Exam details. Final Review Session. Things to Review
|
|
- Anastasia Rose
- 5 years ago
- Views:
Transcription
1 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 1 ( A ) Things to Review Concepts Basic formulae Statistical tests
2 Concepts Basic formulae Statistical tests Things to Review Populations Samples Random sample Parameters Estimates Mean Median Mode Variance Standard deviation Categorical Nominal, ordinal Numerical Discrete, continuous First Half Alternative hypothesis P-value Type I error Type II error Sampling distribution Standard error Central limit theorem Normal distribution Quantile plot Shapiro-Wilk test Data transformations Nonparametric tests Independent contrasts Second Half Observations vs. experiments Confounding variables Control group Replication and pseudoreplication Blocking Factorial design Power analysis Simulation Randomization Bootstrap Likelihood Example Conceptual Questions (you ve just done a two-sample t-test comparing body size of lizards on islands and the mainland) What is the probability of committing a type I error with this test? State an example of a confounding variable that may have affected this result State one alternative statistical technique that you could have used to test the null hypothesis, and describe briefly how you would have carried it out.
3 Sample Randomization test Randomized data Things to Review Calculate the same test statistic on the randomized data Concepts Basic formulae Statistical tests Concepts Basic formulae Statistical tests Things to Review
4 Sample Statistical tests Binomial test Chi-squared goodness-of-fit Proportional, binomial, poisson Chi-squared contingency test t-tests One-sample t-test Paired t-test Two-sample t-test F-test for comparing variances Welch s t-test Sign test Mann-Whitney U Correlation Spearman s r Regression ANOVA Binomial test Chi-squared goodnessof-fit Proportional, binomial, poisson Chi-squared contingency test t-tests One-sample t-test Paired t-test Two-sample t-test Statistical tests F-test for comparing variances Welch s t-test Sign test Mann-Whitney U Correlation Spearman s r Regression ANOVA Quick reference summary: Binomial test What is it for? Compares the proportion of successes in a sample to a hypothesized value, p o What does it assume? Individual trials are randomly sampled and independent : X, the number of successes Distribution under H o : binomial with parameters n and p o. Formula: " P(x) = $ n% ' p x ( 1( p) n(x P = * Pr[x!X] # x& P(x) = probability of a total of x successes p = probability of success in each trial n = total number of trials
5 Sample Binomial test Pr[success]=p o Binomial test x = number of successes Binomial n, p o H 0 : The relative frequency of successes in the population is p 0 H A : The relative frequency of successes in the population is not p 0 Binomial test Chi-squared goodnessof-fit Proportional, binomial, poisson Chi-squared contingency test t-tests One-sample t-test Paired t-test Two-sample t-test Statistical tests F-test for comparing variances Welch s t-test Sign test Mann-Whitney U Correlation Spearman s r Regression ANOVA Quick reference summary: " Goodness-of-Fit test What is it for? Compares observed frequencies in categories of a single variable to the expected frequencies under a random model What does it assume? Random samples; no expected values < 1; no more than 0% of expected values < 5 : " Distribution under H o : " with Formula: df=# categories - # parameters - 1 " = ( Observed i # Expected i ) $ all classes Expected i
6 " goodness of fit test Sample Calculate expected values : Data fit a particular Discrete distribution " Goodness-of-Fit test " = ( Observed i # Expected i ) $ all classes Expected i : " With N-1-param. d.f. H 0 : The data come from a certain distribution H A : The data do not come from that distrubition Possible distributions " Pr[x] = $ n% ' p x 1( p # x& ( ) n(x Pr[ X ] = e"µ µ X X! Pr[x] = n * frequency of occurrence Proportional Binomial Poisson Given a number of categories Probability proportional to number of opportunities Days of the week, months of the year Number of successes in n trials Have to know n, p under the null hypothesis Punnett square, many p=0.5 examples Number of events in interval of space or time n not fixed, not given p Car wrecks, flowers in a field
7 Binomial test Chi-squared goodnessof-fit Proportional, binomial, poisson Chi-squared contingency test t-tests One-sample t-test Paired t-test Two-sample t-test Statistical tests F-test for comparing variances Welch s t-test Sign test Mann-Whitney U Correlation Spearman s r Regression ANOVA Quick reference summary: " Contingency Test What is it for? Tests the null hypothesis of no association between two categorical variables What does it assume? Random samples; no expected values < 1; no more than 0% of expected values < 5 : " Distribution under H o : " with df=(r-1)(c-1) where r = # rows, c = # columns Formulae: ( Observed " = i # Expected i ) RowTotal *ColTotal Expected = $ GrandTotal all classes Expected i Sample " Contingency Test Calculate expected values : No association between variables " Contingency test " = ( Observed i # Expected i ) $ all classes Expected i : " With (r-1)(c-1) d.f. H 0 : There is no association between these two variables H A : There is an association between these two variables
8 Binomial test Chi-squared goodnessof-fit Proportional, binomial, poisson Chi-squared contingency test t-tests One-sample t-test Paired t-test Two-sample t-test Statistical tests F-test for comparing variances Welch s t-test Sign test Mann-Whitney U Correlation Spearman s r Regression ANOVA Quick reference summary: One sample t-test What is it for? Compares the mean of a numerical variable to a hypothesized value,! o What does it assume? Individuals are randomly sampled from a population that is normally distributed. : t Distribution under H o : t-distribution with n-1 degrees of freedom. Formula: t = Y " µ o SE Y Sample One-sample t-test The population mean is equal to µ o One-sample t-test t = Y " µ o s/ n t with n-1 df H o : The population mean is equal to µ o H a : The population mean is not equal to µ o
9 Paired vs. sample comparisons Quick reference summary: Paired t-test What is it for? To test whether the mean difference in a population equals a null hypothesized value,! do What does it assume? Pairs are randomly sampled from a population. The differences are normally distributed : t Distribution under H o : t-distribution with n-1 degrees of freedom, where n is the number of pairs Formula: t = d " µ do SE d Paired t-test Sample The mean difference is equal to µ o Paired t-test t = d " µ do SE d t with n-1 df *n is the number of pairs H o : The mean difference is equal to 0 H a : The mean difference is not equal 0
10 Quick reference summary: Two-sample t-test What is it for? Tests whether two groups have the same mean What does it assume? Both samples are random samples. The numerical variable is normally distributed within both populations. The variance of the distribution is the same in the two populations : t Distribution under H o : t-distribution with n 1 +n - degrees of freedom. Formulae: t = Y 1 "Y SE Y 1 "Y # 1 SE Y 1 "Y = s p + 1 & % ( $ n 1 n ' s p = df 1s 1 + df s df 1 + df Sample t = Y 1 "Y SE Y 1 "Y Two-sample t-test The two populations have the same mean µ 1 =µ t with n 1 +n - df Two-sample t-test Statistical tests H o : The means of the two populations are equal H a : The means of the two populations are not equal Binomial test Chi-squared goodnessof-fit Proportional, binomial, poisson Chi-squared contingency test t-tests One-sample t-test Paired t-test Two-sample t-test F-test for comparing variances Welch s t-test Sign test Mann-Whitney U Correlation Spearman s r Regression ANOVA
11 F-test for Comparing the variance of two groups Sample F-test The two populations have the same variance! 1 =! H 0 :" 1 = " H A :" 1 # " F = s 1 s F with n 1-1, n -1 df Binomial test Chi-squared goodness-of-fit Proportional, binomial, poisson Chi-squared contingency test t-tests One-sample t-test Paired t-test Two-sample t-test Statistical tests F-test for comparing variances Welch s t-test Sign test Mann-Whitney U Correlation Spearman s r Regression ANOVA Sample t = Y 1 " Y s 1 + s n 1 n Welch s t-test The two populations have the same mean µ 1 =µ t with df from formula
12 Binomial test Chi-squared goodness-of-fit Proportional, binomial, poisson Chi-squared contingency test t-tests One-sample t-test Paired t-test Two-sample t-test Statistical tests F-test for comparing variances Welch s t-test Sign test Mann-Whitney U Correlation Spearman s r Regression ANOVA Parametric One-sample and Paired t-test Two-sample t-test Nonparametric Sign test Mann-Whitney U-test Quick Reference Summary: Sign Test What is it for? A non-parametric test to the medians of a group to some constant What does it assume? Random samples Formula: Identical to a binomial test with p o = 0.5. Uses the number of subjects with values greater than and less than a hypothesized median as the test statistic. " P(x) = probability of a total of x successes p = probability of success in each trial n = total number of trials P(x) = n% $ ' p x 1( p # x& ( ) n(x P = * Pr[x!X] Sample x = number of values greater than m o Sign test Median = m o Binomial n, 0.5
13 Sign Test H o : The median is equal to some value m o H a : The median is not equal to m o Quick Reference Summary: Mann-Whitney U Test What is it for? A non-parametric test to the central tendencies of two groups What does it assume? Random samples : U Distribution under H o : U distribution, with sample sizes n 1 and n Formulae: ( ) U 1 = n 1 n + n n U = n 1 n " U 1 " R 1 n 1 = sample size of group 1 n = sample size of group R 1 = sum of ranks of group 1 Use the larger of U1 or U for a two-tailed test Sample U 1 or U (use the largest) Mann-Whitney U test The two groups Have the same median U with n 1, n Binomial test Chi-squared goodness-of-fit Proportional, binomial, poisson Chi-squared contingency test t-tests One-sample t-test Paired t-test Two-sample t-test Statistical tests F-test for comparing variances Welch s t-test Sign test Mann-Whitney U Correlation Spearman s r Regression ANOVA
14 Quick Reference Guide - Correlation Coefficient What is it for? Measuring the strength of a linear association between two numerical variables What does it assume? Bivariate normality and random sampling Parameter: # Estimate: r Formulae: #( X i " X )( Y i " Y ) r = SE #( X i " X ) #( Y i " Y ) r = 1" r n " Quick Reference Guide - t-test for zero linear correlation What is it for? To test the null hypothesis that the population parameter, #, is zero What does it assume? Bivariate normality and random sampling : t : t with n- degrees of freedom t = r Formulae: SE r Sample T-test for correlation #=0 Statistical tests t = r SE r t with n- d.f. Binomial test Chi-squared goodness-of-fit Proportional, binomial, poisson Chi-squared contingency test t-tests One-sample t-test Paired t-test Two-sample t-test F-test for comparing variances Welch s t-test Sign test Mann-Whitney U Correlation Spearman s r Regression ANOVA
15 Quick Reference Guide - Spearman s Rank Correlation What is it for? To test zero correlation between the ranks of two variables What does it assume? Linear relationship between ranks and random sampling : r s : See table; if n>100, use t- distribution Formulae: Same as linear correlation but based on ranks Sample Spearman s rank correlation #=0 Spearman s rank Table H Statistical tests Assumptions of Regression Binomial test Chi-squared goodness-of-fit Proportional, binomial, poisson Chi-squared contingency test t-tests One-sample t-test Paired t-test Two-sample t-test F-test for comparing variances Welch s t-test Sign test Mann-Whitney U Correlation Spearman s r Regression ANOVA At each value of X, there is a population of Y values whose mean lies on the true regression line At each value of X, the distribution of Y values is normal The variance of Y values is the same at all values of X At each value of X the Y measurements represent a random sample from the population of Y values
16 OK Non-linear Non-normal Unequal variance Quick Reference Summary: Confidence Interval for Regression Slope What is it for? Estimating the slope of the linear equation Y = $ + %X between an explanatory variable X and a response variable Y What does it assume? Relationship between X and Y is linear; each Y at a given X is a random sample from a normal distribution with equal variance Parameter: % Estimate: b Degrees of freedom: n- Formulae: b " t #(),df SE b < $ < b + t #(),df SE b SE b = MS residual = # MS residual #( X i " X ) # (Y i "Y ) " b (X i " X )(Y i "Y ) n " Quick Reference Summary: t-test for Regression Slope What is it for? To test the null hypothesis that the population parameter % equals a null hypothesized value, usually 0 What does it assume? Same as regression slope C.I. : t : t with n- d.f. Formula: t = b SE b
17 Sample T-test for Regression Slope %=0 Statistical tests t = b SE b t with n- df Binomial test Chi-squared goodness-of-fit Proportional, binomial, poisson Chi-squared contingency test t-tests One-sample t-test Paired t-test Two-sample t-test F-test for comparing variances Welch s t-test Sign test Mann-Whitney U Correlation Spearman s r Regression ANOVA Quick Reference Summary: ANOVA (analysis of variance) What is it for? Testing the difference among k means simultaneously What does it assume? The variable is normally distributed with equal standard deviations (and variances) in all k populations; each sample is a random sample : F Distribution under H o : F distribution with k-1 and N-k degrees of freedom Quick Reference Summary: ANOVA (analysis of variance) Formulae: MS group = SS group df group F = MS group MS error = SS group k "1 SS group = # n i (Y i "Y) Y i Y = mean of group i = overall mean MS error = SS error df error = SS error N " k SS error = # s i (n i "1) n i = size of sample i N = total sample size
18 k Samples ANOVA All groups have the same mean ANOVA F = MS group MS error F with k-1, N-k df H o : All of the groups have the same mean H a : At least one of the groups has a mean that differs from the others ANOVA Tables Picture of ANOVA Terms Source of variation Sum of squares df Mean Squares F ratio P Treatment SS group = # n i (Y i "Y) k-1 MS group = SS group df group Error SS error = # s i (n i "1) N-k MS error = SS error df error Total SS group + SS error N-1 SS Total MS Total SS Group MS Group SS Error MS Error
19 Source of variation Treatment 1 Treatment Treatment 1 * Treatment Error Total Two-factor ANOVA Table Sum of Squares SS 1 SS SS 1* SS error SS total df k 1-1 k - 1 (k 1-1)*(k - 1) XXX N-1 Mean Square SS 1 k 1-1 SS k - 1 SS 1* (k 1-1)*(k - 1) SS error XXX F ratio MS 1 MSE MS MSE MS 1* MSE P Interpretations of -way ANOVA Terms Interpretations of -way ANOVA Terms Interpretations of -way ANOVA Terms Effect of Temperature, Not ph Effect of ph, Not Temperature
20 Interpretations of -way ANOVA Terms Effect of ph and Temperature, No interaction Interpretations of -way ANOVA Terms Effect of ph and Temperature, with interaction Quick Reference Summary: -Way ANOVA What is it for? Testing the difference among means from a -way factorial experiment What does it assume? The variable is normally distributed with equal standard deviations (and variances) in all populations; each sample is a random sample : F (for three different hypotheses) Distribution under H o : F distribution Quick Reference Summary: - Way ANOVA Formulae: Just need to know how to fill in the table
21 -way ANOVA -way ANOVA Samples Null hypotheses (three of them) Samples Null hypotheses (three of them) F = MS group MS error F F = MS group MS error Treatment 1 F -way ANOVA -way ANOVA Samples Null hypotheses (three of them) Samples Null hypotheses (three of them) F = MS group MS error Treatment F F = MS group MS error Interaction F
22 General Linear Models First step: formulate a model statement Example: General Linear Models Second step: Make an ANOVA table Example: Y = µ + TREATMENT Source of variation Treatme nt Error Total Sum of squares SS group = # n i (Y i "Y) SS error = # s i (n i "1) SS group + SS error df k-1 N-k N-1 Mean Squares MS group = SS group df group MS error = SS error df error F ratio P F = MS group MS error * Sample Randomization test Randomized data Calculate the same test statistic on the randomized data Which test do I use?
23 1 Methods for a single variable 1 Methods for a single variable How many variables am I comparing? Methods for comparing two variables How many variables am I comparing? 3 Methods for comparing two variables Methods for comparing three or more variables Methods for one variable Categorical Comparing to a single proportion p o or to a distribution? p o Is the variable categorical or numerical? distribution Numerical Y Methods for two variables X Explanatory variable Response variable Categorical Numerical Categorical Contingency table Contingency Logistic Grouped bar graph analysis regression Mosaic plot Numerical Multiple histograms t-test Correlation Scatter plot Cumulative frequency distributions ANOVA Regression Binomial test " Goodnessof-fit test One-sample t-test
24 How many variables am I comparing? 1 Is the variable categorical or numerical? Categorical Comparing to a single proportion p o or to a distribution? Numerical Explanatory variable Response variable Categorical Numerical Categorical Contingency table Grouped Contingency Logistic bar graph analysis Mosaic plot regression Numerical Multiple t-test histograms Correlation Scatter plot Cumulative frequency distributions ANOVA Regression One-sample t-test p o distribution Binomial test " Goodnessof-fit test Contingency analysis
GROUPED DATA E.G. FOR SAMPLE OF RAW DATA (E.G. 4, 12, 7, 5, MEAN G x / n STANDARD DEVIATION MEDIAN AND QUARTILES STANDARD DEVIATION
FOR SAMPLE OF RAW DATA (E.G. 4, 1, 7, 5, 11, 6, 9, 7, 11, 5, 4, 7) BE ABLE TO COMPUTE MEAN G / STANDARD DEVIATION MEDIAN AND QUARTILES Σ ( Σ) / 1 GROUPED DATA E.G. AGE FREQ. 0-9 53 10-19 4...... 80-89
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 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 informationTransition Passage to Descriptive Statistics 28
viii Preface xiv chapter 1 Introduction 1 Disciplines That Use Quantitative Data 5 What Do You Mean, Statistics? 6 Statistics: A Dynamic Discipline 8 Some Terminology 9 Problems and Answers 12 Scales of
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 informationIntroduction and Descriptive Statistics p. 1 Introduction to Statistics p. 3 Statistics, Science, and Observations p. 5 Populations and Samples p.
Preface p. xi Introduction and Descriptive Statistics p. 1 Introduction to Statistics p. 3 Statistics, Science, and Observations p. 5 Populations and Samples p. 6 The Scientific Method and the Design of
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 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 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 information3 Joint Distributions 71
2.2.3 The Normal Distribution 54 2.2.4 The Beta Density 58 2.3 Functions of a Random Variable 58 2.4 Concluding Remarks 64 2.5 Problems 64 3 Joint Distributions 71 3.1 Introduction 71 3.2 Discrete Random
More informationCHI SQUARE ANALYSIS 8/18/2011 HYPOTHESIS TESTS SO FAR PARAMETRIC VS. NON-PARAMETRIC
CHI SQUARE ANALYSIS I N T R O D U C T I O N T O N O N - P A R A M E T R I C A N A L Y S E S HYPOTHESIS TESTS SO FAR We ve discussed One-sample t-test Dependent Sample t-tests Independent Samples t-tests
More informationTextbook Examples of. SPSS Procedure
Textbook s of IBM SPSS Procedures Each SPSS procedure listed below has its own section in the textbook. These sections include a purpose statement that describes the statistical test, identification of
More informationSubject CS1 Actuarial Statistics 1 Core Principles
Institute of Actuaries of India Subject CS1 Actuarial Statistics 1 Core Principles For 2019 Examinations Aim The aim of the Actuarial Statistics 1 subject is to provide a grounding in mathematical and
More informationContents. Acknowledgments. xix
Table of Preface Acknowledgments page xv xix 1 Introduction 1 The Role of the Computer in Data Analysis 1 Statistics: Descriptive and Inferential 2 Variables and Constants 3 The Measurement of Variables
More informationDover- Sherborn High School Mathematics Curriculum Probability and Statistics
Mathematics Curriculum A. DESCRIPTION This is a full year courses designed to introduce students to the basic elements of statistics and probability. Emphasis is placed on understanding terminology and
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 informationTHE ROYAL STATISTICAL SOCIETY HIGHER CERTIFICATE
THE ROYAL STATISTICAL SOCIETY 004 EXAMINATIONS SOLUTIONS HIGHER CERTIFICATE PAPER II STATISTICAL METHODS The Society provides these solutions to assist candidates preparing for the examinations in future
More informationTables Table A Table B Table C Table D Table E 675
BMTables.indd Page 675 11/15/11 4:25:16 PM user-s163 Tables Table A Standard Normal Probabilities Table B Random Digits Table C t Distribution Critical Values Table D Chi-square Distribution Critical Values
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 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 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 informationSTATISTICS ANCILLARY SYLLABUS. (W.E.F. the session ) Semester Paper Code Marks Credits Topic
STATISTICS ANCILLARY SYLLABUS (W.E.F. the session 2014-15) Semester Paper Code Marks Credits Topic 1 ST21012T 70 4 Descriptive Statistics 1 & Probability Theory 1 ST21012P 30 1 Practical- Using Minitab
More informationConfidence Intervals, Testing and ANOVA Summary
Confidence Intervals, Testing and ANOVA Summary 1 One Sample Tests 1.1 One Sample z test: Mean (σ known) Let X 1,, X n a r.s. from N(µ, σ) or n > 30. Let The test statistic is H 0 : µ = µ 0. z = x µ 0
More informationTurning a research question into a statistical question.
Turning a research question into a statistical question. IGINAL QUESTION: Concept Concept Concept ABOUT ONE CONCEPT ABOUT RELATIONSHIPS BETWEEN CONCEPTS TYPE OF QUESTION: DESCRIBE what s going on? DECIDE
More informationBasic Statistical Analysis
indexerrt.qxd 8/21/2002 9:47 AM Page 1 Corrected index pages for Sprinthall Basic Statistical Analysis Seventh Edition indexerrt.qxd 8/21/2002 9:47 AM Page 656 Index Abscissa, 24 AB-STAT, vii ADD-OR rule,
More informationNonparametric Statistics. Leah Wright, Tyler Ross, Taylor Brown
Nonparametric Statistics Leah Wright, Tyler Ross, Taylor Brown Before we get to nonparametric statistics, what are parametric statistics? These statistics estimate and test population means, while holding
More informationSTATISTICS ( CODE NO. 08 ) PAPER I PART - I
STATISTICS ( CODE NO. 08 ) PAPER I PART - I 1. Descriptive Statistics Types of data - Concepts of a Statistical population and sample from a population ; qualitative and quantitative data ; nominal and
More informationBivariate Relationships Between Variables
Bivariate Relationships Between Variables BUS 735: Business Decision Making and Research 1 Goals Specific goals: Detect relationships between variables. Be able to prescribe appropriate statistical methods
More informationBIOS 6222: Biostatistics II. Outline. Course Presentation. Course Presentation. Review of Basic Concepts. Why Nonparametrics.
BIOS 6222: Biostatistics II Instructors: Qingzhao Yu Don Mercante Cruz Velasco 1 Outline Course Presentation Review of Basic Concepts Why Nonparametrics The sign test 2 Course Presentation Contents Justification
More informationFrom Practical Data Analysis with JMP, Second Edition. Full book available for purchase here. About This Book... xiii About The Author...
From Practical Data Analysis with JMP, Second Edition. Full book available for purchase here. Contents About This Book... xiii About The Author... xxiii Chapter 1 Getting Started: Data Analysis with JMP...
More informationTypes of Statistical Tests DR. MIKE MARRAPODI
Types of Statistical Tests DR. MIKE MARRAPODI Tests t tests ANOVA Correlation Regression Multivariate Techniques Non-parametric t tests One sample t test Independent t test Paired sample t test One sample
More informationIntroduction to Statistical Analysis
Introduction to Statistical Analysis Changyu Shen Richard A. and Susan F. Smith Center for Outcomes Research in Cardiology Beth Israel Deaconess Medical Center Harvard Medical School Objectives Descriptive
More informationFinding Relationships Among Variables
Finding Relationships Among Variables BUS 230: Business and Economic Research and Communication 1 Goals Specific goals: Re-familiarize ourselves with basic statistics ideas: sampling distributions, hypothesis
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 informationPSY 307 Statistics for the Behavioral Sciences. Chapter 20 Tests for Ranked Data, Choosing Statistical Tests
PSY 307 Statistics for the Behavioral Sciences Chapter 20 Tests for Ranked Data, Choosing Statistical Tests What To Do with Non-normal Distributions Tranformations (pg 382): The shape of the distribution
More informationChapter Fifteen. Frequency Distribution, Cross-Tabulation, and Hypothesis Testing
Chapter Fifteen Frequency Distribution, Cross-Tabulation, and Hypothesis Testing Copyright 2010 Pearson Education, Inc. publishing as Prentice Hall 15-1 Internet Usage Data Table 15.1 Respondent Sex Familiarity
More informationNon-parametric tests, part A:
Two types of statistical test: Non-parametric tests, part A: Parametric tests: Based on assumption that the data have certain characteristics or "parameters": Results are only valid if (a) the data are
More informationHypothesis testing, part 2. With some material from Howard Seltman, Blase Ur, Bilge Mutlu, Vibha Sazawal
Hypothesis testing, part 2 With some material from Howard Seltman, Blase Ur, Bilge Mutlu, Vibha Sazawal 1 CATEGORICAL IV, NUMERIC DV 2 Independent samples, one IV # Conditions Normal/Parametric Non-parametric
More informationNon-parametric methods
Eastern Mediterranean University Faculty of Medicine Biostatistics course Non-parametric methods March 4&7, 2016 Instructor: Dr. Nimet İlke Akçay (ilke.cetin@emu.edu.tr) Learning Objectives 1. Distinguish
More informationName: Biostatistics 1 st year Comprehensive Examination: Applied in-class exam. June 8 th, 2016: 9am to 1pm
Name: Biostatistics 1 st year Comprehensive Examination: Applied in-class exam June 8 th, 2016: 9am to 1pm Instructions: 1. This is exam is to be completed independently. Do not discuss your work with
More informationTHE PRINCIPLES AND PRACTICE OF STATISTICS IN BIOLOGICAL RESEARCH. Robert R. SOKAL and F. James ROHLF. State University of New York at Stony Brook
BIOMETRY THE PRINCIPLES AND PRACTICE OF STATISTICS IN BIOLOGICAL RESEARCH THIRD E D I T I O N Robert R. SOKAL and F. James ROHLF State University of New York at Stony Brook W. H. FREEMAN AND COMPANY New
More informationInstitute of Actuaries of India
Institute of Actuaries of India Subject CT3 Probability and Mathematical Statistics For 2018 Examinations Subject CT3 Probability and Mathematical Statistics Core Technical Syllabus 1 June 2017 Aim The
More information16.400/453J Human Factors Engineering. Design of Experiments II
J Human Factors Engineering Design of Experiments II Review Experiment Design and Descriptive Statistics Research question, independent and dependent variables, histograms, box plots, etc. Inferential
More informationSPSS Guide For MMI 409
SPSS Guide For MMI 409 by John Wong March 2012 Preface Hopefully, this document can provide some guidance to MMI 409 students on how to use SPSS to solve many of the problems covered in the D Agostino
More informationInferential Statistics
Inferential Statistics Eva Riccomagno, Maria Piera Rogantin DIMA Università di Genova riccomagno@dima.unige.it rogantin@dima.unige.it Part G Distribution free hypothesis tests 1. Classical and distribution-free
More informationLecture 7: Hypothesis Testing and ANOVA
Lecture 7: Hypothesis Testing and ANOVA Goals Overview of key elements of hypothesis testing Review of common one and two sample tests Introduction to ANOVA Hypothesis Testing The intent of hypothesis
More informationExperimental Design and Data Analysis for Biologists
Experimental Design and Data Analysis for Biologists Gerry P. Quinn Monash University Michael J. Keough University of Melbourne CAMBRIDGE UNIVERSITY PRESS Contents Preface page xv I I Introduction 1 1.1
More informationBusiness Statistics. Lecture 10: Course Review
Business Statistics Lecture 10: Course Review 1 Descriptive Statistics for Continuous Data Numerical Summaries Location: mean, median Spread or variability: variance, standard deviation, range, percentiles,
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 informationNonparametric Statistics
Nonparametric Statistics Nonparametric or Distribution-free statistics: used when data are ordinal (i.e., rankings) used when ratio/interval data are not normally distributed (data are converted to ranks)
More informationPreface Introduction to Statistics and Data Analysis Overview: Statistical Inference, Samples, Populations, and Experimental Design The Role of
Preface Introduction to Statistics and Data Analysis Overview: Statistical Inference, Samples, Populations, and Experimental Design The Role of Probability Sampling Procedures Collection of Data Measures
More informationFormulas and Tables by Mario F. Triola
Copyright 010 Pearson Education, Inc. Ch. 3: Descriptive Statistics x f # x x f Mean 1x - x s - 1 n 1 x - 1 x s 1n - 1 s B variance s Ch. 4: Probability Mean (frequency table) Standard deviation P1A or
More informationCorrelation and Simple Linear Regression
Correlation and Simple Linear Regression Sasivimol Rattanasiri, Ph.D Section for Clinical Epidemiology and Biostatistics Ramathibodi Hospital, Mahidol University E-mail: sasivimol.rat@mahidol.ac.th 1 Outline
More informationChapter 1 Statistical Inference
Chapter 1 Statistical Inference causal inference To infer causality, you need a randomized experiment (or a huge observational study and lots of outside information). inference to populations Generalizations
More informationChapter 15: Nonparametric Statistics Section 15.1: An Overview of Nonparametric Statistics
Section 15.1: An Overview of Nonparametric Statistics Understand Difference between Parametric and Nonparametric Statistical Procedures Parametric statistical procedures inferential procedures that rely
More informationInference for the Regression Coefficient
Inference for the Regression Coefficient Recall, b 0 and b 1 are the estimates of the slope β 1 and intercept β 0 of population regression line. We can shows that b 0 and b 1 are the unbiased estimates
More informationAP Statistics Cumulative AP Exam Study Guide
AP Statistics Cumulative AP Eam Study Guide Chapters & 3 - Graphs Statistics the science of collecting, analyzing, and drawing conclusions from data. Descriptive methods of organizing and summarizing statistics
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 informationInferences About the Difference Between Two Means
7 Inferences About the Difference Between Two Means Chapter Outline 7.1 New Concepts 7.1.1 Independent Versus Dependent Samples 7.1. Hypotheses 7. Inferences About Two Independent Means 7..1 Independent
More informationKumaun University Nainital
Kumaun University Nainital Department of Statistics B. Sc. Semester system course structure: 1. The course work shall be divided into six semesters with three papers in each semester. 2. Each paper in
More informationThe goodness-of-fit test Having discussed how to make comparisons between two proportions, we now consider comparisons of multiple proportions.
The goodness-of-fit test Having discussed how to make comparisons between two proportions, we now consider comparisons of multiple proportions. A common problem of this type is concerned with determining
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 informationANALYSIS OF VARIANCE OF BALANCED DAIRY SCIENCE DATA USING SAS
ANALYSIS OF VARIANCE OF BALANCED DAIRY SCIENCE DATA USING SAS Ravinder Malhotra and Vipul Sharma National Dairy Research Institute, Karnal-132001 The most common use of statistics in dairy science is testing
More informationESP 178 Applied Research Methods. 2/23: Quantitative Analysis
ESP 178 Applied Research Methods 2/23: Quantitative Analysis Data Preparation Data coding create codebook that defines each variable, its response scale, how it was coded Data entry for mail surveys and
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 informationTABLE OF CONTENTS CHAPTER 1 COMBINATORIAL PROBABILITY 1
TABLE OF CONTENTS CHAPTER 1 COMBINATORIAL PROBABILITY 1 1.1 The Probability Model...1 1.2 Finite Discrete Models with Equally Likely Outcomes...5 1.2.1 Tree Diagrams...6 1.2.2 The Multiplication Principle...8
More informationData analysis and Geostatistics - lecture VII
Data analysis and Geostatistics - lecture VII t-tests, ANOVA and goodness-of-fit Statistical testing - significance of r Testing the significance of the correlation coefficient: t = r n - 2 1 - r 2 with
More informationStatistical. Psychology
SEVENTH у *i km m it* & П SB Й EDITION Statistical M e t h o d s for Psychology D a v i d C. Howell University of Vermont ; \ WADSWORTH f% CENGAGE Learning* Australia Biaall apan Korea Меяко Singapore
More informationComparison of two samples
Comparison of two samples Pierre Legendre, Université de Montréal August 009 - Introduction This lecture will describe how to compare two groups of observations (samples) to determine if they may possibly
More informationSEVERAL μs AND MEDIANS: MORE ISSUES. Business Statistics
SEVERAL μs AND MEDIANS: MORE ISSUES Business Statistics CONTENTS Post-hoc analysis ANOVA for 2 groups The equal variances assumption The Kruskal-Wallis test Old exam question Further study POST-HOC ANALYSIS
More informationMy data doesn t look like that..
Testing assumptions My data doesn t look like that.. We have made a big deal about testing model assumptions each week. Bill Pine Testing assumptions Testing assumptions We have made a big deal about testing
More informationPractical Statistics for the Analytical Scientist Table of Contents
Practical Statistics for the Analytical Scientist Table of Contents Chapter 1 Introduction - Choosing the Correct Statistics 1.1 Introduction 1.2 Choosing the Right Statistical Procedures 1.2.1 Planning
More informationBiostatistics for physicists fall Correlation Linear regression Analysis of variance
Biostatistics for physicists fall 2015 Correlation Linear regression Analysis of variance Correlation Example: Antibody level on 38 newborns and their mothers There is a positive correlation in antibody
More information1 Introduction to Minitab
1 Introduction to Minitab Minitab is a statistical analysis software package. The software is freely available to all students and is downloadable through the Technology Tab at my.calpoly.edu. When you
More informationSTATISTICS REVIEW. D. Parameter: a constant for the case or population under consideration.
STATISTICS REVIEW I. Why do we need statistics? A. As human beings, we consciously and unconsciously evaluate whether variables affect phenomena of interest, but sometimes our common sense reasoning is
More informationCorrelation and Regression
Correlation and Regression Dr. Bob Gee Dean Scott Bonney Professor William G. Journigan American Meridian University 1 Learning Objectives Upon successful completion of this module, the student should
More informationFinal Exam. Name: Solution:
Final Exam. Name: Instructions. Answer all questions on the exam. Open books, open notes, but no electronic devices. The first 13 problems are worth 5 points each. The rest are worth 1 point each. HW1.
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 informationInference for Regression Inference about the Regression Model and Using the Regression Line
Inference for Regression Inference about the Regression Model and Using the Regression Line PBS Chapter 10.1 and 10.2 2009 W.H. Freeman and Company Objectives (PBS Chapter 10.1 and 10.2) Inference about
More informationReview: what is a linear model. Y = β 0 + β 1 X 1 + β 2 X 2 + A model of the following form:
Outline for today What is a generalized linear model Linear predictors and link functions Example: fit a constant (the proportion) Analysis of deviance table Example: fit dose-response data using logistic
More informationSix Sigma Black Belt Study Guides
Six Sigma Black Belt Study Guides 1 www.pmtutor.org Powered by POeT Solvers Limited. Analyze Correlation and Regression Analysis 2 www.pmtutor.org Powered by POeT Solvers Limited. Variables and relationships
More information4/6/16. Non-parametric Test. Overview. Stephen Opiyo. Distinguish Parametric and Nonparametric Test Procedures
Non-parametric Test Stephen Opiyo Overview Distinguish Parametric and Nonparametric Test Procedures Explain commonly used Nonparametric Test Procedures Perform Hypothesis Tests Using Nonparametric Procedures
More informationREVIEW: Midterm Exam. Spring 2012
REVIEW: Midterm Exam Spring 2012 Introduction Important Definitions: - Data - Statistics - A Population - A census - A sample Types of Data Parameter (Describing a characteristic of the Population) Statistic
More informationSTA 4504/5503 Sample Exam 1 Spring 2011 Categorical Data Analysis. 1. Indicate whether each of the following is true (T) or false (F).
STA 4504/5503 Sample Exam 1 Spring 2011 Categorical Data Analysis 1. Indicate whether each of the following is true (T) or false (F). (a) (b) (c) (d) (e) In 2 2 tables, statistical independence is equivalent
More informationIndex. Cambridge University Press Data Analysis for Physical Scientists: Featuring Excel Les Kirkup Index More information
χ 2 distribution, 410 χ 2 test, 410, 412 degrees of freedom, 414 accuracy, 176 adjusted coefficient of multiple determination, 323 AIC, 324 Akaike s Information Criterion, 324 correction for small data
More informationOne-way ANOVA Model Assumptions
One-way ANOVA Model Assumptions STAT:5201 Week 4: Lecture 1 1 / 31 One-way ANOVA: Model Assumptions Consider the single factor model: Y ij = µ + α }{{} i ij iid with ɛ ij N(0, σ 2 ) mean structure random
More informationEverything is not normal
Everything is not normal According to the dictionary, one thing is considered normal when it s in its natural state or conforms to standards set in advance. And this is its normal meaning. But, like many
More informationThe material for categorical data follows Agresti closely.
Exam 2 is Wednesday March 8 4 sheets of notes The material for categorical data follows Agresti closely A categorical variable is one for which the measurement scale consists of a set of categories Categorical
More informationNote: The problem numbering below may not reflect actual numbering in DGE.
Stat664 Year 1999 DGE Note: The problem numbering below may not reflect actual numbering in DGE. 1. For a balanced one-way random effect model, (a) write down the model and assumptions; (b) write down
More informationdf=degrees of freedom = n - 1
One sample t-test test of the mean Assumptions: Independent, random samples Approximately normal distribution (from intro class: σ is unknown, need to calculate and use s (sample standard deviation)) Hypotheses:
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 informationFactorial designs. Experiments
Chapter 5: Factorial designs Petter Mostad mostad@chalmers.se Experiments Actively making changes and observing the result, to find causal relationships. Many types of experimental plans Measuring response
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 informationSelection should be based on the desired biological interpretation!
Statistical tools to compare levels of parasitism Jen_ Reiczigel,, Lajos Rózsa Hungary What to compare? The prevalence? The mean intensity? The median intensity? Or something else? And which statistical
More informationIntroduction to hypothesis testing
Introduction to hypothesis testing Review: Logic of Hypothesis Tests Usually, we test (attempt to falsify) a null hypothesis (H 0 ): includes all possibilities except prediction in hypothesis (H A ) If
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 informationSTATISTICS; An Introductory Analysis. 2nd hidition TARO YAMANE NEW YORK UNIVERSITY A HARPER INTERNATIONAL EDITION
2nd hidition TARO YAMANE NEW YORK UNIVERSITY STATISTICS; An Introductory Analysis A HARPER INTERNATIONAL EDITION jointly published by HARPER & ROW, NEW YORK, EVANSTON & LONDON AND JOHN WEATHERHILL, INC.,
More information* Tuesday 17 January :30-16:30 (2 hours) Recored on ESSE3 General introduction to the course.
Name of the course Statistical methods and data analysis Audience The course is intended for students of the first or second year of the Graduate School in Materials Engineering. The aim of the course
More informationCh. 1: Data and Distributions
Ch. 1: Data and Distributions Populations vs. Samples How to graphically display data Histograms, dot plots, stem plots, etc Helps to show how samples are distributed Distributions of both continuous and
More informationSTA 4504/5503 Sample Exam 1 Spring 2011 Categorical Data Analysis. 1. Indicate whether each of the following is true (T) or false (F).
STA 4504/5503 Sample Exam 1 Spring 2011 Categorical Data Analysis 1. Indicate whether each of the following is true (T) or false (F). (a) T In 2 2 tables, statistical independence is equivalent to a population
More information