LAB 2. HYPOTHESIS TESTING IN THE BIOLOGICAL SCIENCES- Part 2
|
|
- Samuel Gardner
- 5 years ago
- Views:
Transcription
1 LAB 2. HYPOTHESIS TESTING IN THE BIOLOGICAL SCIENCES- Part 2 Data Analysis: The mean egg masses (g) of the two different types of eggs may be exactly the same, in which case you may be tempted to accept your null hypothesis. It is more likely, however, that the two sample means will differ by some amount. Are the means different enough to enable you to reject your null hypothesis? Remember, the null hypothesis is there is no difference in the average mass in grams between the two different types of eggs. Your sample means are really only estimates of the true mean of egg masses (g) of the two different types of eggs that you chose to compare. Although you have a total of 12 observations, your samples are still small relative to the total number of eggs sold in stores across the state. In order to test your hypothesis, you must have some basis for deciding whether or not the difference between the two sample means could have arisen simply by chance when, in fact, there is no real difference in the average egg mass (g) of the two different types. In other words, before you can compare them, you need to know how accurately your sample means represent the true means. The accuracy of any sample mean is related to: 1) the amount of variation in the data that were collected; and 2) the number of observations (n). The sample variance (s 2 ) is a statistic that describes the variation within the sample on the basis of the deviations of individual observations from the mean. The sample variance is equal to the sum of the squared deviations of individual observations (x) from their sample mean ( - x - ), divided by one less than the total number of observations (n): s 2 = ( - x - x) 2 n 1 t-test for comparison of sample means The two sample variances (s 2 1 and s 2 2) may be combined and used in a test of difference between the sample means, the so-called t-test. Here, the difference between the sample means is compared to the standard error of the difference (s x1 - x2 ). (s x1 - x2 ) = ( (n 1 1) s (n 2 1) s 2 2) ( ) n 1 + n 2-2 n 1 n 2 Using the standard error of the difference (s x1 - x2 ), it is possible to calculated a t- calculated (t calc ) value. The t calc value is compared to the tabled critical value (t table value), (Table 1) with 0.05 probability (95% confidence level) and n 1 + n 2-2 degrees of freedom. t calc = - x x - 2 s x1 - x2
2 The t table value is obtained from a table of critical values of the t distribution (Table 1) for the desired probability of confidence level and n 1 degrees of freedom. The statistical concept of degrees of freedom refers to the number of items that can vary independently. Once these n -1 observations are determined, the last observation is automatically set because it must be equal to the observed sample mean. The level of confidence refers to the desired probability, selected by the investigator (you), that the true mean will be included in the calculated limits. If t calc < t table, then accept the null hypothesis, (in other words, there is no statistically significant difference between the means). If t calc > t table, then reject your null hypothesis, (in other words, there is a statistically significant difference between the means). We will utilize these statistical concepts to test the null hypothesis that the difference between the calculated mean egg masses in grams is no greater than expected for two different types of eggs.
3 Steps for statistical analysis: Step 1. Calculate the sample variance (s 2 ) for Group 1 (s 2 1) and Group 2 (s 2 2) using example from Table 1., Hypothesis Testing Lab, part 1. s 2 = ( - x - x) 2 (Equation 1) n 1 Group 1 = large white eggs Mass Average egg mass (x 1 ) ( - x - 1) ( - x x 1 ) ( - x x 1 ) Group 2 = extra-large white eggs s 2 1 = ( - x x 1 ) 2 = n-1 Mass Average egg mass (x 2 ) ( - x - 2) ( - x - 2 x 2 ) ( - x - 2 x 2 ) s 2 2 = ( - x - 2 x 2 ) 2 = n-1
4 t-test for comparison of sample means The two sample variances may be combined and used in a test of difference between the sample means, the so-called t-test. Here, the difference between the sample means is compared to the standard error of the difference (s x1 - x2 ). Step 2. Calculate the standard error of the difference according to the following formula: (s x1 - x2 ) = ( (n 1 1) s (n 2 1) s 2 2) ( ) n 1 + n 2-2 n 1 n 2 Where: x 1, s 2 1, n 1 = values for Group 1 (large white eggs) x 2, s 2 2, n 2 = values for Group 2 (extra large white eggs) (s x1 - x2 ) = (11 (4.3256) + 11 (6.0789) ) ( ) = Step 3. Calculate a t value by the formula: t calc = - x x - 2 s x1 - x2 t calc = = Step 4. Compare the absolute value of calculated t value to the tabled critical value (Table 1) with 0.05 probability (95% confidence level) and n 1 + n 2-2 degrees of freedom. t table (0.95; 22) = (from Table 1) t calc = In this example, t calc > t table, > 2.074
5 Step 5. If t calc < t table, then accept the null hypothesis, (in other words, there is no statistically significant difference between the means). Conclusion: There is no statistically significant difference in the average mass in grams between large white chicken eggs and extra-large white chicken eggs. If t calc > t table, then reject your null hypothesis, (in other words, there is a statistically significant difference between the means). Conclusion: There is a statistically significant difference in the average mass in grams between large white chicken eggs and extra-large white chicken eggs.
T.I.H.E. IT 233 Statistics and Probability: Sem. 1: 2013 ESTIMATION AND HYPOTHESIS TESTING OF TWO POPULATIONS
ESTIMATION AND HYPOTHESIS TESTING OF TWO POPULATIONS In our work on hypothesis testing, we used the value of a sample statistic to challenge an accepted value of a population parameter. We focused only
More informationReview: General Approach to Hypothesis Testing. 1. Define the research question and formulate the appropriate null and alternative hypotheses.
1 Review: Let X 1, X,..., X n denote n independent random variables sampled from some distribution might not be normal!) with mean µ) and standard deviation σ). Then X µ σ n In other words, X is approximately
More informationHow do we compare the relative performance among competing models?
How do we compare the relative performance among competing models? 1 Comparing Data Mining Methods Frequent problem: we want to know which of the two learning techniques is better How to reliably say Model
More informationDesign of Engineering Experiments Part 2 Basic Statistical Concepts Simple comparative experiments
Design of Engineering Experiments Part 2 Basic Statistical Concepts Simple comparative experiments The hypothesis testing framework The two-sample t-test Checking assumptions, validity Comparing more that
More informationTesting Research and Statistical Hypotheses
Testing Research and Statistical Hypotheses Introduction In the last lab we analyzed metric artifact attributes such as thickness or width/thickness ratio. Those were continuous variables, which as you
More informationStats Review Chapter 14. Mary Stangler Center for Academic Success Revised 8/16
Stats Review Chapter 14 Revised 8/16 Note: This review is meant to highlight basic concepts from the course. It does not cover all concepts presented by your instructor. Refer back to your notes, unit
More informationVisual interpretation with normal approximation
Visual interpretation with normal approximation H 0 is true: H 1 is true: p =0.06 25 33 Reject H 0 α =0.05 (Type I error rate) Fail to reject H 0 β =0.6468 (Type II error rate) 30 Accept H 1 Visual interpretation
More information4.1 Hypothesis Testing
4.1 Hypothesis Testing z-test for a single value double-sided and single-sided z-test for one average z-test for two averages double-sided and single-sided t-test for one average the F-parameter and F-table
More informationChapter 23: Inferences About Means
Chapter 3: Inferences About Means Sample of Means: number of observations in one sample the population mean (theoretical mean) sample mean (observed mean) is the theoretical standard deviation of the population
More informationUsing SPSS for One Way Analysis of Variance
Using SPSS for One Way Analysis of Variance This tutorial will show you how to use SPSS version 12 to perform a one-way, between- subjects analysis of variance and related post-hoc tests. This tutorial
More informationAnalysis of Variance (ANOVA)
Analysis of Variance (ANOVA) Two types of ANOVA tests: Independent measures and Repeated measures Comparing 2 means: X 1 = 20 t - test X 2 = 30 How can we Compare 3 means?: X 1 = 20 X 2 = 30 X 3 = 35 ANOVA
More informationNote: k = the # of conditions n = # of data points in a condition N = total # of data points
The ANOVA for2 Dependent Groups -- Analysis of 2-Within (or Matched)-Group Data with a Quantitative Response Variable Application: This statistic has two applications that can appear very different, but
More informationCBA4 is live in practice mode this week exam mode from Saturday!
Announcements CBA4 is live in practice mode this week exam mode from Saturday! Material covered: Confidence intervals (both cases) 1 sample hypothesis tests (both cases) Hypothesis tests for 2 means as
More informationData Mining. Chapter 5. Credibility: Evaluating What s Been Learned
Data Mining Chapter 5. Credibility: Evaluating What s Been Learned 1 Evaluating how different methods work Evaluation Large training set: no problem Quality data is scarce. Oil slicks: a skilled & labor-intensive
More informationChem 321 Lecture 5 - Experimental Errors and Statistics 9/10/13
Chem 321 Lecture 5 - Experimental Errors and Statistics 9/10/13 Student Learning Objectives Experimental Errors and Statistics Calibration Results for a 2.0-mL Transfer Pipet 1.998 ml 1.991 ml 2.001 ml
More informationMultiple Regression Analysis
Multiple Regression Analysis y = β 0 + β 1 x 1 + β 2 x 2 +... β k x k + u 2. Inference 0 Assumptions of the Classical Linear Model (CLM)! So far, we know: 1. The mean and variance of the OLS estimators
More informationY11MST Short Test (Statistical Applications)
2013-2014 Y11MST Short Test (Statistical Applications) [44 marks] Members of a certain club are required to register for one of three sports, badminton, volleyball or table tennis. The number of club members
More informationThe Chi-Square Distributions
MATH 03 The Chi-Square Distributions Dr. Neal, Spring 009 The chi-square distributions can be used in statistics to analyze the standard deviation of a normally distributed measurement and to test the
More informationWe need to define some concepts that are used in experiments.
Chapter 0 Analysis of Variance (a.k.a. Designing and Analysing Experiments) Section 0. Introduction In Chapter we mentioned some different ways in which we could get data: Surveys, Observational Studies,
More informationThe Chi-Square Distributions
MATH 183 The Chi-Square Distributions Dr. Neal, WKU The chi-square distributions can be used in statistics to analyze the standard deviation σ of a normally distributed measurement and to test the goodness
More informationHYPOTHESIS TESTING. Hypothesis Testing
MBA 605 Business Analytics Don Conant, PhD. HYPOTHESIS TESTING Hypothesis testing involves making inferences about the nature of the population on the basis of observations of a sample drawn from the population.
More informationSlides for Data Mining by I. H. Witten and E. Frank
Slides for Data Mining by I. H. Witten and E. Frank Predicting performance Assume the estimated error rate is 5%. How close is this to the true error rate? Depends on the amount of test data Prediction
More informationThe Purpose of Hypothesis Testing
Section 8 1A:! An Introduction to Hypothesis Testing The Purpose of Hypothesis Testing See s Candy states that a box of it s candy weighs 16 oz. They do not mean that every single box weights exactly 16
More informationPower of a hypothesis test
Power of a hypothesis test Scenario #1 Scenario #2 H 0 is true H 0 is not true test rejects H 0 type I error test rejects H 0 OK test does not reject H 0 OK test does not reject H 0 type II error Power
More informationTwo-Sample Inferential Statistics
The t Test for Two Independent Samples 1 Two-Sample Inferential Statistics In an experiment there are two or more conditions One condition is often called the control condition in which the treatment is
More informationSection 9.1 (Part 2) (pp ) Type I and Type II Errors
Section 9.1 (Part 2) (pp. 547-551) Type I and Type II Errors Because we are basing our conclusion in a significance test on sample data, there is always a chance that our conclusions will be in error.
More informationLecture 5: Clustering, Linear Regression
Lecture 5: Clustering, Linear Regression Reading: Chapter 10, Sections 3.1-3.2 STATS 202: Data mining and analysis October 4, 2017 1 / 22 .0.0 5 5 1.0 7 5 X2 X2 7 1.5 1.0 0.5 3 1 2 Hierarchical clustering
More informationDescriptive Statistics
Descriptive Statistics Once an experiment is carried out and the results are measured, the researcher has to decide whether the results of the treatments are different. This would be easy if the results
More informationLECTURE 5. Introduction to Econometrics. Hypothesis testing
LECTURE 5 Introduction to Econometrics Hypothesis testing October 18, 2016 1 / 26 ON TODAY S LECTURE We are going to discuss how hypotheses about coefficients can be tested in regression models We will
More informationSummary: the confidence interval for the mean (σ 2 known) with gaussian assumption
Summary: the confidence interval for the mean (σ known) with gaussian assumption on X Let X be a Gaussian r.v. with mean µ and variance σ. If X 1, X,..., X n is a random sample drawn from X then the confidence
More informationStatistics 224 Solution key to EXAM 2 FALL 2007 Friday 11/2/07 Professor Michael Iltis (Lecture 2)
NOTE : For the purpose of review, I have added some additional parts not found on the original exam. These parts are indicated with a ** beside them Statistics 224 Solution key to EXAM 2 FALL 2007 Friday
More informationLecture 30. DATA 8 Summer Regression Inference
DATA 8 Summer 2018 Lecture 30 Regression Inference Slides created by John DeNero (denero@berkeley.edu) and Ani Adhikari (adhikari@berkeley.edu) Contributions by Fahad Kamran (fhdkmrn@berkeley.edu) and
More informationHypothesis Testing One Sample Tests
STATISTICS Lecture no. 13 Department of Econometrics FEM UO Brno office 69a, tel. 973 442029 email:jiri.neubauer@unob.cz 12. 1. 2010 Tests on Mean of a Normal distribution Tests on Variance of a Normal
More informationHypothesis Tests and Estimation for Population Variances. Copyright 2014 Pearson Education, Inc.
Hypothesis Tests and Estimation for Population Variances 11-1 Learning Outcomes Outcome 1. Formulate and carry out hypothesis tests for a single population variance. Outcome 2. Develop and interpret confidence
More informationStatistical Inference for Means
Statistical Inference for Means Jamie Monogan University of Georgia February 18, 2011 Jamie Monogan (UGA) Statistical Inference for Means February 18, 2011 1 / 19 Objectives By the end of this meeting,
More informationLecture 5: Clustering, Linear Regression
Lecture 5: Clustering, Linear Regression Reading: Chapter 10, Sections 3.1-3.2 STATS 202: Data mining and analysis October 4, 2017 1 / 22 Hierarchical clustering Most algorithms for hierarchical clustering
More informationLOOKING FOR RELATIONSHIPS
LOOKING FOR RELATIONSHIPS One of most common types of investigation we do is to look for relationships between variables. Variables may be nominal (categorical), for example looking at the effect of an
More informationUniversität Potsdam Institut für Informatik Lehrstuhl Maschinelles Lernen. Hypothesis testing. Anna Wegloop Niels Landwehr/Tobias Scheffer
Universität Potsdam Institut für Informatik Lehrstuhl Maschinelles Lernen Hypothesis testing Anna Wegloop iels Landwehr/Tobias Scheffer Why do a statistical test? input computer model output Outlook ull-hypothesis
More informationINTERVAL ESTIMATION AND HYPOTHESES TESTING
INTERVAL ESTIMATION AND HYPOTHESES TESTING 1. IDEA An interval rather than a point estimate is often of interest. Confidence intervals are thus important in empirical work. To construct interval estimates,
More informationAtoms, Molecules, and the Mole
The Mole Now that we know how to write and name chemical compounds, we need to understand how chemists use these formulas quantitatively. As chemists, we need to know how many atoms or molecules are reacting
More informationStudy Ch. 9.3, #47 53 (45 51), 55 61, (55 59)
GOALS: 1. Understand that 2 approaches of hypothesis testing exist: classical or critical value, and p value. We will use the p value approach. 2. Understand the critical value for the classical approach
More informationBackground to Statistics
FACT SHEET Background to Statistics Introduction Statistics include a broad range of methods for manipulating, presenting and interpreting data. Professional scientists of all kinds need to be proficient
More informationStatistics Primer. ORC Staff: Jayme Palka Peter Boedeker Marcus Fagan Trey Dejong
Statistics Primer ORC Staff: Jayme Palka Peter Boedeker Marcus Fagan Trey Dejong 1 Quick Overview of Statistics 2 Descriptive vs. Inferential Statistics Descriptive Statistics: summarize and describe data
More informationMultiple comparisons - subsequent inferences for two-way ANOVA
1 Multiple comparisons - subsequent inferences for two-way ANOVA the kinds of inferences to be made after the F tests of a two-way ANOVA depend on the results if none of the F tests lead to rejection of
More informationME3620. Theory of Engineering Experimentation. Spring Chapter IV. Decision Making for a Single Sample. Chapter IV
Theory of Engineering Experimentation Chapter IV. Decision Making for a Single Sample Chapter IV 1 4 1 Statistical Inference The field of statistical inference consists of those methods used to make decisions
More informationOne-way ANOVA. Experimental Design. One-way ANOVA
Method to compare more than two samples simultaneously without inflating Type I Error rate (α) Simplicity Few assumptions Adequate for highly complex hypothesis testing 09/30/12 1 Outline of this class
More informationYou may not use your books/notes on this exam. You may use calculator.
MATH 450 Fall 2018 Review problems 12/03/18 Time Limit: 60 Minutes Name (Print: This exam contains 6 pages (including this cover page and 5 problems. Check to see if any pages are missing. Enter all requested
More informationSingle Sample Means. SOCY601 Alan Neustadtl
Single Sample Means SOCY601 Alan Neustadtl The Central Limit Theorem If we have a population measured by a variable with a mean µ and a standard deviation σ, and if all possible random samples of size
More informationAnalysis of variance (ANOVA) Comparing the means of more than two groups
Analysis of variance (ANOVA) Comparing the means of more than two groups Example: Cost of mating in male fruit flies Drosophila Treatments: place males with and without unmated (virgin) females Five treatments
More informationGeneral Certificate of Education Advanced Level Examination June 2014
General Certificate of Education Advanced Level Examination June 2014 Biology BIO6T/Q14/task Unit 6T A2 Investigative Skills Assignment Task Sheet Introduction Investigating populations You will use leaves
More information1 Matched pair comparison(p430-)
[1] ST301(AKI) LEC 25 2010/11/30 ST 301 (AKI) LECTURE #25 1 Matched pair comparison(p430-) This has a quite different assumption (matched pair) from the other three methods. Remember LEC 32 page 1 example:
More information10.4 Hypothesis Testing: Two Independent Samples Proportion
10.4 Hypothesis Testing: Two Independent Samples Proportion Example 3: Smoking cigarettes has been known to cause cancer and other ailments. One politician believes that a higher tax should be imposed
More informationChapter 7 Comparison of two independent samples
Chapter 7 Comparison of two independent samples 7.1 Introduction Population 1 µ σ 1 1 N 1 Sample 1 y s 1 1 n 1 Population µ σ N Sample y s n 1, : population means 1, : population standard deviations N
More informationSection 9.4. Notation. Requirements. Definition. Inferences About Two Means (Matched Pairs) Examples
Objective Section 9.4 Inferences About Two Means (Matched Pairs) Compare of two matched-paired means using two samples from each population. Hypothesis Tests and Confidence Intervals of two dependent means
More informationCHAPTER 9: HYPOTHESIS TESTING
CHAPTER 9: HYPOTHESIS TESTING THE SECOND LAST EXAMPLE CLEARLY ILLUSTRATES THAT THERE IS ONE IMPORTANT ISSUE WE NEED TO EXPLORE: IS THERE (IN OUR TWO SAMPLES) SUFFICIENT STATISTICAL EVIDENCE TO CONCLUDE
More informationPSY 305. Module 3. Page Title. Introduction to Hypothesis Testing Z-tests. Five steps in hypothesis testing
Page Title PSY 305 Module 3 Introduction to Hypothesis Testing Z-tests Five steps in hypothesis testing State the research and null hypothesis Determine characteristics of comparison distribution Five
More informationPOLI 443 Applied Political Research
POLI 443 Applied Political Research Session 6: Tests of Hypotheses Contingency Analysis Lecturer: Prof. A. Essuman-Johnson, Dept. of Political Science Contact Information: aessuman-johnson@ug.edu.gh College
More informationTHE ROYAL STATISTICAL SOCIETY 2015 EXAMINATIONS SOLUTIONS HIGHER CERTIFICATE MODULE 3
THE ROYAL STATISTICAL SOCIETY 015 EXAMINATIONS SOLUTIONS HIGHER CERTIFICATE MODULE 3 The Society is providing these solutions to assist candidates preparing for the examinations in 017. The solutions are
More informationTwo sample Test. Paired Data : Δ = 0. Lecture 3: Comparison of Means. d s d where is the sample average of the differences and is the
Gene$cs 300: Sta$s$cal Analysis of Biological Data Lecture 3: Comparison of Means Two sample t test Analysis of variance Type I and Type II errors Power More R commands September 23, 2010 Two sample Test
More informationCH.9 Tests of Hypotheses for a Single Sample
CH.9 Tests of Hypotheses for a Single Sample Hypotheses testing Tests on the mean of a normal distributionvariance known Tests on the mean of a normal distributionvariance unknown Tests on the variance
More informationStat 529 (Winter 2011) Experimental Design for the Two-Sample Problem. Motivation: Designing a new silver coins experiment
Stat 529 (Winter 2011) Experimental Design for the Two-Sample Problem Reading: 2.4 2.6. Motivation: Designing a new silver coins experiment Sample size calculations Margin of error for the pooled two sample
More informationAn inferential procedure to use sample data to understand a population Procedures
Hypothesis Test An inferential procedure to use sample data to understand a population Procedures Hypotheses, the alpha value, the critical region (z-scores), statistics, conclusion Two types of errors
More informationSolutions to Practice Test 2 Math 4753 Summer 2005
Solutions to Practice Test Math 4753 Summer 005 This test is worth 00 points. Questions 5 are worth 4 points each. Circle the letter of the correct answer. Each question in Question 6 9 is worth the same
More information9-7: THE POWER OF A TEST
CD9-1 9-7: THE POWER OF A TEST In the initial discussion of statistical hypothesis testing the two types of risks that are taken when decisions are made about population parameters based only on sample
More informationOne-Way Analysis of Variance (ANOVA) Paul K. Strode, Ph.D.
One-Way Analysis of Variance (ANOVA) Paul K. Strode, Ph.D. Purpose While the T-test is useful to compare the means of two samples, many biology experiments involve the parallel measurement of three or
More informationChapter 5 Confidence Intervals
Chapter 5 Confidence Intervals Confidence Intervals about a Population Mean, σ, Known Abbas Motamedi Tennessee Tech University A point estimate: a single number, calculated from a set of data, that is
More informationLECTURE 6. Introduction to Econometrics. Hypothesis testing & Goodness of fit
LECTURE 6 Introduction to Econometrics Hypothesis testing & Goodness of fit October 25, 2016 1 / 23 ON TODAY S LECTURE We will explain how multiple hypotheses are tested in a regression model We will define
More informationM(t) = 1 t. (1 t), 6 M (0) = 20 P (95. X i 110) i=1
Math 66/566 - Midterm Solutions NOTE: These solutions are for both the 66 and 566 exam. The problems are the same until questions and 5. 1. The moment generating function of a random variable X is M(t)
More informationAnswer keys for Assignment 10: Measurement of study variables (The correct answer is underlined in bold text)
Answer keys for Assignment 10: Measurement of study variables (The correct answer is underlined in bold text) 1. A quick and easy indicator of dispersion is a. Arithmetic mean b. Variance c. Standard deviation
More informationStatistical Analysis How do we know if it works? Group workbook: Cartoon from XKCD.com. Subscribe!
Statistical Analysis How do we know if it works? Group workbook: Cartoon from XKCD.com. Subscribe! http://www.xkcd.com/552/ Significant Concepts We structure the presentation and processing of data to
More informationAMS7: WEEK 7. CLASS 1. More on Hypothesis Testing Monday May 11th, 2015
AMS7: WEEK 7. CLASS 1 More on Hypothesis Testing Monday May 11th, 2015 Testing a Claim about a Standard Deviation or a Variance We want to test claims about or 2 Example: Newborn babies from mothers taking
More informationSTAT Chapter 11: Regression
STAT 515 -- Chapter 11: Regression Mostly we have studied the behavior of a single random variable. Often, however, we gather data on two random variables. We wish to determine: Is there a relationship
More informationLet the x-axis have the following intervals:
1 & 2. For the following sets of data calculate the mean and standard deviation. Then graph the data as a frequency histogram on the corresponding set of axes. Set 1: Length of bass caught in Conesus Lake
More informationBayesian Inference for Normal Mean
Al Nosedal. University of Toronto. November 18, 2015 Likelihood of Single Observation The conditional observation distribution of y µ is Normal with mean µ and variance σ 2, which is known. Its density
More information1. How will an increase in the sample size affect the width of the confidence interval?
Study Guide Concept Questions 1. How will an increase in the sample size affect the width of the confidence interval? 2. How will an increase in the sample size affect the power of a statistical test?
More informationData Analysis and Statistical Methods Statistics 651
Data Analysis and Statistical Methods Statistics 65 http://www.stat.tamu.edu/~suhasini/teaching.html Suhasini Subba Rao Comparing populations Suppose I want to compare the heights of males and females
More informationQuestion. Hypothesis testing. Example. Answer: hypothesis. Test: true or not? Question. Average is not the mean! μ average. Random deviation or not?
Hypothesis testing Question Very frequently: what is the possible value of μ? Sample: we know only the average! μ average. Random deviation or not? Standard error: the measure of the random deviation.
More informationInference for Regression Simple Linear Regression
Inference for Regression Simple Linear Regression IPS Chapter 10.1 2009 W.H. Freeman and Company Objectives (IPS Chapter 10.1) Simple linear regression p Statistical model for linear regression p Estimating
More information20.0 Experimental Design
20.0 Experimental Design Answer Questions 1 Philosophy One-Way ANOVA Egg Sample Multiple Comparisons 20.1 Philosophy Experiments are often expensive and/or dangerous. One wants to use good techniques that
More informationChapter 22. Comparing Two Proportions 1 /29
Chapter 22 Comparing Two Proportions 1 /29 Homework p519 2, 4, 12, 13, 15, 17, 18, 19, 24 2 /29 Objective Students test null and alternate hypothesis about two population proportions. 3 /29 Comparing Two
More informationChapter 12: Estimation
Chapter 12: Estimation Estimation In general terms, estimation uses a sample statistic as the basis for estimating the value of the corresponding population parameter. Although estimation and hypothesis
More informationSIMPLE REGRESSION ANALYSIS. Business Statistics
SIMPLE REGRESSION ANALYSIS Business Statistics CONTENTS Ordinary least squares (recap for some) Statistical formulation of the regression model Assessing the regression model Testing the regression coefficients
More informationChapter 23. Inference About Means
Chapter 23 Inference About Means 1 /57 Homework p554 2, 4, 9, 10, 13, 15, 17, 33, 34 2 /57 Objective Students test null and alternate hypotheses about a population mean. 3 /57 Here We Go Again Now that
More informationCHAPTER 9, 10. Similar to a courtroom trial. In trying a person for a crime, the jury needs to decide between one of two possibilities:
CHAPTER 9, 10 Hypothesis Testing Similar to a courtroom trial. In trying a person for a crime, the jury needs to decide between one of two possibilities: The person is guilty. The person is innocent. To
More informationPreliminary Statistics Lecture 5: Hypothesis Testing (Outline)
1 School of Oriental and African Studies September 2015 Department of Economics Preliminary Statistics Lecture 5: Hypothesis Testing (Outline) Gujarati D. Basic Econometrics, Appendix A.8 Barrow M. Statistics
More informationSampling distribution of t. 2. Sampling distribution of t. 3. Example: Gas mileage investigation. II. Inferential Statistics (8) t =
2. The distribution of t values that would be obtained if a value of t were calculated for each sample mean for all possible random of a given size from a population _ t ratio: (X - µ hyp ) t s x The result
More informationChapter 7: Hypothesis Testing
Chapter 7: Hypothesis Testing *Mathematical statistics with applications; Elsevier Academic Press, 2009 The elements of a statistical hypothesis 1. The null hypothesis, denoted by H 0, is usually the nullification
More informationChapter 24. Comparing Means. Copyright 2010 Pearson Education, Inc.
Chapter 24 Comparing Means Copyright 2010 Pearson Education, Inc. Plot the Data The natural display for comparing two groups is boxplots of the data for the two groups, placed side-by-side. For example:
More informationMachine Learning: Evaluation
Machine Learning: Evaluation Information Systems and Machine Learning Lab (ISMLL) University of Hildesheim Wintersemester 2007 / 2008 Comparison of Algorithms Comparison of Algorithms Is algorithm A better
More informationUnderstanding p Values
Understanding p Values James H. Steiger Vanderbilt University James H. Steiger Vanderbilt University Understanding p Values 1 / 29 Introduction Introduction In this module, we introduce the notion of a
More informationThe t-test: A z-score for a sample mean tells us where in the distribution the particular mean lies
The t-test: So Far: Sampling distribution benefit is that even if the original population is not normal, a sampling distribution based on this population will be normal (for sample size > 30). Benefit
More informationNonparametric tests. Mark Muldoon School of Mathematics, University of Manchester. Mark Muldoon, November 8, 2005 Nonparametric tests - p.
Nonparametric s Mark Muldoon School of Mathematics, University of Manchester Mark Muldoon, November 8, 2005 Nonparametric s - p. 1/31 Overview The sign, motivation The Mann-Whitney Larger Larger, in pictures
More information1 Statistical inference for a population mean
1 Statistical inference for a population mean 1. Inference for a large sample, known variance Suppose X 1,..., X n represents a large random sample of data from a population with unknown mean µ and known
More informationCIVL /8904 T R A F F I C F L O W T H E O R Y L E C T U R E - 8
CIVL - 7904/8904 T R A F F I C F L O W T H E O R Y L E C T U R E - 8 Chi-square Test How to determine the interval from a continuous distribution I = Range 1 + 3.322(logN) I-> Range of the class interval
More informationCHAPTER 10 Comparing Two Populations or Groups
CHAPTER 10 Comparing Two Populations or Groups 10. Comparing Two Means The Practice of Statistics, 5th Edition Starnes, Tabor, Yates, Moore Bedford Freeman Worth Publishers Comparing Two Means Learning
More informationCHAPTER 10 Comparing Two Populations or Groups
CHAPTER 10 Comparing Two Populations or Groups 10.2 Comparing Two Means The Practice of Statistics, 5th Edition Starnes, Tabor, Yates, Moore Bedford Freeman Worth Publishers Comparing Two Means Learning
More informationChi square test of independence
Chi square test of independence Eyeball differences between percentages: large enough to be important Better: Are they statistically significant? Statistical significance: are observed differences significantly
More informationBiostatistics and Design of Experiments Prof. Mukesh Doble Department of Biotechnology Indian Institute of Technology, Madras. Lecture 11 t- Tests
Biostatistics and Design of Experiments Prof. Mukesh Doble Department of Biotechnology Indian Institute of Technology, Madras Lecture 11 t- Tests Welcome to the course on Biostatistics and Design of Experiments.
More information7.2 One-Sample Correlation ( = a) Introduction. Correlation analysis measures the strength and direction of association between
7.2 One-Sample Correlation ( = a) Introduction Correlation analysis measures the strength and direction of association between variables. In this chapter we will test whether the population correlation
More informationSTAT 515 fa 2016 Lec Statistical inference - hypothesis testing
STAT 515 fa 2016 Lec 20-21 Statistical inference - hypothesis testing Karl B. Gregory Wednesday, Oct 12th Contents 1 Statistical inference 1 1.1 Forms of the null and alternate hypothesis for µ and p....................
More information