# Stat 411/511 THE RANDOMIZATION TEST. Charlotte Wickham. stat511.cwick.co.nz. Oct

Size: px
Start display at page:

Download "Stat 411/511 THE RANDOMIZATION TEST. Charlotte Wickham. stat511.cwick.co.nz. Oct 16 2015" Transcription

1 Stat 411/511 THE RANDOMIZATION TEST Oct Charlotte Wickham stat511.cwick.co.nz

2 Today Review randomization model Conduct randomization test What about CIs? Using a t-distribution as an approximation to the randomization distribution.

3 Read: in Sleuth Display 1.1 p. 2 Creativity scores in two motivation groups, and their summary statistics Motivation Group Assigned randomly by researcher Intrinsic Extrinsic score 4.1 points 19.3 higher 24.3than the 16.8 extrinsic Does intrinsic motivation improve creativity? The intrinsic group has an average creativity Sample Size: Average: Sample Standard Deviation: group = 4.1

5 The randomized experiment model Key idea: there is no population, and no sampling! get treatment 1 Some experimental units assigned at random observed responses for units assigned to treatment 1 Doesn t matter where they came from. get treatment 2 observed responses for units assigned to treatment 2 Chance only enters through the random assignment of units to treatments

6 Remember: Statistical testing 1. Set up the null hypothesis (and alternative hypothesis) 2. Calculate the test statistic 3 Evaluate the evidence against the null hypothesis by comparing the test statistic to test statistics expected under the null hypothesis, the null distribution. To do a test all we really need to know is the null distribution. I.e. the randomization distribution if the null was true. The evidence is summarized by a p-value, the probability we would see such an extreme test-statistic if the null hypothesis is true. 4. If the p is low, the null must go! Reject or fail to reject the null hypothesis

7 Randomization Distribution The randomization distribution is the histogram of all values for the statistic from all possible ways the experimental units could have been randomly assigned to groups. In the sampling model, the reason there is variability in a sample statistic is because we induced variability by taking a random sample. We describe the variability using the sampling distribution of the statistic. In the randomized experiment model, the only reason we see variability in group statistics is because we induced variability by randomly assigning people to groups. We describe the variability using the randomization distribution of the statistic. In randomized experiments it s the relationship between the randomization distribution and the effect of the treatment that allow us to make inferences.

8 subject 1 subject 2...

9 500,000 test-statistics, from 500,000 random regroupings An approximation to the distribution we would expect from chance alone null distribution 1302/ are as small or smaller than / are as large or larger than 4.14 The value from the data two-sided p-value = ( )/ =

10 A statistical summary There is strong evidence that the effect of the intrinsic questionnaire is not the same as the extrinsic questionnaire in this set of subjects (randomization test, p-value = 0.005). no population inference

11 Randomization test Procedure We pick a test-statistic and calculate the observed value. To get a p-value we compare our observed teststatistic to the randomization distribution of teststatistics obtained by assuming the null is true. The p-value will be the proportion of teststatistics in the randomization distribution that are as or more extreme than the observed teststatistic. Explain the steps in a randomization test for testing for a treatment effect in a controlled experiment.

12 The Randomization test No sampling from a population, so no assumptions on a population. Assumed random allocations to groups. We used the difference in sample averages as our test statistic, but we could have used something else. Null hypothesis: there is no difference between treatments (for any subject) What s the alternative?

13 Alternative hypothesis: there is some difference between treatments for at least one subject. Some ways the alternative could be true: one treatment induces a fixed additive change in response, δ, for all subjects (a.k.a the additive treatment model) one treatment induces a larger mean response across subjects one treatment induces a larger variance in response across subjects one treatment induces more skewness in response across subjects We might tailor our test statistic to the type of deviation from the null we expect to see, but different test statistics don t change the alternative hypothesis

14 Confidence Intervals There are no parameters of interest so, there are no confidence intervals of interest. We could assume a particular type of alternative that is parameterized. Then we could make confidence intervals on that parameter. (e.g. additive treatment model). this is what the Sleuth does Section 2.4.1

15 The additive treatment model The additive treatment model, says: A subject s response on treatment 2 is their response on treatment 1 plus some fixed number, δ, that is the same for everyone. In math, consider subject i Y i1 = Observed value of subject i under treatment 1 Y i2 = Observed value of subject i under treatment 2 Y i2 = Y i1 + δ for all i unknown parameter If we have random allocation to groups and we are willing to assume the additive treatment model, then our hypotheses in the randomization test become: Null hypothesis: the treatment effect is zero, δ = 0 Alternative hypothesis: the treatment effect is not zero, δ 0

16 Creativity case study Let s assume the additive treatment model. Creativity score given Intrinsic Questionnaire = Creativity score given Extrinsic Questionnaire + δ Let s also use the t-statistic, instead of the difference in sample averages, as our test statistic. Y 1 Y 2 SE Y 1 Y 2

17 subject 1 subject 2... Actual grouping Extrinsic Intrinsic sample avg sample sd sample n two sample t-stat = 2.92 Another grouping 1 2 sample avg sample sd sample n two sample t-stat = 1.37

18 A histogram of 500,000 t-statistics, from random regroupings of the creativity study. a t-distribution curve with d.f. 45 value of the t-statistic The t-distribution is a very good approximation to the randomization distribution of the t-statistic

19 In a randomized experiment, The result from a two sample t-test is approximately the same as a randomization test, when: you assume the additive treatment model the observed responses aren t too non-normal This is pretty amazing! The two sample t-test arose from a completely different model, random sampling from populations.

20 This means we have increased the number of situations we can do a t-test. We can do a two sample t-test when we have samples from Normal populations, and when we have a randomized experiment of two treatments, with data that isn t too non-normal. more on too non-normal later... The scope of inference (population or causal) is still completely restricted by the study design.

21 > t.test(score ~ Treatment, data = case0101, var.equal = TRUE) Two Sample t-test data: Score by Treatment t = , df = 45, p-value = alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: sample estimates: mean in group Extrinsic mean in group Intrinsic

22 Creativity case study A statistical summary based on the t-test There is strong evidence that the effect of the intrinsic questionnaire is not the same as the extrinsic questionnaire in this set of subjects (two sample t-test, p-value = 0.005). We estimate the effect of the intrinsic questionnaire is to add 4.14 points to the creativity score compared to the extrinsic questionnaire. With 95% confidence, the effect of the intrinsic questionnaire is to add between 1.29 and 7.00 points to the creativity score compared to the extrinsic questionnaire. note the language of an additive treatment model the effect is to add

### LAB 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.

### Chapter 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

### MULTIPLE 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

### THE 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

### Lecture 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

### Statistics Review PSY379 Statistics Review PSY379 Basic concepts Measurement scales Populations vs. samples Continuous vs. discrete variable Independent vs. dependent variable Descriptive vs. inferential stats Common analyses

### Lesson 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

### CHAPTER 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

### How To Test For Significance On A Data Set Non-Parametric Univariate Tests: 1 Sample Sign Test 1 1 SAMPLE SIGN TEST A non-parametric equivalent of the 1 SAMPLE T-TEST. ASSUMPTIONS: Data is non-normally distributed, even after log transforming.

### Comparing Two Groups. Standard Error of ȳ 1 ȳ 2. Setting. Two Independent Samples Comparing Two Groups Chapter 7 describes two ways to compare two populations on the basis of independent samples: a confidence interval for the difference in population means and a hypothesis test. The

### Chapter 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

### Good luck! BUSINESS STATISTICS FINAL EXAM INSTRUCTIONS. Name: Glo bal Leadership M BA BUSINESS STATISTICS FINAL EXAM Name: INSTRUCTIONS 1. Do not open this exam until instructed to do so. 2. Be sure to fill in your name before starting the exam. 3. You have two hours

### Independent 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

### Descriptive Statistics Descriptive Statistics Primer Descriptive statistics Central tendency Variation Relative position Relationships Calculating descriptive statistics Descriptive Statistics Purpose to describe or summarize

### Unit 31 A Hypothesis Test about Correlation and Slope in a Simple Linear Regression Unit 31 A Hypothesis Test about Correlation and Slope in a Simple Linear Regression Objectives: To perform a hypothesis test concerning the slope of a least squares line To recognize that testing for a

### Study 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

### Simple 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

### Recall this chart that showed how most of our course would be organized: Chapter 4 One-Way ANOVA Recall this chart that showed how most of our course would be organized: Explanatory Variable(s) Response Variable Methods Categorical Categorical Contingency Tables Categorical

### Two-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

### Inference 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

### UNDERSTANDING THE DEPENDENT-SAMPLES t TEST UNDERSTANDING THE DEPENDENT-SAMPLES t TEST A dependent-samples t test (a.k.a. matched or paired-samples, matched-pairs, samples, or subjects, simple repeated-measures or within-groups, or correlated groups)

### Section 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

### Chapter 23 Inferences About Means Chapter 23 Inferences About Means Chapter 23 - Inferences About Means 391 Chapter 23 Solutions to Class Examples 1. See Class Example 1. 2. We want to know if the mean battery lifespan exceeds the 300-minute

### General 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

### Independent 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

### Unit 26: Small Sample Inference for One Mean Unit 26: Small Sample Inference for One Mean Prerequisites Students need the background on confidence intervals and significance tests covered in Units 24 and 25. Additional Topic Coverage Additional coverage

### Hypothesis Testing for Beginners Hypothesis Testing for Beginners Michele Piffer LSE August, 2011 Michele Piffer (LSE) Hypothesis Testing for Beginners August, 2011 1 / 53 One year ago a friend asked me to put down some easy-to-read notes

### 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 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

### Part 3. Comparing Groups. Chapter 7 Comparing Paired Groups 189. Chapter 8 Comparing Two Independent Groups 217 Part 3 Comparing Groups Chapter 7 Comparing Paired Groups 189 Chapter 8 Comparing Two Independent Groups 217 Chapter 9 Comparing More Than Two Groups 257 188 Elementary Statistics Using SAS Chapter 7 Comparing

### Comparing 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

### Unit 27: Comparing Two Means Unit 27: Comparing Two Means Prerequisites Students should have experience with one-sample t-procedures before they begin this unit. That material is covered in Unit 26, Small Sample Inference for One

### Two-sample t-tests. - Independent samples - Pooled standard devation - The equal variance assumption Two-sample t-tests. - Independent samples - Pooled standard devation - The equal variance assumption Last time, we used the mean of one sample to test against the hypothesis that the true mean was a particular

### Hypothesis Testing: Two Means, Paired Data, Two Proportions Chapter 10 Hypothesis Testing: Two Means, Paired Data, Two Proportions 10.1 Hypothesis Testing: Two Population Means and Two Population Proportions 1 10.1.1 Student Learning Objectives By the end of this

### HYPOTHESIS 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

### Introduction. Hypothesis Testing. Hypothesis Testing. Significance Testing Introduction Hypothesis Testing Mark Lunt Arthritis Research UK Centre for Ecellence in Epidemiology University of Manchester 13/10/2015 We saw last week that we can never know the population parameters

### Lecture 19: Chapter 8, Section 1 Sampling Distributions: Proportions Lecture 19: Chapter 8, Section 1 Sampling Distributions: Proportions Typical Inference Problem Definition of Sampling Distribution 3 Approaches to Understanding Sampling Dist. Applying 68-95-99.7 Rule

### Chapter 7. One-way ANOVA Chapter 7 One-way ANOVA One-way ANOVA examines equality of population means for a quantitative outcome and a single categorical explanatory variable with any number of levels. The t-test of Chapter 6 looks

### Principles 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

### The t-test and Basic Inference Principles Chapter 6 The t-test and Basic Inference Principles The t-test is used as an example of the basic principles of statistical inference. One of the simplest situations for which we might design an experiment

### Chapter 7 Section 7.1: Inference for the Mean of a Population Chapter 7 Section 7.1: Inference for the Mean of a Population Now let s look at a similar situation Take an SRS of size n Normal Population : N(, ). Both and are unknown parameters. Unlike what we used

### Two-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,

### 2 Sample t-test (unequal sample sizes and unequal variances) Variations of the t-test: Sample tail Sample t-test (unequal sample sizes and unequal variances) Like the last example, below we have ceramic sherd thickness measurements (in cm) of two samples representing

### p 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

### 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

### CALCULATIONS & 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

### Testing 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

### Section 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

### Hypothesis 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

### ISyE 2028 Basic Statistical Methods - Fall 2015 Bonus Project: Big Data Analytics Final Report: Time spent on social media ISyE 2028 Basic Statistical Methods - Fall 2015 Bonus Project: Big Data Analytics Final Report: Time spent on social media Abstract: The growth of social media is astounding and part of that success was

### Statistics courses often teach the two-sample t-test, linear regression, and analysis of variance 2 Making Connections: The Two-Sample t-test, Regression, and ANOVA In theory, there s no difference between theory and practice. In practice, there is. Yogi Berra 1 Statistics courses often teach the two-sample

### Introduction to Hypothesis Testing OPRE 6301 Introduction to Hypothesis Testing OPRE 6301 Motivation... The purpose of hypothesis testing is to determine whether there is enough statistical evidence in favor of a certain belief, or hypothesis, about

### Two-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

### C. The null hypothesis is not rejected when the alternative hypothesis is true. A. population parameters. Sample Multiple Choice Questions for the material since Midterm 2. Sample questions from Midterms and 2 are also representative of questions that may appear on the final exam.. A randomly selected sample

### Analysis of Variance ANOVA Analysis of Variance ANOVA Overview We ve used the t -test to compare the means from two independent groups. Now we ve come to the final topic of the course: how to compare means from more than two populations.

### Once saved, if the file was zipped you will need to unzip it. For the files that I will be posting you need to change the preferences. 1 Commands in JMP and Statcrunch Below are a set of commands in JMP and Statcrunch which facilitate a basic statistical analysis. The first part concerns commands in JMP, the second part is for analysis

### SCHOOL 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

### Permutation Tests for Comparing Two Populations Permutation Tests for Comparing Two Populations Ferry Butar Butar, Ph.D. Jae-Wan Park Abstract Permutation tests for comparing two populations could be widely used in practice because of flexibility of

### MONT 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

### UNDERSTANDING THE INDEPENDENT-SAMPLES t TEST UNDERSTANDING The independent-samples t test evaluates the difference between the means of two independent or unrelated groups. That is, we evaluate whether the means for two independent groups are significantly

### An Introduction to Statistics Course (ECOE 1302) Spring Semester 2011 Chapter 10- TWO-SAMPLE TESTS The Islamic University of Gaza Faculty of Commerce Department of Economics and Political Sciences An Introduction to Statistics Course (ECOE 130) Spring Semester 011 Chapter 10- TWO-SAMPLE TESTS Practice

### Math 251, Review Questions for Test 3 Rough Answers Math 251, Review Questions for Test 3 Rough Answers 1. (Review of some terminology from Section 7.1) In a state with 459,341 voters, a poll of 2300 voters finds that 45 percent support the Republican candidate,

### HYPOTHESIS TESTING (ONE SAMPLE) - CHAPTER 7 1. used confidence intervals to answer questions such as... HYPOTHESIS TESTING (ONE SAMPLE) - CHAPTER 7 1 PREVIOUSLY used confidence intervals to answer questions such as... You know that 0.25% of women have red/green color blindness. You conduct a study of men

### HYPOTHESIS 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,

### Introduction. Statistics Toolbox Introduction A hypothesis test is a procedure for determining if an assertion about a characteristic of a population is reasonable. For example, suppose that someone says that the average price of a gallon

### Projects 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,

### Two-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

### Chapter 2. Hypothesis testing in one population Chapter 2. Hypothesis testing in one population Contents Introduction, the null and alternative hypotheses Hypothesis testing process Type I and Type II errors, power Test statistic, level of significance

### " 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

### 3.4 Statistical inference for 2 populations based on two samples 3.4 Statistical inference for 2 populations based on two samples Tests for a difference between two population means The first sample will be denoted as X 1, X 2,..., X m. The second sample will be denoted

### STATISTICS PROJECT: Hypothesis Testing STATISTICS PROJECT: Hypothesis Testing See my comments in red. Scoring last page. INTRODUCTION My topic is the average tuition cost of a 4-yr. public college. Since I will soon be transferring to a 4-yr.

### Introduction 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

### Friedman's Two-way Analysis of Variance by Ranks -- Analysis of k-within-group Data with a Quantitative Response Variable Friedman's Two-way Analysis of Variance by Ranks -- Analysis of k-within-group Data with a Quantitative Response Variable Application: This statistic has two applications that can appear very different,

### Testing for differences I exercises with SPSS Testing for differences I exercises with SPSS Introduction The exercises presented here are all about the t-test and its non-parametric equivalents in their various forms. In SPSS, all these tests can

### Non-Inferiority Tests for Two Means using Differences Chapter 450 on-inferiority Tests for Two Means using Differences Introduction This procedure computes power and sample size for non-inferiority tests in two-sample designs in which the outcome is a continuous

### Calculating P-Values. Parkland College. Isela Guerra Parkland College. Recommended Citation Parkland College A with Honors Projects Honors Program 2014 Calculating P-Values Isela Guerra Parkland College Recommended Citation Guerra, Isela, "Calculating P-Values" (2014). A with Honors Projects.

### Introduction to Quantitative Methods Introduction to Quantitative Methods October 15, 2009 Contents 1 Definition of Key Terms 2 2 Descriptive Statistics 3 2.1 Frequency Tables......................... 4 2.2 Measures of Central Tendencies.................

### Chapter 26: Tests of Significance Chapter 26: Tests of Significance Procedure: 1. State the null and alternative in words and in terms of a box model. 2. Find the test statistic: z = observed EV. SE 3. Calculate the P-value: The area under

### Chapter 7: One-Sample Inference Chapter 7: One-Sample Inference Now that you have all this information about descriptive statistics and probabilities, it is time to start inferential statistics. There are two branches of inferential

### Odds ratio, Odds ratio test for independence, chi-squared statistic. Odds ratio, Odds ratio test for independence, chi-squared statistic. Announcements: Assignment 5 is live on webpage. Due Wed Aug 1 at 4:30pm. (9 days, 1 hour, 58.5 minutes ) Final exam is Aug 9. Review

### Hypothesis testing - Steps Hypothesis testing - Steps Steps to do a two-tailed test of the hypothesis that β 1 0: 1. Set up the hypotheses: H 0 : β 1 = 0 H a : β 1 0. 2. Compute the test statistic: t = b 1 0 Std. error of b 1 =

### Sample Size Planning, Calculation, and Justification Sample Size Planning, Calculation, and Justification Theresa A Scott, MS Vanderbilt University Department of Biostatistics theresa.scott@vanderbilt.edu http://biostat.mc.vanderbilt.edu/theresascott Theresa

### Introduction to Analysis of Variance (ANOVA) Limitations of the t-test Introduction to Analysis of Variance (ANOVA) The Structural Model, The Summary Table, and the One- Way ANOVA Limitations of the t-test Although the t-test is commonly used, it has limitations Can only

### Outline. 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

### HYPOTHESIS TESTING (ONE SAMPLE) - CHAPTER 7 1. used confidence intervals to answer questions such as... HYPOTHESIS TESTING (ONE SAMPLE) - CHAPTER 7 1 PREVIOUSLY used confidence intervals to answer questions such as... You know that 0.25% of women have red/green color blindness. You conduct a study of men

### This 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

### Hypothesis Test for Mean Using Given Data (Standard Deviation Known-z-test) Hypothesis Test for Mean Using Given Data (Standard Deviation Known-z-test) A hypothesis test is conducted when trying to find out if a claim is true or not. And if the claim is true, is it significant.

### Regression Analysis: A Complete Example Regression Analysis: A Complete Example This section works out an example that includes all the topics we have discussed so far in this chapter. A complete example of regression analysis. PhotoDisc, Inc./Getty

### STAT 350 Practice Final Exam Solution (Spring 2015) PART 1: Multiple Choice Questions: 1) A study was conducted to compare five different training programs for improving endurance. Forty subjects were randomly divided into five groups of eight subjects

### 5.1 Identifying the Target Parameter University of California, Davis Department of Statistics Summer Session II Statistics 13 August 20, 2012 Date of latest update: August 20 Lecture 5: Estimation with Confidence intervals 5.1 Identifying

### Fairfield 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

### Hypothesis Testing. Steps for a hypothesis test: Hypothesis Testing Steps for a hypothesis test: 1. State the claim H 0 and the alternative, H a 2. Choose a significance level or use the given one. 3. Draw the sampling distribution based on the assumption

### Bootstrap Hypothesis Test Bootstrap Hypothesis Test In 1882 Simon Newcomb performed an experiment to measure the speed of light. The numbers below represent the measured time it took for light to travel from Fort Myer on the west

### Name: Date: Use the following to answer questions 3-4: Name: Date: 1. Determine whether each of the following statements is true or false. A) The margin of error for a 95% confidence interval for the mean increases as the sample size increases. B) The margin

### BA 275 Review Problems - Week 5 (10/23/06-10/27/06) CD Lessons: 48, 49, 50, 51, 52 Textbook: pp. 380-394 BA 275 Review Problems - Week 5 (10/23/06-10/27/06) CD Lessons: 48, 49, 50, 51, 52 Textbook: pp. 380-394 1. Does vigorous exercise affect concentration? In general, the time needed for people to complete

### Class 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

### Psychology 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 Lecture 5: Non-Parametric Tests (I) KimHuat LIM lim@stats.ox.ac.uk http://www.stats.ox.ac.uk/~lim/teaching.html Slide 1 5.1 Outline (i) Overview of Distribution-Free Tests (ii) Median Test for Two Independent WHAT IS A JOURNAL CLUB? With its September 2002 issue, the American Journal of Critical Care debuts a new feature, the AJCC Journal Club. Each issue of the journal will now feature an AJCC Journal Club