compare two populations. B. depends on
More informationHYPOTHESIS TESTING: POWER OF THE TEST
HYPOTHESIS TESTING: POWER OF THE TEST The first 6 steps of the 9-step test of hypothesis are called "the test". These steps are not dependent on the observed data values. When planning a research project,
More information" Y. Notation and Equations for Regression Lecture 11/4. Notation:
Notation: Notation and Equations for Regression Lecture 11/4 m: The number of predictor variables in a regression Xi: One of multiple predictor variables. The subscript i represents any number from 1 through
More informationCALCULATIONS & STATISTICS
CALCULATIONS & STATISTICS CALCULATION OF SCORES Conversion of 1-5 scale to 0-100 scores When you look at your report, you will notice that the scores are reported on a 0-100 scale, even though respondents
More informationLesson 1: Comparison of Population Means Part c: Comparison of Two- Means
Lesson : Comparison of Population Means Part c: Comparison of Two- Means Welcome to lesson c. This third lesson of lesson will discuss hypothesis testing for two independent means. Steps in Hypothesis
More informationSCHOOL OF HEALTH AND HUMAN SCIENCES DON T FORGET TO RECODE YOUR MISSING VALUES
SCHOOL OF HEALTH AND HUMAN SCIENCES Using SPSS Topics addressed today: 1. Differences between groups 2. Graphing Use the s4data.sav file for the first part of this session. DON T FORGET TO RECODE YOUR
More informationSection 7.1. Introduction to Hypothesis Testing. Schrodinger s cat quantum mechanics thought experiment (1935)
Section 7.1 Introduction to Hypothesis Testing Schrodinger s cat quantum mechanics thought experiment (1935) Statistical Hypotheses A statistical hypothesis is a claim about a population. Null hypothesis
More informationTwo-Sample T-Tests Allowing Unequal Variance (Enter Difference)
Chapter 45 Two-Sample T-Tests Allowing Unequal Variance (Enter Difference) Introduction This procedure provides sample size and power calculations for one- or two-sided two-sample t-tests when no assumption
More informationMathematical goals. Starting points. Materials required. Time needed
Level S2 of challenge: B/C S2 Mathematical goals Starting points Materials required Time needed Evaluating probability statements To help learners to: discuss and clarify some common misconceptions about
More informationIndependent samples t-test. Dr. Tom Pierce Radford University
Independent samples t-test Dr. Tom Pierce Radford University The logic behind drawing causal conclusions from experiments The sampling distribution of the difference between means The standard error of
More informationSample Size and Power in Clinical Trials
Sample Size and Power in Clinical Trials Version 1.0 May 011 1. Power of a Test. Factors affecting Power 3. Required Sample Size RELATED ISSUES 1. Effect Size. Test Statistics 3. Variation 4. Significance
More informationQUANTITATIVE METHODS BIOLOGY FINAL HONOUR SCHOOL NON-PARAMETRIC TESTS
QUANTITATIVE METHODS BIOLOGY FINAL HONOUR SCHOOL NON-PARAMETRIC TESTS This booklet contains lecture notes for the nonparametric work in the QM course. This booklet may be online at http://users.ox.ac.uk/~grafen/qmnotes/index.html.
More informationDDBA 8438: Introduction to Hypothesis Testing Video Podcast Transcript
DDBA 8438: Introduction to Hypothesis Testing Video Podcast Transcript JENNIFER ANN MORROW: Welcome to "Introduction to Hypothesis Testing." My name is Dr. Jennifer Ann Morrow. In today's demonstration,
More informationResearch Methods & Experimental Design
Research Methods & Experimental Design 16.422 Human Supervisory Control April 2004 Research Methods Qualitative vs. quantitative Understanding the relationship between objectives (research question) and
More informationLecture Notes Module 1
Lecture Notes Module 1 Study Populations A study population is a clearly defined collection of people, animals, plants, or objects. In psychological research, a study population usually consists of a specific
More informationAP STATISTICS (Warm-Up Exercises)
AP STATISTICS (Warm-Up Exercises) 1. Describe the distribution of ages in a city: 2. Graph a box plot on your calculator for the following test scores: {90, 80, 96, 54, 80, 95, 100, 75, 87, 62, 65, 85,
More informationSurvey Research: Choice of Instrument, Sample. Lynda Burton, ScD Johns Hopkins University
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike License. Your use of this material constitutes acceptance of that license and the conditions of use of materials on this
More informationChapter 2 Probability Topics SPSS T tests
Chapter 2 Probability Topics SPSS T tests Data file used: gss.sav In the lecture about chapter 2, only the One-Sample T test has been explained. In this handout, we also give the SPSS methods to perform
More informationHow To Check For Differences In The One Way Anova
MINITAB ASSISTANT WHITE PAPER This paper explains the research conducted by Minitab statisticians to develop the methods and data checks used in the Assistant in Minitab 17 Statistical Software. One-Way
More informationInference for two Population Means
Inference for two Population Means Bret Hanlon and Bret Larget Department of Statistics University of Wisconsin Madison October 27 November 1, 2011 Two Population Means 1 / 65 Case Study Case Study Example
More informationWISE Power Tutorial All Exercises
ame Date Class WISE Power Tutorial All Exercises Power: The B.E.A.. Mnemonic Four interrelated features of power can be summarized using BEA B Beta Error (Power = 1 Beta Error): Beta error (or Type II
More informationLikelihood: Frequentist vs Bayesian Reasoning
"PRINCIPLES OF PHYLOGENETICS: ECOLOGY AND EVOLUTION" Integrative Biology 200B University of California, Berkeley Spring 2009 N Hallinan Likelihood: Frequentist vs Bayesian Reasoning Stochastic odels and
More informationCONTENTS OF DAY 2. II. Why Random Sampling is Important 9 A myth, an urban legend, and the real reason NOTES FOR SUMMER STATISTICS INSTITUTE COURSE
1 2 CONTENTS OF DAY 2 I. More Precise Definition of Simple Random Sample 3 Connection with independent random variables 3 Problems with small populations 8 II. Why Random Sampling is Important 9 A myth,
More informationUsing R for Linear Regression
Using R for Linear Regression In the following handout words and symbols in bold are R functions and words and symbols in italics are entries supplied by the user; underlined words and symbols are optional
More informationError Type, Power, Assumptions. Parametric Tests. Parametric vs. Nonparametric Tests
Error Type, Power, Assumptions Parametric vs. Nonparametric tests Type-I & -II Error Power Revisited Meeting the Normality Assumption - Outliers, Winsorizing, Trimming - Data Transformation 1 Parametric
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Sample Practice problems - chapter 12-1 and 2 proportions for inference - Z Distributions Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Provide
More informationHypothesis testing. c 2014, Jeffrey S. Simonoff 1
Hypothesis testing So far, we ve talked about inference from the point of estimation. We ve tried to answer questions like What is a good estimate for a typical value? or How much variability is there
More informationCorrelational Research
Correlational Research Chapter Fifteen Correlational Research Chapter Fifteen Bring folder of readings The Nature of Correlational Research Correlational Research is also known as Associational Research.
More informationTHE FIRST SET OF EXAMPLES USE SUMMARY DATA... EXAMPLE 7.2, PAGE 227 DESCRIBES A PROBLEM AND A HYPOTHESIS TEST IS PERFORMED IN EXAMPLE 7.
THERE ARE TWO WAYS TO DO HYPOTHESIS TESTING WITH STATCRUNCH: WITH SUMMARY DATA (AS IN EXAMPLE 7.17, PAGE 236, IN ROSNER); WITH THE ORIGINAL DATA (AS IN EXAMPLE 8.5, PAGE 301 IN ROSNER THAT USES DATA FROM
More informationChicago Booth BUSINESS STATISTICS 41000 Final Exam Fall 2011
Chicago Booth BUSINESS STATISTICS 41000 Final Exam Fall 2011 Name: Section: I pledge my honor that I have not violated the Honor Code Signature: This exam has 34 pages. You have 3 hours to complete this
More informationA Primer on Mathematical Statistics and Univariate Distributions; The Normal Distribution; The GLM with the Normal Distribution
A Primer on Mathematical Statistics and Univariate Distributions; The Normal Distribution; The GLM with the Normal Distribution PSYC 943 (930): Fundamentals of Multivariate Modeling Lecture 4: September
More informationA full analysis example Multiple correlations Partial correlations
A full analysis example Multiple correlations Partial correlations New Dataset: Confidence This is a dataset taken of the confidence scales of 41 employees some years ago using 4 facets of confidence (Physical,
More informationVariables Control Charts
MINITAB ASSISTANT WHITE PAPER This paper explains the research conducted by Minitab statisticians to develop the methods and data checks used in the Assistant in Minitab 17 Statistical Software. Variables
More informationHYPOTHESIS TESTING WITH SPSS:
HYPOTHESIS TESTING WITH SPSS: A NON-STATISTICIAN S GUIDE & TUTORIAL by Dr. Jim Mirabella SPSS 14.0 screenshots reprinted with permission from SPSS Inc. Published June 2006 Copyright Dr. Jim Mirabella CHAPTER
More informationComparing Means in Two Populations
Comparing Means in Two Populations Overview The previous section discussed hypothesis testing when sampling from a single population (either a single mean or two means from the same population). Now we
More informationMTH 140 Statistics Videos
MTH 140 Statistics Videos Chapter 1 Picturing Distributions with Graphs Individuals and Variables Categorical Variables: Pie Charts and Bar Graphs Categorical Variables: Pie Charts and Bar Graphs Quantitative
More informationUnit 26 Estimation with Confidence Intervals
Unit 26 Estimation with Confidence Intervals Objectives: To see how confidence intervals are used to estimate a population proportion, a population mean, a difference in population proportions, or a difference
More informationCurriculum Map Statistics and Probability Honors (348) Saugus High School Saugus Public Schools 2009-2010
Curriculum Map Statistics and Probability Honors (348) Saugus High School Saugus Public Schools 2009-2010 Week 1 Week 2 14.0 Students organize and describe distributions of data by using a number of different
More informationCOMPARISONS OF CUSTOMER LOYALTY: PUBLIC & PRIVATE INSURANCE COMPANIES.
277 CHAPTER VI COMPARISONS OF CUSTOMER LOYALTY: PUBLIC & PRIVATE INSURANCE COMPANIES. This chapter contains a full discussion of customer loyalty comparisons between private and public insurance companies
More informationRank-Based Non-Parametric Tests
Rank-Based Non-Parametric Tests Reminder: Student Instructional Rating Surveys You have until May 8 th to fill out the student instructional rating surveys at https://sakai.rutgers.edu/portal/site/sirs
More informationLecture 9: Bayesian hypothesis testing
Lecture 9: Bayesian hypothesis testing 5 November 27 In this lecture we ll learn about Bayesian hypothesis testing. 1 Introduction to Bayesian hypothesis testing Before we go into the details of Bayesian
More informationLesson 9 Hypothesis Testing
Lesson 9 Hypothesis Testing Outline Logic for Hypothesis Testing Critical Value Alpha (α) -level.05 -level.01 One-Tail versus Two-Tail Tests -critical values for both alpha levels Logic for Hypothesis
More informationTwo-Group Hypothesis Tests: Excel 2013 T-TEST Command
Two group hypothesis tests using Excel 2013 T-TEST command 1 Two-Group Hypothesis Tests: Excel 2013 T-TEST Command by Milo Schield Member: International Statistical Institute US Rep: International Statistical
More informationThe Mann-Whitney U test. Peter Shaw
The Mann-Whitney U test Peter Shaw Introduction We meet our first inferential test. You should not get put off by the messy-looking formulae it s usually run on a PC anyway. The important bit is to understand
More informationLAB : THE CHI-SQUARE TEST. Probability, Random Chance, and Genetics
Period Date LAB : THE CHI-SQUARE TEST Probability, Random Chance, and Genetics Why do we study random chance and probability at the beginning of a unit on genetics? Genetics is the study of inheritance,
More informationSTA-201-TE. 5. Measures of relationship: correlation (5%) Correlation coefficient; Pearson r; correlation and causation; proportion of common variance
Principles of Statistics STA-201-TE This TECEP is an introduction to descriptive and inferential statistics. Topics include: measures of central tendency, variability, correlation, regression, hypothesis
More informationNCSS Statistical Software
Chapter 06 Introduction This procedure provides several reports for the comparison of two distributions, including confidence intervals for the difference in means, two-sample t-tests, the z-test, the
More informationBA 275 Review Problems - Week 6 (10/30/06-11/3/06) CD Lessons: 53, 54, 55, 56 Textbook: pp. 394-398, 404-408, 410-420
BA 275 Review Problems - Week 6 (10/30/06-11/3/06) CD Lessons: 53, 54, 55, 56 Textbook: pp. 394-398, 404-408, 410-420 1. Which of the following will increase the value of the power in a statistical test
More informationAdditional sources Compilation of sources: http://lrs.ed.uiuc.edu/tseportal/datacollectionmethodologies/jin-tselink/tselink.htm
Mgt 540 Research Methods Data Analysis 1 Additional sources Compilation of sources: http://lrs.ed.uiuc.edu/tseportal/datacollectionmethodologies/jin-tselink/tselink.htm http://web.utk.edu/~dap/random/order/start.htm
More informationTesting a claim about a population mean
Introductory Statistics Lectures Testing a claim about a population mean One sample hypothesis test of the mean Department of Mathematics Pima Community College Redistribution of this material is prohibited
More informationMind on Statistics. Chapter 12
Mind on Statistics Chapter 12 Sections 12.1 Questions 1 to 6: For each statement, determine if the statement is a typical null hypothesis (H 0 ) or alternative hypothesis (H a ). 1. There is no difference
More informationCHAPTER 14 NONPARAMETRIC TESTS
CHAPTER 14 NONPARAMETRIC TESTS Everything that we have done up until now in statistics has relied heavily on one major fact: that our data is normally distributed. We have been able to make inferences
More informationNONPARAMETRIC STATISTICS 1. depend on assumptions about the underlying distribution of the data (or on the Central Limit Theorem)
NONPARAMETRIC STATISTICS 1 PREVIOUSLY parametric statistics in estimation and hypothesis testing... construction of confidence intervals computing of p-values classical significance testing depend on assumptions
More informationp-values and significance levels (false positive or false alarm rates)
p-values and significance levels (false positive or false alarm rates) Let's say 123 people in the class toss a coin. Call it "Coin A." There are 65 heads. Then they toss another coin. Call it "Coin B."
More informationLean Six Sigma Black Belt Body of Knowledge
General Lean Six Sigma Defined UN Describe Nature and purpose of Lean Six Sigma Integration of Lean and Six Sigma UN Compare and contrast focus and approaches (Process Velocity and Quality) Y=f(X) Input
More informationTI-Inspire manual 1. Instructions. Ti-Inspire for statistics. General Introduction
TI-Inspire manual 1 General Introduction Instructions Ti-Inspire for statistics TI-Inspire manual 2 TI-Inspire manual 3 Press the On, Off button to go to Home page TI-Inspire manual 4 Use the to navigate
More informationConfidence Intervals for Cpk
Chapter 297 Confidence Intervals for Cpk Introduction This routine calculates the sample size needed to obtain a specified width of a Cpk confidence interval at a stated confidence level. Cpk is a process
More informationp ˆ (sample mean and sample
Chapter 6: Confidence Intervals and Hypothesis Testing When analyzing data, we can t just accept the sample mean or sample proportion as the official mean or proportion. When we estimate the statistics
More informationFirst-year Statistics for Psychology Students Through Worked Examples
First-year Statistics for Psychology Students Through Worked Examples 1. THE CHI-SQUARE TEST A test of association between categorical variables by Charles McCreery, D.Phil Formerly Lecturer in Experimental
More informationAP: LAB 8: THE CHI-SQUARE TEST. Probability, Random Chance, and Genetics
Ms. Foglia Date AP: LAB 8: THE CHI-SQUARE TEST Probability, Random Chance, and Genetics Why do we study random chance and probability at the beginning of a unit on genetics? Genetics is the study of inheritance,
More informationThis chapter discusses some of the basic concepts in inferential statistics.
Research Skills for Psychology Majors: Everything You Need to Know to Get Started Inferential Statistics: Basic Concepts This chapter discusses some of the basic concepts in inferential statistics. Details
More informationIndependent t- Test (Comparing Two Means)
Independent t- Test (Comparing Two Means) The objectives of this lesson are to learn: the definition/purpose of independent t-test when to use the independent t-test the use of SPSS to complete an independent
More informationTwo Related Samples t Test
Two Related Samples t Test In this example 1 students saw five pictures of attractive people and five pictures of unattractive people. For each picture, the students rated the friendliness of the person
More informationBowerman, O'Connell, Aitken Schermer, & Adcock, Business Statistics in Practice, Canadian edition
Bowerman, O'Connell, Aitken Schermer, & Adcock, Business Statistics in Practice, Canadian edition Online Learning Centre Technology Step-by-Step - Excel Microsoft Excel is a spreadsheet software application
More informationA Hands-On Exercise Improves Understanding of the Standard Error. of the Mean. Robert S. Ryan. Kutztown University
A Hands-On Exercise 1 Running head: UNDERSTANDING THE STANDARD ERROR A Hands-On Exercise Improves Understanding of the Standard Error of the Mean Robert S. Ryan Kutztown University A Hands-On Exercise
More informationHow Does My TI-84 Do That
How Does My TI-84 Do That A guide to using the TI-84 for statistics Austin Peay State University Clarksville, Tennessee How Does My TI-84 Do That A guide to using the TI-84 for statistics Table of Contents
More informationt Tests in Excel The Excel Statistical Master By Mark Harmon Copyright 2011 Mark Harmon
t-tests in Excel By Mark Harmon Copyright 2011 Mark Harmon No part of this publication may be reproduced or distributed without the express permission of the author. mark@excelmasterseries.com www.excelmasterseries.com
More informationTesting Hypotheses About Proportions
Chapter 11 Testing Hypotheses About Proportions Hypothesis testing method: uses data from a sample to judge whether or not a statement about a population may be true. Steps in Any Hypothesis Test 1. Determine
More informationChapter Eight: Quantitative Methods
Chapter Eight: Quantitative Methods RESEARCH DESIGN Qualitative, Quantitative, and Mixed Methods Approaches Third Edition John W. Creswell Chapter Outline Defining Surveys and Experiments Components of
More information