Chapter 19 main topics. Sociology 360 Statistics for Sociologists I Chapter 19 TwoSample Problems. Chapter 19 homework assignment


 Lynne Lillian Baldwin
 2 years ago
 Views:
Transcription
1 Sociology 360 Statistics for Sociologists I Chapter 19 TwoSample Problems Chapter 19 main topics Twosample t procedures Robustness of twosample t procedures Details of the t approximation Avoid the pooled twosample t procedures Avoid inference about standard deviations Topic to omit: The F test for comparing two standard deviations 1 Chapter 19 homework assignment Problems: 19.6,.7,.9,.14,.16,.30,.3 One vs. twosample ttests Onesample test: Is a population mean >, <, or different from some fixed value? Twosample test: Goal: Compare responses to two treatments or characteristics of two populations. Independent samples for each treatment or population (i.e., the data are not matched pairs). Are the population means the same as each other, or is one greater than the other? 3 4
2 Examples of twosample tests Research questions: Do men have higher salaries than women? Where do people travel farther to work, Detroit or Los Angeles? Twosample ttest: assumptions We have an SRS from each of two populations or an experiment with two randomly assigned groups. We can consider subgroups of individuals in a random sample (e.g., men, women) as independent samples from their respective populations. The samples are independent. The individuals that make up the two samples are not related to each other (cannot be paired or matched). If cases in the two samples can be paired or matched, used a matched pairs design. 5 6 Problems: Identify the appropriate method Is this a onesample, twosample, onesample matched pairs problem? Would you perform a hypothesis test or find a confidence interval? 1. Do Burger King Whoppers have more than 670 calories?. Do Whoppers have more calories than Big Macs? 3. Mothers of twins were surveyed and asked how often in the past month strangers had asked whether the twins were identical. 4. Are parents equally strict with boys and girls? In a random sample of families, researchers asked a brother and sister from each family to rate how strict their parents were. Null hypothesis for a twosample test Most frequently, the null hypothesis is that the two means are the same. Optio: H0:!1 =! Option : H0:!1 ! = 0 Of course both options mean the same thing since Option is obtained algebraically from Optio by subtracting! from both sides. Option, however, in stating that the difference between the two population means is zero, focusses our attention on the proper sample statistic for inference, the difference in sample means: ( x 1 x ) 7 8
3 Possible alternative hypotheses Twotailed: Optio: H A :! 1!! or Option : H A :! 1 !! 0 Onetailed (right): Optio: H A :! 1 >! or Option : H A :! 1 ! > 0 Onetailed (left) Optio: H A :! 1 <! or Option : H A :! 1 ! < 0 In each case, Optio is equivalent to Option. Whoppers and Big Macs Do Whoppers have more calories than Big Macs? Let! w = Mean calories in Whoppers Let! bm = Mean calories in Big Macs Write the null and alternative hypotheses using both methods (optio and option ) 9 10 Sampling distribution of the difference in means Our interest centers on the difference between the two population means,!1 !, which I will emphasize is a single numerical value by writing it within parentheses, like this: (!1 !). We can estimate (!1 !) by its sample analog, ( x 1 x ). Since ( x 1 x ) is a number calculated only from sample information, it is a statistic. As a statistic, ( x 1 x ) has a sampling distribution. The sampling distribution of ( x 1 x ) will be Normal under the right circumstances. And the mean of that sampling distribution will be (!1 !). All that remains to be discovered about the sampling distribution is its standard error (or estimated standard deviation). Sampling distribution of the difference in means µ G µ B =
4 Standard error The twosample t statistic follows approximately the t distribution with a standard error SE reflecting variation from both samples. In fact, its standard error is simply the square root of the sum of the standard errors of each sample considered separately: s 1 SE = + s n df Degrees of freedom Since we are using a standard error, estimated from the data, rather than a known standard deviation, the procedures will be t rather than z based. That means we need to have a value for the degrees of freedom of the t distribution. A conservative approach is to use the smaller of (n11) and (n  1) as the degrees of freedom. This rule is conservative in that it may give a value larger than is really appropriate, which leads to wider confidence intervals and larger Pvalues (meaning we are a bit less likely to reject H0). You should use this rule for problems done by hand; for example, on the exam. µ 1 "µ Twosample ttest The null hypothesis is that both population means! 1 and! are equal, thus their difference is equal to zero: H 0 : (µ 1 µ ) = 0 with either a onesided or a twosided alternative hypothesis. We construct a t statistic via the usual comparison of the observed statistic to the hypothesized value: t = ( x 1 x ) (µ 1 µ ) 0 SE = ( x 1 x ) 0 s 1 + s n Ideal number of children Do men and women have different beliefs about the ideal number of children in a family? 004 General Social Survey asked, What do you think is the ideal number of children for a family to have? Here is a summary of the responses: Gender x s n Male Female This statistic has an approximate t distribution if H0 is true
5 Ideal number of children Gender x s n Male Female What are the null and alternative hypotheses? Choose an # level. Draw a picture of the sampling distribution and the pvalue you are looking for. Perform the test and evaluate the result..89 Note: =.064 Confidence interval As before, we often supplement a hypothesis test by a CI. (And sometimes we omit the test.) For twosample problems, the question is to estimate the mean of the distribution of the difference scores in the population. The statistic continues to be ( x 1 x ) and the confidence interval is CI = ( x 1 x ) ±t s 1 + s n % CI for the example Gender x s n Male Female df = min(373,416) = 373 For C =.95, t 373 z = Effects of Reading Program on Reading Comprehension New reading activities for elementary school children RA 3 rd graders to treatment group and control group Compare reading comprehension s CI = ( x 1 x ) ±t 1 + s n Note: =.064 Calculate a 95% CI for the effect of the new reading activities on reading comprehension Note: =
6 Robustness of the twosample t procedures We must have an SRS or randomized comparative experiment. t procedures are only exact if the population distribution is exactly normal. But, we will consider twosample t procedures good enough approximations in these cases: 1. When n1 + n < 15, the data from both samples must be close to normal (roughly symmetric, single peak) and without outliers.. Whe5 " n1 + n < 40, mild skewness is acceptable, but not outliers. 3. When n1 + n " 40, the t statistic will be valid even with strong skewness. Details of the t approximation The actual distribution of the twosample t statistic is not really t (!). But it is a distribution that can be very closely approximated by a t distribution with this number of degrees of freedom: df = ( s 1 ) + s n ( ) 1 s n 1 This is known as the Satterthwaite approximation. The formula typically produces a noninteger degree of freedom value. Computers routinely calculate this approximation. You should recognize it when you see it. ( s n ) But on exams, use the smaller of (n11) and (n  1) instead. 1 Avoid the pooled twosample t procedures Your textbook s author, Moore, recommends completely avoiding the pooled twosample t procedures, and I agree. Pooled procedures are often the default choice in stat packages (e.g., Stata, including the current version, 10.0). The reasons that the pooled approach is often used are: 1) it was historically easier to calculate; ) it leads to a smaller estimated standard error when the assumptions are met; 3) it amounts to a special case of a very important technique called the analysis of variance. But Moore is right to emphasize: 1) the assumption of normality and equal variances can t be tested effectively when the sample sizes are small (i.e., when the pooled procedure would be most advantageous); ) the pooled procedure can lead to incorrect inferences when the assumptions aren t met; 3) the reduction in SE s is small for large n s. So you are asked to know not to accept a default assumption of equal (pooled) variances, and why not! Avoid inference about standard deviations In an extension of the ideas behind not using the pooled t procedures, Moore also warns us not to try to make inferences about standard deviations at all, at least in smaller samples, and at least without expert statistical help. The problem is that it is hard to make a useful test of the hypothesis that the standard deviations in two populations are the same unless we are willing to assume the shapes of the two distributions are the same. (Things are even easier if we assume the shapes are normal.) But when the sample is small there is no easy way to tell if the shapes of two distributions are the same. So, says Moore, avoid testing of hypotheses that standard deviations are the same. My only reservation about this recommendation would be in cases where there are strong reasons to expect normality in both populations. 3 4
General Method: Difference of Means. 3. Calculate df: either WelchSatterthwaite 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 WelchSatterthwaite formula or simpler df = min(n
More informationSPSS on two independent samples. Two sample test with proportions. Paired ttest (with more SPSS)
SPSS on two independent samples. Two sample test with proportions. Paired ttest (with more SPSS) State of the course address: The Final exam is Aug 9, 3:30pm 6:30pm in B9201 in the Burnaby Campus. (One
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 informationGood 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
More informationName: Date: Use the following to answer questions 34:
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
More informationStatistiek I. ttests. John Nerbonne. CLCG, Rijksuniversiteit Groningen. John Nerbonne 1/35
Statistiek I ttests John Nerbonne CLCG, Rijksuniversiteit Groningen http://wwwletrugnl/nerbonne/teach/statistieki/ John Nerbonne 1/35 ttests To test an average or pair of averages when σ is known, we
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 informationAn Introduction to Statistics Course (ECOE 1302) Spring Semester 2011 Chapter 10 TWOSAMPLE 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 TWOSAMPLE TESTS Practice
More informationUnit 27: Comparing Two Means
Unit 27: Comparing Two Means Prerequisites Students should have experience with onesample tprocedures before they begin this unit. That material is covered in Unit 26, Small Sample Inference for One
More informationChapter 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 300minute
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 informationStatistical Inference and ttests
1 Statistical Inference and ttests Objectives Evaluate the difference between a sample mean and a target value using a onesample ttest. Evaluate the difference between a sample mean and a target value
More informationModule 5 Hypotheses Tests: Comparing Two Groups
Module 5 Hypotheses Tests: Comparing Two Groups Objective: In medical research, we often compare the outcomes between two groups of patients, namely exposed and unexposed groups. At the completion of this
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 informationInferences About Differences Between Means Edpsy 580
Inferences About Differences Between Means Edpsy 580 Carolyn J. Anderson Department of Educational Psychology University of Illinois at UrbanaChampaign Inferences About Differences Between Means Slide
More informationInferential Statistics
Inferential Statistics Sampling and the normal distribution Zscores Confidence levels and intervals Hypothesis testing Commonly used statistical methods Inferential Statistics Descriptive statistics are
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 informationC. 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
More informationHypothesis testing  Steps
Hypothesis testing  Steps Steps to do a twotailed 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 =
More informationMind on Statistics. Chapter 13
Mind on Statistics Chapter 13 Sections 13.113.2 1. Which statement is not true about hypothesis tests? A. Hypothesis tests are only valid when the sample is representative of the population for the question
More informationNonparametric TwoSample Tests. Nonparametric Tests. Sign Test
Nonparametric TwoSample Tests Sign test MannWhitney Utest (a.k.a. Wilcoxon twosample test) KolmogorovSmirnov Test Wilcoxon SignedRank Test TukeyDuckworth Test 1 Nonparametric Tests Recall, nonparametric
More informationSuppose we want to compare the average effectiveness of two treatments in a completely randomized experiment. In this case, the parameters µ 1
AP Statistics: 10.2: Comparing Two Means Name: Suppose we want to compare the average effectiveness of two treatments in a completely randomized experiment. In this case, the parameters µ 1 and µ 2 are
More informationTwosample ttests.  Independent samples  Pooled standard devation  The equal variance assumption
Twosample ttests.  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
More informationPaired vs. 2 sample comparisons. Comparing means. Paired comparisons allow us to account for a lot of extraneous variation.
Comparing means! Tests with one categorical and one numerical variable Paired vs. sample comparisons! Goal: to compare the mean of a numerical variable for different groups. Paired comparisons allow us
More informationIntroduction. 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
More informationIntroduction to Stata
Introduction to Stata September 23, 2014 Stata is one of a few statistical analysis programs that social scientists use. Stata is in the midrange of how easy it is to use. Other options include SPSS,
More informationHypothesis testing S2
Basic medical statistics for clinical and experimental research Hypothesis testing S2 Katarzyna Jóźwiak k.jozwiak@nki.nl 2nd November 2015 1/43 Introduction Point estimation: use a sample statistic to
More informationChapter 8. Hypothesis Testing
Chapter 8 Hypothesis Testing Hypothesis In statistics, a hypothesis is a claim or statement about a property of a population. A hypothesis test (or test of significance) is a standard procedure for testing
More informationAnalysis of numerical data S4
Basic medical statistics for clinical and experimental research Analysis of numerical data S4 Katarzyna Jóźwiak k.jozwiak@nki.nl 3rd November 2015 1/42 Hypothesis tests: numerical and ordinal data 1 group:
More informationTwosample hypothesis testing, I 9.07 3/09/2004
Twosample hypothesis testing, I 9.07 3/09/2004 But first, from last time More on the tradeoff between Type I and Type II errors The null and the alternative: Sampling distribution of the mean, m, given
More informationUnit 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
More informationUnit 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
More informationDifference of Means and ANOVA Problems
Difference of Means and Problems Dr. Tom Ilvento FREC 408 Accounting Firm Study An accounting firm specializes in auditing the financial records of large firm It is interested in evaluating its fee structure,particularly
More informationOutline. Definitions Descriptive vs. Inferential Statistics The ttest  Onesample ttest
The ttest Outline Definitions Descriptive vs. Inferential Statistics The ttest  Onesample ttest  Dependent (related) groups ttest  Independent (unrelated) groups ttest Comparing means Correlation
More informationChapter Additional: Standard Deviation and Chi Square
Chapter Additional: Standard Deviation and Chi Square Chapter Outline: 6.4 Confidence Intervals for the Standard Deviation 7.5 Hypothesis testing for Standard Deviation Section 6.4 Objectives Interpret
More information2 Sample ttest (unequal sample sizes and unequal variances)
Variations of the ttest: Sample tail Sample ttest (unequal sample sizes and unequal variances) Like the last example, below we have ceramic sherd thickness measurements (in cm) of two samples representing
More informationChapter 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
More informationHypothesis Testing. Bluman Chapter 8
CHAPTER 8 Learning Objectives C H A P T E R E I G H T Hypothesis Testing 1 Outline 81 Steps in Traditional Method 82 z Test for a Mean 83 t Test for a Mean 84 z Test for a Proportion 85 2 Test for
More informationTwosample hypothesis testing, II 9.07 3/16/2004
Twosample hypothesis testing, II 9.07 3/16/004 Small sample tests for the difference between two independent means For twosample tests of the difference in mean, things get a little confusing, here,
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 informationUCLA STAT 13 Statistical Methods  Final Exam Review Solutions Chapter 7 Sampling Distributions of Estimates
UCLA STAT 13 Statistical Methods  Final Exam Review Solutions Chapter 7 Sampling Distributions of Estimates 1. (a) (i) µ µ (ii) σ σ n is exactly Normally distributed. (c) (i) is approximately Normally
More informationHypothesis Testing Level I Quantitative Methods. IFT Notes for the CFA exam
Hypothesis Testing 2014 Level I Quantitative Methods IFT Notes for the CFA exam Contents 1. Introduction... 3 2. Hypothesis Testing... 3 3. Hypothesis Tests Concerning the Mean... 10 4. Hypothesis Tests
More informationAP Statistics 2012 Scoring Guidelines
AP Statistics 2012 Scoring Guidelines The College Board The College Board is a missiondriven notforprofit organization that connects students to college success and opportunity. Founded in 1900, the
More informationStats for Strategy Exam 1 InClass Practice Questions DIRECTIONS
Stats for Strategy Exam 1 InClass Practice Questions DIRECTIONS Choose the single best answer for each question. Discuss questions with classmates, TAs and Professor Whitten. Raise your hand to check
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 informationOutline of Topics. Statistical Methods I. Types of Data. Descriptive Statistics
Statistical Methods I Tamekia L. Jones, Ph.D. (tjones@cog.ufl.edu) Research Assistant Professor Children s Oncology Group Statistics & Data Center Department of Biostatistics Colleges of Medicine and Public
More information3.4 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
More informationAP Statistics 2011 Scoring Guidelines
AP Statistics 2011 Scoring Guidelines The College Board The College Board is a notforprofit membership association whose mission is to connect students to college success and opportunity. Founded in
More informationNonparametric tests I
Nonparametric tests I Objectives MannWhitney Wilcoxon Signed Rank Relation of Parametric to Nonparametric tests 1 the problem Our testing procedures thus far have relied on assumptions of independence,
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 information1.5 Oneway Analysis of Variance
Statistics: Rosie Cornish. 200. 1.5 Oneway Analysis of Variance 1 Introduction Oneway analysis of variance (ANOVA) is used to compare several means. This method is often used in scientific or medical experiments
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 informationNonparametric Statistics
1 14.1 Using the Binomial Table Nonparametric Statistics In this chapter, we will survey several methods of inference from Nonparametric Statistics. These methods will introduce us to several new tables
More informationStat 411/511 THE RANDOMIZATION TEST. Charlotte Wickham. stat511.cwick.co.nz. Oct 16 2015
Stat 411/511 THE RANDOMIZATION TEST Oct 16 2015 Charlotte Wickham stat511.cwick.co.nz Today Review randomization model Conduct randomization test What about CIs? Using a tdistribution as an approximation
More informationAP Statistics 2002 Scoring Guidelines
AP Statistics 2002 Scoring Guidelines The materials included in these files are intended for use by AP teachers for course and exam preparation in the classroom; permission for any other use must be sought
More informationRecall this chart that showed how most of our course would be organized:
Chapter 4 OneWay 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
More information1. What is the critical value for this 95% confidence interval? CV = z.025 = invnorm(0.025) = 1.96
1 Final Review 2 Review 2.1 CI 1propZint Scenario 1 A TV manufacturer claims in its warranty brochure that in the past not more than 10 percent of its TV sets needed any repair during the first two years
More informationNonparametric Test Procedures
Nonparametric Test Procedures 1 Introduction to Nonparametrics Nonparametric tests do not require that samples come from populations with normal distributions or any other specific distribution. Hence
More informationUnit 29 ChiSquare GoodnessofFit Test
Unit 29 ChiSquare GoodnessofFit Test Objectives: To perform the chisquare hypothesis test concerning proportions corresponding to more than two categories of a qualitative variable To perform the Bonferroni
More informationClass 19: Two Way Tables, Conditional Distributions, ChiSquare (Text: Sections 2.5; 9.1)
Spring 204 Class 9: Two Way Tables, Conditional Distributions, ChiSquare (Text: Sections 2.5; 9.) Big Picture: More than Two Samples In Chapter 7: We looked at quantitative variables and compared the
More informationReporting Statistics in Psychology
This document contains general guidelines for the reporting of statistics in psychology research. The details of statistical reporting vary slightly among different areas of science and also among different
More informationStatistics 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
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 informationTesting Group Differences using Ttests, ANOVA, and Nonparametric Measures
Testing Group Differences using Ttests, ANOVA, and Nonparametric Measures Jamie DeCoster Department of Psychology University of Alabama 348 Gordon Palmer Hall Box 870348 Tuscaloosa, AL 354870348 Phone:
More informationHypothesis Testing or How to Decide to Decide Edpsy 580
Hypothesis Testing or How to Decide to Decide Edpsy 580 Carolyn J. Anderson Department of Educational Psychology University of Illinois at UrbanaChampaign Hypothesis Testing or How to Decide to Decide
More informationHints for Success on the AP Statistics Exam. (Compiled by Zack Bigner)
Hints for Success on the AP Statistics Exam. (Compiled by Zack Bigner) The Exam The AP Stat exam has 2 sections that take 90 minutes each. The first section is 40 multiple choice questions, and the second
More informationData Analysis Tools. Tools for Summarizing Data
Data Analysis Tools This section of the notes is meant to introduce you to many of the tools that are provided by Excel under the Tools/Data Analysis menu item. If your computer does not have that tool
More informationSTAT 145 (Notes) Al Nosedal anosedal@unm.edu Department of Mathematics and Statistics University of New Mexico. Fall 2013
STAT 145 (Notes) Al Nosedal anosedal@unm.edu Department of Mathematics and Statistics University of New Mexico Fall 2013 CHAPTER 18 INFERENCE ABOUT A POPULATION MEAN. Conditions for Inference about mean
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 informationChapter 9. TwoSample Tests. Effect Sizes and Power Paired t Test Calculation
Chapter 9 TwoSample Tests Paired t Test (Correlated Groups t Test) Effect Sizes and Power Paired t Test Calculation Summary Independent t Test Chapter 9 Homework Power and TwoSample Tests: Paired Versus
More informationt Tests in Excel The Excel Statistical Master By Mark Harmon Copyright 2011 Mark Harmon
ttests 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 informationSections 4.54.7: TwoSample Problems. Paired ttest (Section 4.6)
Sections 4.54.7: TwoSample Problems Paired ttest (Section 4.6) Examples of Paired Differences studies: Similar subjects are paired off and one of two treatments is given to each subject in the pair.
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Sample Practice problems  chapter 121 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 information= $96 = $24. (b) The degrees of freedom are. s n. 7.3. For the mean monthly rent, the 95% confidence interval for µ is
Chapter 7 Solutions 71 (a) The standard error of the mean is df = n 1 = 15 s n = $96 = $24 (b) The degrees of freedom are 16 72 In each case, use df = n 1; if that number is not in Table D, drop to the
More informationNull Hypothesis Significance Testing Signifcance Level, Power, ttests Spring 2014 Jeremy Orloff and Jonathan Bloom
Null Hypothesis Significance Testing Signifcance Level, Power, ttests 18.05 Spring 2014 Jeremy Orloff and Jonathan Bloom Simple and composite hypotheses Simple hypothesis: the sampling distribution is
More information6. Statistical Inference: Significance Tests
6. Statistical Inference: Significance Tests Goal: Use statistical methods to check hypotheses such as Women's participation rates in elections in France is higher than in Germany. (an effect) Ethnic divisions
More informationSimple Regression Theory II 2010 Samuel L. Baker
SIMPLE REGRESSION THEORY II 1 Simple Regression Theory II 2010 Samuel L. Baker Assessing how good the regression equation is likely to be Assignment 1A gets into drawing inferences about how close the
More informationANOVA Analysis of Variance
ANOVA Analysis of Variance What is ANOVA and why do we use it? Can test hypotheses about mean differences between more than 2 samples. Can also make inferences about the effects of several different IVs,
More informationDDBA 8438: The t Test for Independent Samples Video Podcast Transcript
DDBA 8438: The t Test for Independent Samples Video Podcast Transcript JENNIFER ANN MORROW: Welcome to The t Test for Independent Samples. My name is Dr. Jennifer Ann Morrow. In today's demonstration,
More informationConfidence intervals, t tests, P values
Confidence intervals, t tests, P values Joe Felsenstein Department of Genome Sciences and Department of Biology Confidence intervals, t tests, P values p.1/31 Normality Everybody believes in the normal
More informationIntroduction to Analysis of Variance (ANOVA) Limitations of the ttest
Introduction to Analysis of Variance (ANOVA) The Structural Model, The Summary Table, and the One Way ANOVA Limitations of the ttest Although the ttest is commonly used, it has limitations Can only
More informationP(every one of the seven intervals covers the true mean yield at its location) = 3.
1 Let = number of locations at which the computed confidence interval for that location hits the true value of the mean yield at its location has a binomial(7,095) (a) P(every one of the seven intervals
More informationTwoSample TTests Allowing Unequal Variance (Enter Difference)
Chapter 45 TwoSample TTests Allowing Unequal Variance (Enter Difference) Introduction This procedure provides sample size and power calculations for one or twosided twosample ttests when no assumption
More informationIndependent samples ttest. Dr. Tom Pierce Radford University
Independent samples ttest 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 informationNull Hypothesis H 0. The null hypothesis (denoted by H 0
Hypothesis test In statistics, a hypothesis is a claim or statement about a property of a population. A hypothesis test (or test of significance) is a standard procedure for testing a claim about a property
More informationHYPOTHESIS 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
More informationTwoSample TTests Assuming Equal Variance (Enter Means)
Chapter 4 TwoSample TTests Assuming Equal Variance (Enter Means) Introduction This procedure provides sample size and power calculations for one or twosided twosample ttests when the variances of
More informationChapter Five: Paired Samples Methods 1/38
Chapter Five: Paired Samples Methods 1/38 5.1 Introduction 2/38 Introduction Paired data arise with some frequency in a variety of research contexts. Patients might have a particular type of laser surgery
More informationPart 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
More informationTutorial 5: Hypothesis Testing
Tutorial 5: Hypothesis Testing Rob Nicholls nicholls@mrclmb.cam.ac.uk MRC LMB Statistics Course 2014 Contents 1 Introduction................................ 1 2 Testing distributional assumptions....................
More informationStatistical Significance and Bivariate Tests
Statistical Significance and Bivariate Tests BUS 735: Business Decision Making and Research 1 1.1 Goals Goals Specific goals: Refamiliarize ourselves with basic statistics ideas: sampling distributions,
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 ttest when to use the independent ttest the use of SPSS to complete an independent
More informationCHAPTER 11 CHISQUARE: NONPARAMETRIC COMPARISONS OF FREQUENCY
CHAPTER 11 CHISQUARE: NONPARAMETRIC COMPARISONS OF FREQUENCY The hypothesis testing statistics detailed thus far in this text have all been designed to allow comparison of the means of two or more samples
More informationModule 7: Hypothesis Testing I Statistics (OA3102)
Module 7: Hypothesis Testing I Statistics (OA3102) Professor Ron Fricker Naval Postgraduate School Monterey, California Reading assignment: WM&S chapter 10.110.5 Revision: 212 1 Goals for this Module
More informationChapter 8 Hypothesis Tests. Chapter Table of Contents
Chapter 8 Hypothesis Tests Chapter Table of Contents Introduction...157 OneSample ttest...158 Paired ttest...164 TwoSample Test for Proportions...169 TwoSample Test for Variances...172 Discussion
More informationChapter 1112 1 Review
Chapter 1112 Review Name 1. In formulating hypotheses for a statistical test of significance, the null hypothesis is often a statement of no effect or no difference. the probability of observing the data
More informationIntroduction to Hypothesis Testing
I. Terms, Concepts. Introduction to Hypothesis Testing A. In general, we do not know the true value of population parameters  they must be estimated. However, we do have hypotheses about what the true
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 2001 Solutions and Scoring Guidelines
AP Statistics 2001 Solutions and Scoring Guidelines The materials included in these files are intended for noncommercial use by AP teachers for course and exam preparation; permission for any other use
More informationHomework 6 Solutions
Math 17, Section 2 Spring 2011 Assignment Chapter 20: 12, 14, 20, 24, 34 Chapter 21: 2, 8, 14, 16, 18 Chapter 20 20.12] Got Milk? The student made a number of mistakes here: Homework 6 Solutions 1. Null
More information