Parametric and nonparametric statistical methods for the life sciences  Session I


 Aron Allen
 4 years ago
 Views:
Transcription
1 Why nonparametric methods What test to use? Rank Tests Parametric and nonparametric statistical methods for the life sciences  Session I Liesbeth Bruckers Geert Molenberghs Interuniversity Institute for Biostatistics and statistical Bioinformatics (IBiostat) Universiteit Hasselt June 7, 2011
2 Why nonparametric methods What test to use? Rank Tests Table of contents 1 Why nonparametric methods Introductory example Nonparametric test of hypotheses 2 What test to use? Two independent samples More then two independent samples Two dependent samples More then two dependent samples Ordered hypotheses 3 Rank Tests Wilcoxon Rank Sum Test KruskalWallis Test Friedmann Statistic Sign Test JonckheereTerpstra Test
3 Why nonparametric methods What test to use? Rank Tests Introductory example Nonparametric test of hypotheses Why nonparametric methods?
4 Why nonparametric methods What test to use? Rank Tests Introductory example Nonparametric test of hypotheses Introductory Example The paper Hypertension in Terminal Renal Failure, Observations Pre and Post Bilateral Nephrectomy (J. Chronic Diseases (1973): ) gave blood pressure readings for five terminal renal patients before and 2 months after surgery (removal of kidney). Patient Before surgery After surgery Question: Does the mean blood pressure before surgery exceed the mean blood pressure two months after surgery?
5 Why nonparametric methods What test to use? Rank Tests Introductory example Nonparametric test of hypotheses Classical Approach Paired ttest: Patient Before surgery After surgery Difference D i Hypotheses: H 0 : µ d = 0 versus H 1 : µ d > 0 µ d : mean difference in blood pressure TestStatistic : t = D 1 (Di D) n(n 1) 2 follows a t distribution with n 1 d.f.
6 Why nonparametric methods What test to use? Rank Tests Introductory example Nonparametric test of hypotheses Assumptions The statistic follows a tdistribution if the differences are normally distributed ttest = parametric method Observations are made independent: selection of a patient does not influence chance of any other patient for inclusion (Two sample t test): populations must have same variances Variables must be measured in an interval scale, to interpret the results These assumptions are often not tested, but accepted.
7 Why nonparametric methods What test to use? Rank Tests Introductory example Nonparametric test of hypotheses Normal probability plot Normality is questionable!
8 Why nonparametric methods What test to use? Rank Tests Introductory example Nonparametric test of hypotheses Nonparametric Test of Hypotheses Follow same general procedure as parametric tests: State null and alternative hypothesis Calculate the value of the appropriate test statistic (choice based on the design of the study) Decision rule: either reject or accept depending on the magnitude of the statistic P H0 (T c) =?? Exact distribution Approximation for the exact distribution
9 Why nonparametric methods What test to use? Rank Tests Two independent samples More then two independent samples When to use what test
10 Why nonparametric methods What test to use? Rank Tests Two independent samples More then two independent samples What test to use? Choice of appropriate test statistic depends on the design of the study: number of groups? independent of dependent samples? ordered alternative hypothesis?
11 Why nonparametric methods What test to use? Rank Tests Two independent samples More then two independent samples Two Independent Samples Permeability constants of the human chorioamnion (a placental membrane) for at term (x) and between 12 to 26 weeks gestational age (y) pregnancies are given in the table below. Investigate the alternative of interest that the permeability of the human chorioamnion for a term pregnancy is greater than for a 12 to 26 weeks of gestational age pregnancy. X (at term) Y (1226weeks) Statistical Methods: ttest Wilcoxon Rank Sum Test
12 Why nonparametric methods What test to use? Rank Tests Two independent samples More then two independent samples More Than Two Independent Samples Protoporphyrin levels were determined for three groups of people  a control group of normal workers, a group of alcoholics with sideroblasts in their bone marrow, and a group of alcoholics without sideroblasts. The data is shown below. Does the data suggest that normal workers and alcoholics with and without sideroblasts differ with respect to protoporphyrin level? Group Protoporphyrin level (mg) Normal Alcoholics with sideroblasts Alcoholics without sideroblasts Statistical Methods: ANOVA KruskalWallis Test
13 Why nonparametric methods What test to use? Rank Tests Two independent samples More then two independent samples Two Dependent Samples Twelve adult males were put on liquid diet in a weightreducing plan. Weights were recorded before and after the diet. The data are shown in the table below. Subject Before After Statistical Methods: Paired ttest Sign test; Signedrank test
14 Why nonparametric methods What test to use? Rank Tests Two independent samples More then two independent samples Randomized Blocked Design Effect of Hypnosis: Emotions of fear, happiness, depression and calmness were requested (in random order) from 8 subject during hypnosis Response: skin potential (in millivolts) Subject Fear Happiness Depression Calmness Statistical Methods: Mixed Models Friedmann test
15 Why nonparametric methods What test to use? Rank Tests Two independent samples More then two independent samples Ordered Treatments Patients were treated with a drug a four dose levels (100mg, 200mg, 300mg and 400mg) and then monitored for toxicity. Drug Toxicity Dose Mild Moderate Severe Drug Death 100mg mg mg mg Statistical Methods: Regression JonckheereTerpstra Test
16 Wilcoxon Rank Sum Test
17 Wilxocon Rank Sum Test Detailed Example: Data : GAF scores Control Treatment Does treatment improve the functioning?
18 Parametric Approach: ttest t = X 1 X 0 s S X1, where S X1 X X 0 = s2 0 n 0 1 n0 t test: means of two normally distributed populations are equal H 0 : µ 1 = µ 0 H 1 : µ 1 µ 0 (one sided test H 1 : µ 1 µ 0 equal sample sizes two distributions have the same variance X 1 = 34.00, X 0 = 23.33, S X1 = 7.21, S X0 = t = 1.27 P H0 (t 1.27) =
19 Wilxocon Rank Sum Test Detailed Example: Control Treatment Order data: Position of patients on treatment as compared with position of patients in control arm? Ranks
20 Treatment is effective if treated patients rank sufficiently high in the combined ranking of all patients Test statistic such that: treatment ranks are high value test statistic is high treatment ranks are low value test statistic is low W S = S 1 + S S n (n=3, number of patients in treatment arm) Ranks W S = =14 Control (25) (10) (35) Treatment (36) (26) (40)
21 Reject null hypothesis when W S is sufficiently large : W S c P H0 (W S c) = α (alpha=0.05) Distribution of W S under H 0? Suppose no treatment effect (H 0 ) rank is solely determined by patients health status rank is independent of receiving treatment or placebo rank is assigned to patient before randomisation Random selection of patients for treatment random selection of 3 ranks out of 6 Randomisation divides ranks (1,2,...6) into two groups! Number of possible combinations : ( ) N n = N! n!(n n)!
22 All posibilities: (each as a probability of 1/20 under H 0 ) treatment ranks (4,5,6) (3,5,6) (3,4,6) (3,4,5) (2,5,6) w s treatment ranks (2,4,6) (2,4,5) (2,3,6) (2,3,5) (2,3,4) w treatment ranks (1,5,6) (1,4,6) (1,4,5) (1,3,6) (1,3,5) w s treatment ranks (1,3,4) (1,2,6) (1,2,5) (1,2,4) (1,2,3) w s
23 Distribution of W S under the null hypothesis: w P H0 (W s = w)
24 P HO (W S 14) = 0.1 Do not reject H 0. Conclusion: Treatment does not increase the GAF scores. Power of this study???
25 Large Sample Sizecase ( N ) n increases rapidly with N and n ( 20 ( ) = ) = 924 Asymptotic Null Distribution: Central Limit Theorem Sum T of large number of independent random variables is approximately normally distributed. ( ) T E(T ) P a Φ(a) Var(T ) where Φ(a) is the area to the left of a under a standard normal curve
26 If both n and m are sufficiently large: W S N(E(W S ); Var(W S )) E(W S ) = 1 2n(N + 1) Var(W S ) = 1 12nm(N + 1)
27 KruskalWallis Test
28 Kruskal Wallis test Example: Kruskal Wallis test: The following data represent corn yields per acre from three different fields where different farming methods were used. Method 1 Method 2 Method Question: is the yields different for the 4 methods?
29 Parametric Approach Oneway ANOVA Statistical test of whether or not the means of several groups are all equal Assumptions: Independence of cases The distributions of the residuals are normal : ɛ i (0, σ 2 ). Homoscedasticity variance between groups F = = variance within groups MSTR MSE Statistic follows a F distribution with s 1, n s d.f.
30 Small F: Large F:
31 OneWay ANOVA results X 1 = 89, X 2 = 88.33, X 3 = 99 σ 1 = 3.56, σ 2 = 6.65, σ 3 = 4.08 MSTR= , MSE = F= 6.11 P H0 (F 6.11) =
32 Ranks: Method 1 Method 2 Method R i. :
33 Hypothesis : H 0 : No difference between the treatments H 1 : Any difference between the treatments If treatments do not differ widely (H 0 ): R i. are close to each other R i. close to R.. If treatments do differ (H 1 ): R i. differ substantial R i. not close to R..
34 Evaluate the null hypothesis by investigating: K = 12 N(N + 1) s n i (R i. R.. ) 2 i=1 P H0 (K c) =? Exact distribution of K under H 0 : ranks are determined before assignment to treatment random assignment all possibilities same chance of being observed Number ( of possible combinations: multinomial coefficient : 11 ( 4,3,4) = 11 )( )( 4) = ( ) ( N n 1,n 2,...,n s = N )( N n1 ) ( n 1 n 2... N n1... n s 1 ) n s
35 A few possible configurations: Method 1 Method 2 Method 3 K (1,2,3,4) (5,6,7) (8,9,10,11) 8.91 (1,2,3,5) (4,6,7) (8,9,10,11) 8.32 (1,2,3,6) (4,5,6) (8,9,10,11) 7.84 (1,2,3,7) (4,5,6) (8,9,10,11) 7,48... (1,3,5,6) (2,4,8) (7,9,10,11) Each configuration has a probability of to happen.
36 Exact Distribution of K: P H0 (K 6.16) = Conclusion: Reject H 0 : there is a difference between the farming methods Large sample size approximation χ 2 distribution with s 1 d.f.
37 Friedmann Test
38 Friedmann Statistic Setting 1: complete randomization: KruskalWallis test pvalue = Treatment effect is blurred by the variability between subjects Setting 2: randomisation within age groups: pvalue Conclusion reject H 0
39 Procedure Divide subjects in homogeneous subgroups (BLOCKS) Compare subjects within the blocks w.r.t. treatment effects (Generalisation of the paired comparison design)
40 Example Data Agegroup treatment y y y y A B C Rank subjects within a block: Agegroup treatment y y y y A B C
41 Mean of ranks for: treatment A = R A. = 10 4 = 2.5 treatment B = R B. = 6 4 = 1.5 treatment C = R C. = 9 4 = 2.25 If these mean ranks are different reject H 0 If these mean ranks are close accept H 0
42 Measure for closseness of the mean ranks: if the R i. are all close to each other then they are close to the overall mean R.. and (R i. R.. ) 2 will be close to zero Friedman Statistic Q = 12N s(s + 1) s (R i. R.. ) 2 i=1
43 P H0 (Q c) =? Exact distribution of Q under H 0 : A few possible configurations: Agegroup Q Treatment y y y y A B C A B C A B C A B C
44 Exact Distribution of Q: Q Pr E E E E E02
45 Number of possibilities for the rank combinations: agegroup year: 3! = 6 agegroups are independent total number of possible combinations: (3!) 4 = 1296 Under the null these are all equally likely : (s!) N, s= treatment groups, N = of blocks P H0 (Q 3.5) = Do not reject H 0
46 Sign Test
47 Sign Test Special case of Friedmann test: blocks of size 2 subjects matched on e.g. age, gender,... twins two eyes (hands) of a person subject serves as own control: e.g. blood pressure before and after treatment Example: Pain scores for lower back pain, before and after having acupuncture Pain score Pain score Sign Pain score Pain score Sign Patient Before After Patient Before After
48 9 pairs out 15 where treatment comes out ahead (reduction in pain scores) Sign Test: S N = 9 P H0 (S N 9) =??? Exact Distribution of S N under H 0 is binomial N trials, N = number of pairs Success probability: 1 2 P H0 (S N 9) = ( ( 15 9 P H0 (S N = a) = ) + ( ( ) N 1 a 2 N ) ( ) 15 ) 1 =
49 JonckheereTerpstra Test
50 JonckheereTerpstra Test To be used when the H 1 is ordered. Ordinal data for the responses and an ordering in the treatment/groups. Example: Data: Three diets for rats Response: growth H 1 : Growth rate decreases from A to C : A B C A B C
51 Parametric Approach : Regression Models the relationship between a dependent and independent variable y i = β 0 + β 1 x i + ɛ i Assumptions ɛ i N(0, σ 2 ), ɛ i are independent homoscedasticity x i is measured without error
52 β 0 = 169, pvalue = < β 1 = 16, pvalue = Rsquare =
53 JonckheereTerpstra Test Based on MannWhitney statistics for two treatments Comparing the treatment groups two by two if W BA is large: growth A > growth B : (W BA = 18 if W BC is large: growth B > growth C : (W BC = 18 if W CA is large: growth A > growth C : (W BA = 23 JT Statistic: W = i<j W ij Reject H 0 when W is sufficiently large W = 59 P H0 (W c) = Compare with the result of a KruskalWallis Test: pvalue = The distribution of W follows a normal distribution for large samples
54 Parametric versus nonparametric tests Parametric tests: Assumptions about the distribution in the population Conditions are often not tested Test depends on the validity of the assumptions Most powerful test if all assumptions are met Nonparametric tests: Fewer assumptions about the distribution in the population In case of small sample sizes often the only alternative (unless the nature of the population distribution is known exactly) Less sensitive for measurement error (uses ranks) Can be used for data which are inherently in ranks, even for data measured in a nominal scale Easier to learn
THE KRUSKAL WALLLIS TEST
THE KRUSKAL WALLLIS TEST TEODORA H. MEHOTCHEVA Wednesday, 23 rd April 08 THE KRUSKALWALLIS TEST: The nonparametric alternative to ANOVA: testing for difference between several independent groups 2 NON
More informationNONPARAMETRIC STATISTICS 1. depend on assumptions about the underlying distribution of the data (or on the Central Limit Theorem)
NONPARAMETRIC STATISTICS 1 PREVIOUSLY parametric statistics in estimation and hypothesis testing... construction of confidence intervals computing of pvalues classical significance testing depend on assumptions
More informationStatistics. Onetwo sided test, Parametric and nonparametric test statistics: one group, two groups, and more than two groups samples
Statistics Onetwo sided test, Parametric and nonparametric test statistics: one group, two groups, and more than two groups samples February 3, 00 Jobayer Hossain, Ph.D. & Tim Bunnell, Ph.D. Nemours
More information1 Nonparametric Statistics
1 Nonparametric Statistics When finding confidence intervals or conducting tests so far, we always described the population with a model, which includes a set of parameters. Then we could make decisions
More informationII. DISTRIBUTIONS distribution normal distribution. standard scores
Appendix D Basic Measurement And Statistics The following information was developed by Steven Rothke, PhD, Department of Psychology, Rehabilitation Institute of Chicago (RIC) and expanded by Mary F. Schmidt,
More informationOverview of NonParametric Statistics PRESENTER: ELAINE EISENBEISZ OWNER AND PRINCIPAL, OMEGA STATISTICS
Overview of NonParametric Statistics PRESENTER: ELAINE EISENBEISZ OWNER AND PRINCIPAL, OMEGA STATISTICS About Omega Statistics Private practice consultancy based in Southern California, Medical and Clinical
More informationRankBased NonParametric Tests
RankBased NonParametric Tests Reminder: Student Instructional Rating Surveys You have until May 8 th to fill out the student instructional rating surveys at https://sakai.rutgers.edu/portal/site/sirs
More informationResearch Methodology: Tools
MSc Business Administration Research Methodology: Tools Applied Data Analysis (with SPSS) Lecture 11: Nonparametric Methods May 2014 Prof. Dr. Jürg Schwarz Lic. phil. Heidi Bruderer Enzler Contents Slide
More informationNonparametric tests these test hypotheses that are not statements about population parameters (e.g.,
CHAPTER 13 Nonparametric and DistributionFree Statistics Nonparametric tests these test hypotheses that are not statements about population parameters (e.g., 2 tests for goodness of fit and independence).
More informationNonInferiority Tests for Two Means using Differences
Chapter 450 oninferiority Tests for Two Means using Differences Introduction This procedure computes power and sample size for noninferiority tests in twosample designs in which the outcome is a continuous
More informationResearch Methods & Experimental Design
Research Methods & Experimental Design 16.422 Human Supervisory Control April 2004 Research Methods Qualitative vs. quantitative Understanding the relationship between objectives (research question) and
More informationHYPOTHESIS TESTING (ONE SAMPLE)  CHAPTER 7 1. used confidence intervals to answer questions such as...
HYPOTHESIS TESTING (ONE SAMPLE)  CHAPTER 7 1 PREVIOUSLY used confidence intervals to answer questions such as... You know that 0.25% of women have red/green color blindness. You conduct a study of men
More informationQUANTITATIVE METHODS BIOLOGY FINAL HONOUR SCHOOL NONPARAMETRIC TESTS
QUANTITATIVE METHODS BIOLOGY FINAL HONOUR SCHOOL NONPARAMETRIC TESTS This booklet contains lecture notes for the nonparametric work in the QM course. This booklet may be online at http://users.ox.ac.uk/~grafen/qmnotes/index.html.
More informationSCHOOL OF HEALTH AND HUMAN SCIENCES DON T FORGET TO RECODE YOUR MISSING VALUES
SCHOOL OF HEALTH AND HUMAN SCIENCES Using SPSS Topics addressed today: 1. Differences between groups 2. Graphing Use the s4data.sav file for the first part of this session. DON T FORGET TO RECODE YOUR
More informationSPSS ADVANCED ANALYSIS WENDIANN SETHI SPRING 2011
SPSS ADVANCED ANALYSIS WENDIANN SETHI SPRING 2011 Statistical techniques to be covered Explore relationships among variables Correlation Regression/Multiple regression Logistic regression Factor analysis
More informationBA 275 Review Problems  Week 6 (10/30/0611/3/06) CD Lessons: 53, 54, 55, 56 Textbook: pp. 394398, 404408, 410420
BA 275 Review Problems  Week 6 (10/30/0611/3/06) CD Lessons: 53, 54, 55, 56 Textbook: pp. 394398, 404408, 410420 1. Which of the following will increase the value of the power in a statistical test
More informationNonparametric Statistics
Nonparametric Statistics J. Lozano University of Goettingen Department of Genetic Epidemiology Interdisciplinary PhD Program in Applied Statistics & Empirical Methods Graduate Seminar in Applied Statistics
More informationHYPOTHESIS TESTING: POWER OF THE TEST
HYPOTHESIS TESTING: POWER OF THE TEST The first 6 steps of the 9step test of hypothesis are called "the test". These steps are not dependent on the observed data values. When planning a research project,
More informationTwoSample TTests Assuming Equal Variance (Enter Means)
Chapter 4 TwoSample TTests Assuming Equal Variance (Enter Means) Introduction This procedure provides sample size and power calculations for one or twosided twosample ttests when the variances of
More informationTwoSample TTests Allowing Unequal Variance (Enter Difference)
Chapter 45 TwoSample TTests Allowing Unequal Variance (Enter Difference) Introduction This procedure provides sample size and power calculations for one or twosided twosample ttests when no assumption
More informationStatCrunch and Nonparametric Statistics
StatCrunch and Nonparametric Statistics You can use StatCrunch to calculate the values of nonparametric statistics. It may not be obvious how to enter the data in StatCrunch for various data sets that
More informationNCSS Statistical Software
Chapter 06 Introduction This procedure provides several reports for the comparison of two distributions, including confidence intervals for the difference in means, twosample ttests, the ztest, the
More informationNonparametric TwoSample Tests. Nonparametric Tests. Sign Test
Nonparametric TwoSample Tests Sign test MannWhitney Utest (a.k.a. Wilcoxon twosample test) KolmogorovSmirnov Test Wilcoxon SignedRank Test TukeyDuckworth Test 1 Nonparametric Tests Recall, nonparametric
More informationNonParametric Tests (I)
Lecture 5: NonParametric Tests (I) KimHuat LIM lim@stats.ox.ac.uk http://www.stats.ox.ac.uk/~lim/teaching.html Slide 1 5.1 Outline (i) Overview of DistributionFree Tests (ii) Median Test for Two Independent
More informationUNIVERSITY OF NAIROBI
UNIVERSITY OF NAIROBI MASTERS IN PROJECT PLANNING AND MANAGEMENT NAME: SARU CAROLYNN ELIZABETH REGISTRATION NO: L50/61646/2013 COURSE CODE: LDP 603 COURSE TITLE: RESEARCH METHODS LECTURER: GAKUU CHRISTOPHER
More informationIntroduction to Analysis of Variance (ANOVA) Limitations of the ttest
Introduction to Analysis of Variance (ANOVA) The Structural Model, The Summary Table, and the One Way ANOVA Limitations of the ttest Although the ttest is commonly used, it has limitations Can only
More information1. What is the critical value for this 95% confidence interval? CV = z.025 = invnorm(0.025) = 1.96
1 Final Review 2 Review 2.1 CI 1propZint Scenario 1 A TV manufacturer claims in its warranty brochure that in the past not more than 10 percent of its TV sets needed any repair during the first two years
More informationAnalysis of Variance ANOVA
Analysis of Variance ANOVA Overview We ve used the t test to compare the means from two independent groups. Now we ve come to the final topic of the course: how to compare means from more than two populations.
More informationPart 3. Comparing Groups. Chapter 7 Comparing Paired Groups 189. Chapter 8 Comparing Two Independent Groups 217
Part 3 Comparing Groups Chapter 7 Comparing Paired Groups 189 Chapter 8 Comparing Two Independent Groups 217 Chapter 9 Comparing More Than Two Groups 257 188 Elementary Statistics Using SAS Chapter 7 Comparing
More informationStatistical tests for SPSS
Statistical tests for SPSS Paolo Coletti A.Y. 2010/11 Free University of Bolzano Bozen Premise This book is a very quick, rough and fast description of statistical tests and their usage. It is explicitly
More informationINTERPRETING THE ONEWAY ANALYSIS OF VARIANCE (ANOVA)
INTERPRETING THE ONEWAY ANALYSIS OF VARIANCE (ANOVA) As with other parametric statistics, we begin the oneway ANOVA with a test of the underlying assumptions. Our first assumption is the assumption of
More informationCHAPTER 14 NONPARAMETRIC TESTS
CHAPTER 14 NONPARAMETRIC TESTS Everything that we have done up until now in statistics has relied heavily on one major fact: that our data is normally distributed. We have been able to make inferences
More informationAnalysis of Data. Organizing Data Files in SPSS. Descriptive Statistics
Analysis of Data Claudia J. Stanny PSY 67 Research Design Organizing Data Files in SPSS All data for one subject entered on the same line Identification data Betweensubjects manipulations: variable to
More informationStatistics Review PSY379
Statistics Review PSY379 Basic concepts Measurement scales Populations vs. samples Continuous vs. discrete variable Independent vs. dependent variable Descriptive vs. inferential stats Common analyses
More informationIntroduction to Hypothesis Testing. Hypothesis Testing. Step 1: State the Hypotheses
Introduction to Hypothesis Testing 1 Hypothesis Testing A hypothesis test is a statistical procedure that uses sample data to evaluate a hypothesis about a population Hypothesis is stated in terms of the
More informationBA 275 Review Problems  Week 5 (10/23/0610/27/06) CD Lessons: 48, 49, 50, 51, 52 Textbook: pp. 380394
BA 275 Review Problems  Week 5 (10/23/0610/27/06) CD Lessons: 48, 49, 50, 51, 52 Textbook: pp. 380394 1. Does vigorous exercise affect concentration? In general, the time needed for people to complete
More informationHYPOTHESIS TESTING (ONE SAMPLE)  CHAPTER 7 1. used confidence intervals to answer questions such as...
HYPOTHESIS TESTING (ONE SAMPLE)  CHAPTER 7 1 PREVIOUSLY used confidence intervals to answer questions such as... You know that 0.25% of women have red/green color blindness. You conduct a study of men
More informationNonparametric Statistics
Nonparametric Statistics References Some good references for the topics in this course are 1. Higgins, James (2004), Introduction to Nonparametric Statistics 2. Hollander and Wolfe, (1999), Nonparametric
More informationPermutation & NonParametric Tests
Permutation & NonParametric Tests Statistical tests Gather data to assess some hypothesis (e.g., does this treatment have an effect on this outcome?) Form a test statistic for which large values indicate
More informationAdditional sources Compilation of sources: http://lrs.ed.uiuc.edu/tseportal/datacollectionmethodologies/jintselink/tselink.htm
Mgt 540 Research Methods Data Analysis 1 Additional sources Compilation of sources: http://lrs.ed.uiuc.edu/tseportal/datacollectionmethodologies/jintselink/tselink.htm http://web.utk.edu/~dap/random/order/start.htm
More informationSPSS Explore procedure
SPSS Explore procedure One useful function in SPSS is the Explore procedure, which will produce histograms, boxplots, stemandleaf plots and extensive descriptive statistics. To run the Explore procedure,
More informationParametric and Nonparametric: Demystifying the Terms
Parametric and Nonparametric: Demystifying the Terms By Tanya Hoskin, a statistician in the Mayo Clinic Department of Health Sciences Research who provides consultations through the Mayo Clinic CTSA BERD
More informationIntroduction to Statistics and Quantitative Research Methods
Introduction to Statistics and Quantitative Research Methods Purpose of Presentation To aid in the understanding of basic statistics, including terminology, common terms, and common statistical methods.
More informationStatistiek II. John Nerbonne. October 1, 2010. Dept of Information Science j.nerbonne@rug.nl
Dept of Information Science j.nerbonne@rug.nl October 1, 2010 Course outline 1 Oneway ANOVA. 2 Factorial ANOVA. 3 Repeated measures ANOVA. 4 Correlation and regression. 5 Multiple regression. 6 Logistic
More informationEPS 625 INTERMEDIATE STATISTICS FRIEDMAN TEST
EPS 625 INTERMEDIATE STATISTICS The Friedman test is an extension of the Wilcoxon test. The Wilcoxon test can be applied to repeatedmeasures data if participants are assessed on two occasions or conditions
More informationSimple Linear Regression Inference
Simple Linear Regression Inference 1 Inference requirements The Normality assumption of the stochastic term e is needed for inference even if it is not a OLS requirement. Therefore we have: Interpretation
More informationThe Wilcoxon RankSum Test
1 The Wilcoxon RankSum Test The Wilcoxon ranksum test is a nonparametric alternative to the twosample ttest which is based solely on the order in which the observations from the two samples fall. We
More informationLesson 1: Comparison of Population Means Part c: Comparison of Two Means
Lesson : Comparison of Population Means Part c: Comparison of Two Means Welcome to lesson c. This third lesson of lesson will discuss hypothesis testing for two independent means. Steps in Hypothesis
More informationStudy Guide for the Final Exam
Study Guide for the Final Exam When studying, remember that the computational portion of the exam will only involve new material (covered after the second midterm), that material from Exam 1 will make
More informationC. The null hypothesis is not rejected when the alternative hypothesis is true. A. population parameters.
Sample Multiple Choice Questions for the material since Midterm 2. Sample questions from Midterms and 2 are also representative of questions that may appear on the final exam.. A randomly selected sample
More informationSPSS 3: COMPARING MEANS
SPSS 3: COMPARING MEANS UNIVERSITY OF GUELPH LUCIA COSTANZO lcostanz@uoguelph.ca REVISED SEPTEMBER 2012 CONTENTS SPSS availability... 2 Goals of the workshop... 2 Data for SPSS Sessions... 3 Statistical
More informationHow To Compare Birds To Other Birds
STT 430/630/ES 760 Lecture Notes: Chapter 7: TwoSample Inference 1 February 27, 2009 Chapter 7: Two Sample Inference Chapter 6 introduced hypothesis testing in the onesample setting: one sample is obtained
More informationDescriptive Statistics
Descriptive Statistics Primer Descriptive statistics Central tendency Variation Relative position Relationships Calculating descriptive statistics Descriptive Statistics Purpose to describe or summarize
More informationSPSS Tests for Versions 9 to 13
SPSS Tests for Versions 9 to 13 Chapter 2 Descriptive Statistic (including median) Choose Analyze Descriptive statistics Frequencies... Click on variable(s) then press to move to into Variable(s): list
More informationDATA INTERPRETATION AND STATISTICS
PholC60 September 001 DATA INTERPRETATION AND STATISTICS Books A easy and systematic introductory text is Essentials of Medical Statistics by Betty Kirkwood, published by Blackwell at about 14. DESCRIPTIVE
More informationNonInferiority Tests for One Mean
Chapter 45 NonInferiority ests for One Mean Introduction his module computes power and sample size for noninferiority tests in onesample designs in which the outcome is distributed as a normal random
More informationExperimental Design. Power and Sample Size Determination. Proportions. Proportions. Confidence Interval for p. The Binomial Test
Experimental Design Power and Sample Size Determination Bret Hanlon and Bret Larget Department of Statistics University of Wisconsin Madison November 3 8, 2011 To this point in the semester, we have largely
More informationP(every one of the seven intervals covers the true mean yield at its location) = 3.
1 Let = number of locations at which the computed confidence interval for that location hits the true value of the mean yield at its location has a binomial(7,095) (a) P(every one of the seven intervals
More informationOneWay Analysis of Variance (ANOVA) Example Problem
OneWay Analysis of Variance (ANOVA) Example Problem Introduction Analysis of Variance (ANOVA) is a hypothesistesting technique used to test the equality of two or more population (or treatment) means
More informationOutline. Topic 4  Analysis of Variance Approach to Regression. Partitioning Sums of Squares. Total Sum of Squares. Partitioning sums of squares
Topic 4  Analysis of Variance Approach to Regression Outline Partitioning sums of squares Degrees of freedom Expected mean squares General linear test  Fall 2013 R 2 and the coefficient of correlation
More informationTtest & factor analysis
Parametric tests Ttest & factor analysis Better than non parametric tests Stringent assumptions More strings attached Assumes population distribution of sample is normal Major problem Alternatives Continue
More informationIndependent t Test (Comparing Two Means)
Independent t Test (Comparing Two Means) The objectives of this lesson are to learn: the definition/purpose of independent ttest when to use the independent ttest the use of SPSS to complete an independent
More informationTutorial 5: Hypothesis Testing
Tutorial 5: Hypothesis Testing Rob Nicholls nicholls@mrclmb.cam.ac.uk MRC LMB Statistics Course 2014 Contents 1 Introduction................................ 1 2 Testing distributional assumptions....................
More information1 Basic ANOVA concepts
Math 143 ANOVA 1 Analysis of Variance (ANOVA) Recall, when we wanted to compare two population means, we used the 2sample t procedures. Now let s expand this to compare k 3 population means. As with the
More informationIntroduction to General and Generalized Linear Models
Introduction to General and Generalized Linear Models General Linear Models  part I Henrik Madsen Poul Thyregod Informatics and Mathematical Modelling Technical University of Denmark DK2800 Kgs. Lyngby
More informationProjects Involving Statistics (& SPSS)
Projects Involving Statistics (& SPSS) Academic Skills Advice Starting a project which involves using statistics can feel confusing as there seems to be many different things you can do (charts, graphs,
More informationCHAPTER 11 CHISQUARE AND F DISTRIBUTIONS
CHAPTER 11 CHISQUARE AND F DISTRIBUTIONS CHISQUARE TESTS OF INDEPENDENCE (SECTION 11.1 OF UNDERSTANDABLE STATISTICS) In chisquare tests of independence we use the hypotheses. H0: The variables are independent
More informationSTAT 350 Practice Final Exam Solution (Spring 2015)
PART 1: Multiple Choice Questions: 1) A study was conducted to compare five different training programs for improving endurance. Forty subjects were randomly divided into five groups of eight subjects
More informationANALYSING LIKERT SCALE/TYPE DATA, ORDINAL LOGISTIC REGRESSION EXAMPLE IN R.
ANALYSING LIKERT SCALE/TYPE DATA, ORDINAL LOGISTIC REGRESSION EXAMPLE IN R. 1. Motivation. Likert items are used to measure respondents attitudes to a particular question or statement. One must recall
More informationChapter G08 Nonparametric Statistics
G08 Nonparametric Statistics Chapter G08 Nonparametric Statistics Contents 1 Scope of the Chapter 2 2 Background to the Problems 2 2.1 Parametric and Nonparametric Hypothesis Testing......................
More informationUNDERSTANDING THE TWOWAY ANOVA
UNDERSTANDING THE e have seen how the oneway ANOVA can be used to compare two or more sample means in studies involving a single independent variable. This can be extended to two independent variables
More informationStatistics for Sports Medicine
Statistics for Sports Medicine Suzanne Hecht, MD University of Minnesota (suzanne.hecht@gmail.com) Fellow s Research Conference July 2012: Philadelphia GOALS Try not to bore you to death!! Try to teach
More informationDesign and Analysis of Phase III Clinical Trials
Cancer Biostatistics Center, Biostatistics Shared Resource, Vanderbilt University School of Medicine June 19, 2008 Outline 1 Phases of Clinical Trials 2 3 4 5 6 Phase I Trials: Safety, Dosage Range, and
More informationECON 142 SKETCH OF SOLUTIONS FOR APPLIED EXERCISE #2
University of California, Berkeley Prof. Ken Chay Department of Economics Fall Semester, 005 ECON 14 SKETCH OF SOLUTIONS FOR APPLIED EXERCISE # Question 1: a. Below are the scatter plots of hourly wages
More informationIntroduction. Hypothesis Testing. Hypothesis Testing. Significance Testing
Introduction Hypothesis Testing Mark Lunt Arthritis Research UK Centre for Ecellence in Epidemiology University of Manchester 13/10/2015 We saw last week that we can never know the population parameters
More informationChapter 5 Analysis of variance SPSS Analysis of variance
Chapter 5 Analysis of variance SPSS Analysis of variance Data file used: gss.sav How to get there: Analyze Compare Means Oneway ANOVA To test the null hypothesis that several population means are equal,
More informationChicago Booth BUSINESS STATISTICS 41000 Final Exam Fall 2011
Chicago Booth BUSINESS STATISTICS 41000 Final Exam Fall 2011 Name: Section: I pledge my honor that I have not violated the Honor Code Signature: This exam has 34 pages. You have 3 hours to complete this
More informationOnce saved, if the file was zipped you will need to unzip it. For the files that I will be posting you need to change the preferences.
1 Commands in JMP and Statcrunch Below are a set of commands in JMP and Statcrunch which facilitate a basic statistical analysis. The first part concerns commands in JMP, the second part is for analysis
More informationBiostatistics: Types of Data Analysis
Biostatistics: Types of Data Analysis Theresa A Scott, MS Vanderbilt University Department of Biostatistics theresa.scott@vanderbilt.edu http://biostat.mc.vanderbilt.edu/theresascott Theresa A Scott, MS
More informationNAG C Library Chapter Introduction. g08 Nonparametric Statistics
g08 Nonparametric Statistics Introduction g08 NAG C Library Chapter Introduction g08 Nonparametric Statistics Contents 1 Scope of the Chapter... 2 2 Background to the Problems... 2 2.1 Parametric and Nonparametric
More informationGeneral Method: Difference of Means. 3. Calculate df: either WelchSatterthwaite formula or simpler df = min(n 1, n 2 ) 1.
General Method: Difference of Means 1. Calculate x 1, x 2, SE 1, SE 2. 2. Combined SE = SE1 2 + SE2 2. ASSUMES INDEPENDENT SAMPLES. 3. Calculate df: either WelchSatterthwaite formula or simpler df = min(n
More informationPRACTICE PROBLEMS FOR BIOSTATISTICS
PRACTICE PROBLEMS FOR BIOSTATISTICS BIOSTATISTICS DESCRIBING DATA, THE NORMAL DISTRIBUTION 1. The duration of time from first exposure to HIV infection to AIDS diagnosis is called the incubation period.
More informationUNDERSTANDING THE DEPENDENTSAMPLES t TEST
UNDERSTANDING THE DEPENDENTSAMPLES t TEST A dependentsamples t test (a.k.a. matched or pairedsamples, matchedpairs, samples, or subjects, simple repeatedmeasures or withingroups, or correlated groups)
More informationComparing Means in Two Populations
Comparing Means in Two Populations Overview The previous section discussed hypothesis testing when sampling from a single population (either a single mean or two means from the same population). Now we
More informationHow To Test For Significance On A Data Set
NonParametric Univariate Tests: 1 Sample Sign Test 1 1 SAMPLE SIGN TEST A nonparametric equivalent of the 1 SAMPLE TTEST. ASSUMPTIONS: Data is nonnormally distributed, even after log transforming.
More informationIntroduction to Quantitative Methods
Introduction to Quantitative Methods October 15, 2009 Contents 1 Definition of Key Terms 2 2 Descriptive Statistics 3 2.1 Frequency Tables......................... 4 2.2 Measures of Central Tendencies.................
More informationChapter 8 Hypothesis Testing Chapter 8 Hypothesis Testing 81 Overview 82 Basics of Hypothesis Testing
Chapter 8 Hypothesis Testing 1 Chapter 8 Hypothesis Testing 81 Overview 82 Basics of Hypothesis Testing 83 Testing a Claim About a Proportion 85 Testing a Claim About a Mean: s Not Known 86 Testing
More information1.5 Oneway Analysis of Variance
Statistics: Rosie Cornish. 200. 1.5 Oneway Analysis of Variance 1 Introduction Oneway analysis of variance (ANOVA) is used to compare several means. This method is often used in scientific or medical experiments
More informationTwosample hypothesis testing, II 9.07 3/16/2004
Twosample hypothesis testing, II 9.07 3/16/004 Small sample tests for the difference between two independent means For twosample tests of the difference in mean, things get a little confusing, here,
More informationPermutation Tests for Comparing Two Populations
Permutation Tests for Comparing Two Populations Ferry Butar Butar, Ph.D. JaeWan Park Abstract Permutation tests for comparing two populations could be widely used in practice because of flexibility of
More informationCalculating PValues. Parkland College. Isela Guerra Parkland College. Recommended Citation
Parkland College A with Honors Projects Honors Program 2014 Calculating PValues Isela Guerra Parkland College Recommended Citation Guerra, Isela, "Calculating PValues" (2014). A with Honors Projects.
More informationSection 7.1. Introduction to Hypothesis Testing. Schrodinger s cat quantum mechanics thought experiment (1935)
Section 7.1 Introduction to Hypothesis Testing Schrodinger s cat quantum mechanics thought experiment (1935) Statistical Hypotheses A statistical hypothesis is a claim about a population. Null hypothesis
More informationCHAPTER 13. Experimental Design and Analysis of Variance
CHAPTER 13 Experimental Design and Analysis of Variance CONTENTS STATISTICS IN PRACTICE: BURKE MARKETING SERVICES, INC. 13.1 AN INTRODUCTION TO EXPERIMENTAL DESIGN AND ANALYSIS OF VARIANCE Data Collection
More informationINTRODUCTORY STATISTICS
INTRODUCTORY STATISTICS FIFTH EDITION Thomas H. Wonnacott University of Western Ontario Ronald J. Wonnacott University of Western Ontario WILEY JOHN WILEY & SONS New York Chichester Brisbane Toronto Singapore
More informationAn Introduction to Statistics Course (ECOE 1302) Spring Semester 2011 Chapter 10 TWOSAMPLE TESTS
The Islamic University of Gaza Faculty of Commerce Department of Economics and Political Sciences An Introduction to Statistics Course (ECOE 130) Spring Semester 011 Chapter 10 TWOSAMPLE TESTS Practice
More informationChapter 12 Nonparametric Tests. Chapter Table of Contents
Chapter 12 Nonparametric Tests Chapter Table of Contents OVERVIEW...171 Testing for Normality...... 171 Comparing Distributions....171 ONESAMPLE TESTS...172 TWOSAMPLE TESTS...172 ComparingTwoIndependentSamples...172
More informationUNDERSTANDING THE INDEPENDENTSAMPLES t TEST
UNDERSTANDING The independentsamples t test evaluates the difference between the means of two independent or unrelated groups. That is, we evaluate whether the means for two independent groups are significantly
More informationOutline. Definitions Descriptive vs. Inferential Statistics The ttest  Onesample ttest
The ttest Outline Definitions Descriptive vs. Inferential Statistics The ttest  Onesample ttest  Dependent (related) groups ttest  Independent (unrelated) groups ttest Comparing means Correlation
More informationMEASURES OF LOCATION AND SPREAD
Paper TU04 An Overview of Nonparametric Tests in SAS : When, Why, and How Paul A. Pappas and Venita DePuy Durham, North Carolina, USA ABSTRACT Most commonly used statistical procedures are based on the
More informationBivariate Statistics Session 2: Measuring Associations ChiSquare Test
Bivariate Statistics Session 2: Measuring Associations ChiSquare Test Features Of The ChiSquare Statistic The chisquare test is nonparametric. That is, it makes no assumptions about the distribution
More information