Question. Hypothesis testing. Example. Answer: hypothesis. Test: true or not? Question. Average is not the mean! μ average. Random deviation or not?
|
|
- Aldous May
- 5 years ago
- Views:
Transcription
1 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. Question Answer: hypothesis Test: true or not? Average is not the mean! Why? Example Question: The medicine decreases the fewer or not?. Finite no. of elements (random deviation). Systematic deviation. (the hypothesis is not true, the value of the μ is different)
2 How many trials? Sample Outcome:. Δt >0;. Δt =0; 3. Δt <0 Only? Not only the medicine influences the fewer! We suppose that other effects are random events! Population:. Effective μ 0!. Not effective μ = 0! The average deviates around the mean! The average normally is not 0! Why?. Random event, due to the finite no. of the elements.. Our base hypothesis is not true. Which case is true? Nullhypothesis Why the nullhypothesis? Population:. Effective μ 0!. Not effective μ = 0! Sample: average 0 average should be 0 Symbols. H 0 : nullhypothesis H : alternative hypothesis Alternative hypothesis μ =? Nullhypothesis! Random deviation (finite no. of elements) Nullhypothesis: the mathematical statistics is able to calculate the possible random deviation of the average from the μ!!!
3 Example Medicine decreases the fewer or not? Large difference? What is the measure of the difference? Nullhypothesis: not! μ is 0. But the average is not 0. Standard error: average deviation of the averages around the μ. sample. average -0. C If the difference is larger, ( x ± sx ) ~ 68% - confidence interval C -.5 C seems to be more sure. Base: nullhypothesis! t-value Question: x average may be 0? t = x μ s x Compare the difference to the standard error. (μ is frequently 0) Condition: Known distribution is necessary. The average deviates around the μ, so the t- value deviates around the 0. (if the nullhypothesis is true!)
4 Why is it better? We are able to calculate the random distribution of the t values!!! (Student s t-distribution) This describes the random deviation of the t from the 0!!! Shape of the distribution depends on the no. of the elements. One-sample t-test Question about the possible value of the μ. Nullhypothesis: the difference of the average is random. t = 0, the difference is due to the finite no. of elements. Base of decision t-table p is the probability, that t calc t crit randomly. Different t crit value belong to different significance level. If p is enough small, more probable that the nullhypothesis is not true. α is the significance level: the probability that t- value is randomly out an interval.
5 Base of the decision Decision. if the probability of the random event is small (p( t t crit ) is 5%) reject the nullhypothesis.. if the probability of the random event is high (p( t t crit ) is > 5%) accept the nullhypothesis. The answer is not yes or no, true or false!!! Decision using t-table Decision using computer d.f.: degree of freedom p: the probability of random event that the t t calculated. degree of freedom:
6 Possibility of the mistake Decision Decision: the nullhypothesis accepted rejected Nullhypothesis true false Right decision II. Type error (β) I. Type error (α) Right decision Conditions Test in two groups. Question about the mean of the population.. Variable has normal distribution. Conditions:. Variable has normal distribution.. The standard deviation is same in the two groups, the difference is due to the sampling. 3. The samples are independent from each other.
7 Nullhypothesis: samples derive from the same population. Alternative hypothesis: samples derive from different populations. The nullhypotesis Samples derive from the same population. But, due to the sampling: x x 0 The expected value of the difference is zero. The observed difference is due to the sampling only. The common standard error Calculation of the t-value s Q + Q x x = + n + n n n t = x x two-sample t-test s x x If the standard deviation is really common. σ = σ The degree of the freedom: n +n - Decision: look one-sample t-test!
8 σ = σ? F-test Condition: σ = σ Question: s = s? Nullhypotesis: H 0 : σ = σ. Alternative hypothesis: H : not. F = s s The expected value belonging to the nullhypotesis:. degree of freedom: nominator: n. denominator : n. F-test! (Calculation: s > s. the greater is in the nominator.) Table: (α = 0,05) (. line: d.f. of the nominator,. column: d.f. of the denominator) 6,4 8,5 0,3 7,7 6,6 99,5 9,00 9,55 6,94 5,79 F calc F table, reject. F calc < F table, accept. 3 5,7 9,6 9,8 6,59 5,4 Decision 4 4,6 9,5 9, 6,39 5,9 5 30, 9,30 9,0 6,6 5,05 on the base of the p value: p: the probability, that F calc randomly over the F table. Correlation of two variables Experiment: Data pairs: No. weight (kg) Height (cm)
9 Graphic representation Covariance A B C Q xy = i [( x x) ( y y) ] i i Cov(x, y) Q xy = n Positive tendency: Frequently: If x i > x, then y i > y and if x i < x, then y i < y. no any tendency Positive tendency Negative tendency Consequence: Q xy > 0. Negative tendency: No tendency: Correlation coefficient r Q = xy Qx Q r y Frequently: If x i > x, then y i < y and if x i < x, then y i > y. Consequence: Q xy < 0. The y values are independent from the x-values. Consequence: Q xy = 0. (if n= ) Population: r = 0 no correlation, r 0 correlation (strength is proportional to the actual value of r.
10 Testing of the r Sample: due to the finite no. of the elements we can calculate only the estimation of the r. t r Correlation t-test n r = d.f.: n - Question: Correlation or not? Decision: based on t-value. Look previous cases! Nullhypotesis: No correlation. H 0 : r = 0. Condition: at least one of the variable has normal distribution. Meaning of correlation Linear regression Not necessary being direct causality. (But may be!) In the background there may be quantities, effects that influence both measured variables. If variables have normal distribution, the dependency is linear, and we can describe with straight line.
11 Frequency data Experiment Has no normal distribution! Example: headache Effective: no headache. group: patients introducing the medicine. group: patients introducing the placebo Not effective: headache headache (a) no headache (b) headache (c) no headache (d) Contingency table Nullhypothesis If the effect is independent from the medicine, we expect:. group. group headache a c no headache b d Total a+b c+d a = b c d a d = b c total a+c b+d n Nullhypothesis: the effect is independent from the medicine.
12 χ = χ -distribution n( ad bc) ( a + b)( c + d )( a + c)( b + d ) Nullhypothesis: χ -value is 0, the difference due to the random event only. χ -distribution describes the random deviations of the χ -value. Decision Same, than in the case of t-distribution. We use χ -distribution. Expected value is 0, if the nullhypothesis is true. if calc. crit. - reject the nullhypothesis else accept. degree of freedom: in this special case =. In general: d.f.=(r-)(c-), where r no. of rows c no. of columns
Section 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 information" M A #M B. Standard deviation of the population (Greek lowercase letter sigma) σ 2
Notation and Equations for Final Exam Symbol Definition X The variable we measure in a scientific study n The size of the sample N The size of the population M The mean of the sample µ The mean of the
More informationWithin Cases. The Humble t-test
Within Cases The Humble t-test 1 / 21 Overview The Issue Analysis Simulation Multivariate 2 / 21 Independent Observations Most statistical models assume independent observations. Sometimes the assumption
More informationLab #11. Variable B. Variable A Y a b a+b N c d c+d a+c b+d N = a+b+c+d
BIOS 4120: Introduction to Biostatistics Breheny Lab #11 We will explore observational studies in today s lab and review how to make inferences on contingency tables. We will only use 2x2 tables for today
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 informationGlossary. The ISI glossary of statistical terms provides definitions in a number of different languages:
Glossary The ISI glossary of statistical terms provides definitions in a number of different languages: http://isi.cbs.nl/glossary/index.htm Adjusted r 2 Adjusted R squared measures the proportion of the
More informationContingency Tables. Safety equipment in use Fatal Non-fatal Total. None 1, , ,128 Seat belt , ,878
Contingency Tables I. Definition & Examples. A) Contingency tables are tables where we are looking at two (or more - but we won t cover three or more way tables, it s way too complicated) factors, each
More informationLinear Models and Estimation by Least Squares
Linear Models and Estimation by Least Squares Jin-Lung Lin 1 Introduction Causal relation investigation lies in the heart of economics. Effect (Dependent variable) cause (Independent variable) Example:
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 informationReview. One-way ANOVA, I. What s coming up. Multiple comparisons
Review One-way ANOVA, I 9.07 /15/00 Earlier in this class, we talked about twosample z- and t-tests for the difference between two conditions of an independent variable Does a trial drug work better than
More informationCHAPTER 17 CHI-SQUARE AND OTHER NONPARAMETRIC TESTS FROM: PAGANO, R. R. (2007)
FROM: PAGANO, R. R. (007) I. INTRODUCTION: DISTINCTION BETWEEN PARAMETRIC AND NON-PARAMETRIC TESTS Statistical inference tests are often classified as to whether they are parametric or nonparametric Parameter
More informationChi square test of independence
Chi square test of independence We can eyeball differences between percentages to determine whether they seem large enough to be important Better: Are differences in percentages statistically significant?
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 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 informationBasic Statistics. 1. Gross error analyst makes a gross mistake (misread balance or entered wrong value into calculation).
Basic Statistics There are three types of error: 1. Gross error analyst makes a gross mistake (misread balance or entered wrong value into calculation). 2. Systematic error - always too high or too low
More informationInference for Categorical Data. Chi-Square Tests for Goodness of Fit and Independence
Chi-Square Tests for Goodness of Fit and Independence Chi-Square Tests In this course, we use chi-square tests in two different ways The chi-square test for goodness-of-fit is used to determine whether
More informationSociology 6Z03 Review II
Sociology 6Z03 Review II John Fox McMaster University Fall 2016 John Fox (McMaster University) Sociology 6Z03 Review II Fall 2016 1 / 35 Outline: Review II Probability Part I Sampling Distributions Probability
More informationInferences for Regression
Inferences for Regression An Example: Body Fat and Waist Size Looking at the relationship between % body fat and waist size (in inches). Here is a scatterplot of our data set: Remembering Regression In
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 information2 Regression Analysis
FORK 1002 Preparatory Course in Statistics: 2 Regression Analysis Genaro Sucarrat (BI) http://www.sucarrat.net/ Contents: 1 Bivariate Correlation Analysis 2 Simple Regression 3 Estimation and Fit 4 T -Test:
More informationLast week: Sample, population and sampling distributions finished with estimation & confidence intervals
Past weeks: Measures of central tendency (mean, mode, median) Measures of dispersion (standard deviation, variance, range, etc). Working with the normal curve Last week: Sample, population and sampling
More informationChapter 12 - Lecture 2 Inferences about regression coefficient
Chapter 12 - Lecture 2 Inferences about regression coefficient April 19th, 2010 Facts about slope Test Statistic Confidence interval Hypothesis testing Test using ANOVA Table Facts about slope In previous
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 informationMathematical Notation Math Introduction to Applied Statistics
Mathematical Notation Math 113 - Introduction to Applied Statistics Name : Use Word or WordPerfect to recreate the following documents. Each article is worth 10 points and should be emailed to the instructor
More information, 0 x < 2. a. Find the probability that the text is checked out for more than half an hour but less than an hour. = (1/2)2
Math 205 Spring 206 Dr. Lily Yen Midterm 2 Show all your work Name: 8 Problem : The library at Capilano University has a copy of Math 205 text on two-hour reserve. Let X denote the amount of time the text
More informationLast two weeks: Sample, population and sampling distributions finished with estimation & confidence intervals
Past weeks: Measures of central tendency (mean, mode, median) Measures of dispersion (standard deviation, variance, range, etc). Working with the normal curve Last two weeks: Sample, population and sampling
More informationHypothesis Testing hypothesis testing approach
Hypothesis Testing In this case, we d be trying to form an inference about that neighborhood: Do people there shop more often those people who are members of the larger population To ascertain this, we
More informationChapter Seven: Multi-Sample Methods 1/52
Chapter Seven: Multi-Sample Methods 1/52 7.1 Introduction 2/52 Introduction The independent samples t test and the independent samples Z test for a difference between proportions are designed to analyze
More informationStatistics: revision
NST 1B Experimental Psychology Statistics practical 5 Statistics: revision Rudolf Cardinal & Mike Aitken 29 / 30 April 2004 Department of Experimental Psychology University of Cambridge Handouts: Answers
More informationHypothesis Testing, Power, Sample Size and Confidence Intervals (Part 2)
Hypothesis Testing, Power, Sample Size and Confidence Intervals (Part 2) B.H. Robbins Scholars Series June 23, 2010 1 / 29 Outline Z-test χ 2 -test Confidence Interval Sample size and power Relative effect
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 informationLecture 28 Chi-Square Analysis
Lecture 28 STAT 225 Introduction to Probability Models April 23, 2014 Whitney Huang Purdue University 28.1 χ 2 test for For a given contingency table, we want to test if two have a relationship or not
More informationStatistics Handbook. All statistical tables were computed by the author.
Statistics Handbook Contents Page Wilcoxon rank-sum test (Mann-Whitney equivalent) Wilcoxon matched-pairs test 3 Normal Distribution 4 Z-test Related samples t-test 5 Unrelated samples t-test 6 Variance
More informationChapter 10. Chapter 10. Multinomial Experiments and. Multinomial Experiments and Contingency Tables. Contingency Tables.
Chapter 10 Multinomial Experiments and Contingency Tables 1 Chapter 10 Multinomial Experiments and Contingency Tables 10-1 1 Overview 10-2 2 Multinomial Experiments: of-fitfit 10-3 3 Contingency Tables:
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 informationReview of probability and statistics 1 / 31
Review of probability and statistics 1 / 31 2 / 31 Why? This chapter follows Stock and Watson (all graphs are from Stock and Watson). You may as well refer to the appendix in Wooldridge or any other introduction
More informationStatistics in medicine
Statistics in medicine Lecture 3: Bivariate association : Categorical variables Proportion in one group One group is measured one time: z test Use the z distribution as an approximation to the binomial
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 informationREVIEW 8/2/2017 陈芳华东师大英语系
REVIEW Hypothesis testing starts with a null hypothesis and a null distribution. We compare what we have to the null distribution, if the result is too extreme to belong to the null distribution (p
More informationSleep data, two drugs Ch13.xls
Model Based Statistics in Biology. Part IV. The General Linear Mixed Model.. Chapter 13.3 Fixed*Random Effects (Paired t-test) ReCap. Part I (Chapters 1,2,3,4), Part II (Ch 5, 6, 7) ReCap Part III (Ch
More informationHYPOTHESIS TESTING II TESTS ON MEANS. Sorana D. Bolboacă
HYPOTHESIS TESTING II TESTS ON MEANS Sorana D. Bolboacă OBJECTIVES Significance value vs p value Parametric vs non parametric tests Tests on means: 1 Dec 14 2 SIGNIFICANCE LEVEL VS. p VALUE Materials and
More informationLecture 5: ANOVA and Correlation
Lecture 5: ANOVA and Correlation Ani Manichaikul amanicha@jhsph.edu 23 April 2007 1 / 62 Comparing Multiple Groups Continous data: comparing means Analysis of variance Binary data: comparing proportions
More informationMath Lecture 3 Notes
Math 1010 - Lecture 3 Notes Dylan Zwick Fall 2009 1 Operations with Real Numbers In our last lecture we covered some basic operations with real numbers like addition, subtraction and multiplication. This
More informationWhat is a Hypothesis?
What is a Hypothesis? A hypothesis is a claim (assumption) about a population parameter: population mean Example: The mean monthly cell phone bill in this city is μ = $42 population proportion Example:
More informationy ˆ i = ˆ " T u i ( i th fitted value or i th fit)
1 2 INFERENCE FOR MULTIPLE LINEAR REGRESSION Recall Terminology: p predictors x 1, x 2,, x p Some might be indicator variables for categorical variables) k-1 non-constant terms u 1, u 2,, u k-1 Each u
More informationReview of Statistics
Review of Statistics Topics Descriptive Statistics Mean, Variance Probability Union event, joint event Random Variables Discrete and Continuous Distributions, Moments Two Random Variables Covariance and
More information1 Descriptive statistics. 2 Scores and probability distributions. 3 Hypothesis testing and one-sample t-test. 4 More on t-tests
Overall Overview INFOWO Statistics lecture S3: Hypothesis testing Peter de Waal Department of Information and Computing Sciences Faculty of Science, Universiteit Utrecht 1 Descriptive statistics 2 Scores
More informationOHSU OGI Class ECE-580-DOE :Design of Experiments Steve Brainerd
Why We Use Analysis of Variance to Compare Group Means and How it Works The question of how to compare the population means of more than two groups is an important one to researchers. Let us suppose that
More informationCan you tell the relationship between students SAT scores and their college grades?
Correlation One Challenge Can you tell the relationship between students SAT scores and their college grades? A: The higher SAT scores are, the better GPA may be. B: The higher SAT scores are, the lower
More informationContingency Tables. Contingency tables are used when we want to looking at two (or more) factors. Each factor might have two more or levels.
Contingency Tables Definition & Examples. Contingency tables are used when we want to looking at two (or more) factors. Each factor might have two more or levels. (Using more than two factors gets complicated,
More informationSTT 843 Key to Homework 1 Spring 2018
STT 843 Key to Homework Spring 208 Due date: Feb 4, 208 42 (a Because σ = 2, σ 22 = and ρ 2 = 05, we have σ 2 = ρ 2 σ σ22 = 2/2 Then, the mean and covariance of the bivariate normal is µ = ( 0 2 and Σ
More informationDepartment of Economics. Business Statistics. Chapter 12 Chi-square test of independence & Analysis of Variance ECON 509. Dr.
Department of Economics Business Statistics Chapter 1 Chi-square test of independence & Analysis of Variance ECON 509 Dr. Mohammad Zainal Chapter Goals After completing this chapter, you should be able
More information# of 6s # of times Test the null hypthesis that the dice are fair at α =.01 significance
Practice Final Exam Statistical Methods and Models - Math 410, Fall 2011 December 4, 2011 You may use a calculator, and you may bring in one sheet (8.5 by 11 or A4) of notes. Otherwise closed book. The
More informationLAB 2. HYPOTHESIS TESTING IN THE BIOLOGICAL SCIENCES- Part 2
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
More information9 Correlation and Regression
9 Correlation and Regression SW, Chapter 12. Suppose we select n = 10 persons from the population of college seniors who plan to take the MCAT exam. Each takes the test, is coached, and then retakes the
More informationSampling Distributions: Central Limit Theorem
Review for Exam 2 Sampling Distributions: Central Limit Theorem Conceptually, we can break up the theorem into three parts: 1. The mean (µ M ) of a population of sample means (M) is equal to the mean (µ)
More informationMock Exam - 2 hours - use of basic (non-programmable) calculator is allowed - all exercises carry the same marks - exam is strictly individual
Mock Exam - 2 hours - use of basic (non-programmable) calculator is allowed - all exercises carry the same marks - exam is strictly individual Question 1. Suppose you want to estimate the percentage of
More informationThis gives us an upper and lower bound that capture our population mean.
Confidence Intervals Critical Values Practice Problems 1 Estimation 1.1 Confidence Intervals Definition 1.1 Margin of error. The margin of error of a distribution is the amount of error we predict when
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 informationExample. χ 2 = Continued on the next page. All cells
Section 11.1 Chi Square Statistic k Categories 1 st 2 nd 3 rd k th Total Observed Frequencies O 1 O 2 O 3 O k n Expected Frequencies E 1 E 2 E 3 E k n O 1 + O 2 + O 3 + + O k = n E 1 + E 2 + E 3 + + E
More informationReview of Statistics 101
Review of Statistics 101 We review some important themes from the course 1. Introduction Statistics- Set of methods for collecting/analyzing data (the art and science of learning from data). Provides methods
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 informationExam Applied Statistical Regression. Good Luck!
Dr. M. Dettling Summer 2011 Exam Applied Statistical Regression Approved: Tables: Note: Any written material, calculator (without communication facility). Attached. All tests have to be done at the 5%-level.
More informationχ test statistics of 2.5? χ we see that: χ indicate agreement between the two sets of frequencies.
I. T or F. (1 points each) 1. The χ -distribution is symmetric. F. The χ may be negative, zero, or positive F 3. The chi-square distribution is skewed to the right. T 4. The observed frequency of a cell
More informationDifference between means - t-test /25
Difference between means - t-test 1 Discussion Question p492 Ex 9-4 p492 1-3, 6-8, 12 Assume all variances are not equal. Ignore the test for variance. 2 Students will perform hypothesis tests for two
More informationwith the usual assumptions about the error term. The two values of X 1 X 2 0 1
Sample questions 1. A researcher is investigating the effects of two factors, X 1 and X 2, each at 2 levels, on a response variable Y. A balanced two-factor factorial design is used with 1 replicate. The
More informationGlossary for the Triola Statistics Series
Glossary for the Triola Statistics Series Absolute deviation The measure of variation equal to the sum of the deviations of each value from the mean, divided by the number of values Acceptance sampling
More informationOne-Way ANOVA. Some examples of when ANOVA would be appropriate include:
One-Way ANOVA 1. Purpose Analysis of variance (ANOVA) is used when one wishes to determine whether two or more groups (e.g., classes A, B, and C) differ on some outcome of interest (e.g., an achievement
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 informationFrequency Distribution Cross-Tabulation
Frequency Distribution Cross-Tabulation 1) Overview 2) Frequency Distribution 3) Statistics Associated with Frequency Distribution i. Measures of Location ii. Measures of Variability iii. Measures of Shape
More informationPSYC 331 STATISTICS FOR PSYCHOLOGISTS
PSYC 331 STATISTICS FOR PSYCHOLOGISTS Session 4 A PARAMETRIC STATISTICAL TEST FOR MORE THAN TWO POPULATIONS Lecturer: Dr. Paul Narh Doku, Dept of Psychology, UG Contact Information: pndoku@ug.edu.gh College
More informationChapter 8 Student Lecture Notes 8-1. Department of Economics. Business Statistics. Chapter 12 Chi-square test of independence & Analysis of Variance
Chapter 8 Student Lecture Notes 8-1 Department of Economics Business Statistics Chapter 1 Chi-square test of independence & Analysis of Variance ECON 509 Dr. Mohammad Zainal Chapter Goals After completing
More informationDETAILED CONTENTS PART I INTRODUCTION AND DESCRIPTIVE STATISTICS. 1. Introduction to Statistics
DETAILED CONTENTS About the Author Preface to the Instructor To the Student How to Use SPSS With This Book PART I INTRODUCTION AND DESCRIPTIVE STATISTICS 1. Introduction to Statistics 1.1 Descriptive and
More informationStatistics Introductory Correlation
Statistics Introductory Correlation Session 10 oscardavid.barrerarodriguez@sciencespo.fr April 9, 2018 Outline 1 Statistics are not used only to describe central tendency and variability for a single variable.
More informationInferential statistics
Inferential statistics Inference involves making a Generalization about a larger group of individuals on the basis of a subset or sample. Ahmed-Refat-ZU Null and alternative hypotheses In hypotheses testing,
More informationReview for Final. Chapter 1 Type of studies: anecdotal, observational, experimental Random sampling
Review for Final For a detailed review of Chapters 1 7, please see the review sheets for exam 1 and. The following only briefly covers these sections. The final exam could contain problems that are included
More informationTable of z values and probabilities for the standard normal distribution. z is the first column plus the top row. Each cell shows P(X z).
Table of z values and probabilities for the standard normal distribution. z is the first column plus the top row. Each cell shows P(X z). For example P(X.04) =.8508. For z < 0 subtract the value from,
More informationHypothesis testing: Steps
Review for Exam 2 Hypothesis testing: Steps Exam 2 Review 1. Determine appropriate test and hypotheses 2. Use distribution table to find critical statistic value(s) representing rejection region 3. Compute
More informationTwo sided, two sample t-tests. a) IQ = 100 b) Average height for men = c) Average number of white blood cells per cubic millimeter is 7,000.
Two sided, two sample t-tests. I. Brief review: 1) We are interested in how a sample compares to some pre-conceived notion. For example: a) IQ = 100 b) Average height for men = 5 10. c) Average number
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 informationEcon 325: Introduction to Empirical Economics
Econ 325: Introduction to Empirical Economics Chapter 9 Hypothesis Testing: Single Population Ch. 9-1 9.1 What is a Hypothesis? A hypothesis is a claim (assumption) about a population parameter: population
More informationIntroduction to Statistical Data Analysis Lecture 7: The Chi-Square Distribution
Introduction to Statistical Data Analysis Lecture 7: The Chi-Square Distribution James V. Lambers Department of Mathematics The University of Southern Mississippi James V. Lambers Statistical Data Analysis
More informationStatistical Hypothesis Testing
Statistical Hypothesis Testing Dr. Phillip YAM 2012/2013 Spring Semester Reference: Chapter 7 of Tests of Statistical Hypotheses by Hogg and Tanis. Section 7.1 Tests about Proportions A statistical hypothesis
More informationParametric versus Nonparametric Statistics-when to use them and which is more powerful? Dr Mahmoud Alhussami
Parametric versus Nonparametric Statistics-when to use them and which is more powerful? Dr Mahmoud Alhussami Parametric Assumptions The observations must be independent. Dependent variable should be continuous
More informationSTAT 135 Lab 6 Duality of Hypothesis Testing and Confidence Intervals, GLRT, Pearson χ 2 Tests and Q-Q plots. March 8, 2015
STAT 135 Lab 6 Duality of Hypothesis Testing and Confidence Intervals, GLRT, Pearson χ 2 Tests and Q-Q plots March 8, 2015 The duality between CI and hypothesis testing The duality between CI and hypothesis
More informationWeek 14 Comparing k(> 2) Populations
Week 14 Comparing k(> 2) Populations Week 14 Objectives Methods associated with testing for the equality of k(> 2) means or proportions are presented. Post-testing concepts and analysis are introduced.
More informationmatrix-free Hypothesis Testing in the Regression Model Introduction Kurt Schmidheiny Unversität Basel Short Guides to Microeconometrics Fall 2018
Short Guides to Microeconometrics Fall 2018 Kurt Schmidheiny Unversität Basel Hypothesis Testing in the Regression Model matrix-free Introduction This handout extends the handout on The Multiple Linear
More informationCOGS 14B: INTRODUCTION TO STATISTICAL ANALYSIS
COGS 14B: INTRODUCTION TO STATISTICAL ANALYSIS TA: Sai Chowdary Gullapally scgullap@eng.ucsd.edu Office Hours: Thursday (Mandeville) 3:30PM - 4:30PM (or by appointment) Slides: I am using the amazing slides
More informationSummary of Chapters 7-9
Summary of Chapters 7-9 Chapter 7. Interval Estimation 7.2. Confidence Intervals for Difference of Two Means Let X 1,, X n and Y 1, Y 2,, Y m be two independent random samples of sizes n and m from two
More informationStatistical Modeling and Analysis of Scientific Inquiry: The Basics of Hypothesis Testing
Statistical Modeling and Analysis of Scientific Inquiry: The Basics of Hypothesis Testing So, What is Statistics? Theory and techniques for learning from data How to collect How to analyze How to interpret
More informationTwo-sample Categorical data: Testing
Two-sample Categorical data: Testing Patrick Breheny April 1 Patrick Breheny Introduction to Biostatistics (171:161) 1/28 Separate vs. paired samples Despite the fact that paired samples usually offer
More informationLecture 10: Comparing two populations: proportions
Lecture 10: Comparing two populations: proportions Problem: Compare two sets of sample data: e.g. is the proportion of As in this semester 152 the same as last Fall? Methods: Extend the methods introduced
More informationCorrelation Analysis
Simple Regression Correlation Analysis Correlation analysis is used to measure strength of the association (linear relationship) between two variables Correlation is only concerned with strength of the
More informationQuantitative Analysis and Empirical Methods
Hypothesis testing Sciences Po, Paris, CEE / LIEPP Introduction Hypotheses Procedure of hypothesis testing Two-tailed and one-tailed tests Statistical tests with categorical variables A hypothesis A testable
More informationTutorial 4: Power and Sample Size for the Two-sample t-test with Unequal Variances
Tutorial 4: Power and Sample Size for the Two-sample t-test with Unequal Variances Preface Power is the probability that a study will reject the null hypothesis. The estimated probability is a function
More informationCorrelation & Simple Regression
Chapter 11 Correlation & Simple Regression The previous chapter dealt with inference for two categorical variables. In this chapter, we would like to examine the relationship between two quantitative variables.
More informationBusiness Statistics. Lecture 10: Correlation and Linear Regression
Business Statistics Lecture 10: Correlation and Linear Regression Scatterplot A scatterplot shows the relationship between two quantitative variables measured on the same individuals. It displays the Form
More informationCorrelation and Regression
Correlation and Regression October 25, 2017 STAT 151 Class 9 Slide 1 Outline of Topics 1 Associations 2 Scatter plot 3 Correlation 4 Regression 5 Testing and estimation 6 Goodness-of-fit STAT 151 Class
More informationExam details. Final Review Session. Things to Review
Exam details Final Review Session Short answer, similar to book problems Formulae and tables will be given You CAN use a calculator Date and Time: Dec. 7, 006, 1-1:30 pm Location: Osborne Centre, Unit
More informationCh. 7. One sample hypothesis tests for µ and σ
Ch. 7. One sample hypothesis tests for µ and σ Prof. Tesler Math 18 Winter 2019 Prof. Tesler Ch. 7: One sample hypoth. tests for µ, σ Math 18 / Winter 2019 1 / 23 Introduction Data Consider the SAT math
More information