Nonparametric Test Procedures

Save this PDF as:

Size: px
Start display at page:

Transcription

1 Nonparametric Test Procedures 1 Introduction to Nonparametrics Nonparametric tests do not require that samples come from populations with normal distributions or any other specific distribution. Hence they are sometimes called distribution-free tests. They may have other more easily satisfied assumptions - such as requiring that the population distribution is symmetric. In general, when the parametric assumptions are satisfied, it is better to use parametric test procedures. However, nonparametric test procedures are a valuable tool to use when those assumptions are not satisfied, and most have pretty high efficiency relative to the corresponding parametric test when the parametric assumptions are satisfied. This means you usually don t lose much testing power if you swap to the nonparametric test even when not necessary. The exception is the sign test, discussed below. The following table discusses the parametric and corresponding nonparametric tests we have covered so far. (z-test, t-test, F-test refer to the parametric test statistics used in each procedure). Parameter Parametric Test Nonparametric Test π One sample z-test Exact Binomial µ or µ d One sample t-test Sign test or Wilcoxon Signed-Ranks test µ 1 µ 2 Two sample t-test Wilcoxon Rank-Sum test ANOVA F-test Kruskal-Wallis As a note on p-values before we proceed, details of computations of p-values are left out of this discussion. Usually these are found by considering the distribution of the test statistic across all possible permutations of ranks, etc. in each case. It is very tedious to do by hand, which is why there are established tables for it, or why we rely on the computer to do it. The examples throughout these notes are brief - I do not list the hypotheses or check the assumptions explicitly. Assume α =.05. You should be able to determine the hypotheses as we discuss the examples as well as make a decision based on the reported p-value. Finally, you are NOT expected to know how to do these tests by hand or even the R command. At most, you will be asked which nonparametric test to use (see chart above) and to make a decision based on a p-value from one of these tests (decision rule still applies). You will NOT have to list these assumptions, etc. I am providing some of the details as a reference for you if you want to employ these in your project or some other future time. References: Devore and Peck. Fifth edition. Has short descriptions of each test. Was removed to an optional online chapter in our Sixth edition. Triola. Elementary Statistics. Has a chapter on nonparametrics - no discussion of binomial. Hollander and Wolfe. Nonparametric Statistical Methods. In-depth explanation of each of these and more. 1

2 2 Exact Binomial Test for a Population Proportion π Situation: You observe n (fixed) number of trials with only 2 possible outcomes per trial. Hypotheses: Same forms as for a population proportion z-test (Combined with n fixed these are the conditions for a binomial) 1. The trials must be independent. 2. The two outcomes can be considered successes and failures. 3. Probability of success is constant for all trials. Test Procedure: Let B be the number of successes in your sample. B is used as the test statistic. The p-value is computed based on the Binomial distribution as the probability of observing B successes or more extreme in the direction of your alternative for a given probability of success in the null hypothesis, denoted π 0. Function in R: binom.test(x, n, p = 0.5, alternative = c( two.sided, less, greater )) x is the number of successes, n is the number of trials, p= hypothesized probability of success (can be changed) = π 0, and pick the appropriate alternative Benefits: This allows you to do an exact binomial test for small samples where nπ 0 and n(1 π 0 ) are not both 10. You can also do an exact binomial test for larger samples and see how close the z-test approximation is to the exact p-value. Example: You want to test whether or not a coin is fair by flipping it. Imagine you only have time for 10 flips and 8 come up heads. Is this enough information to conclude that the coin is not fair? binom.test(8,10,p=.5,alternative= two.sided ) Exact binomial test data: 8 and 10 number of successes = 8, number of trials = 10, p-value = alternative hypothesis: true probability of success is not equal to percent confidence interval: sample estimates: probability of success Sign Test for a Population Median Can use as paired test on the differences Situation: You observe n observations from a population or 2n observations which are paired 2

3 leaving you with n differences after the differences have been computed. Hypotheses: Same forms as for µ (or µ d ) except µ is replaced by median - θ (or θ d ). 1. The n observations or n differences are independent. 2. The observations or differences come from a continuous population which has a median θ and which is symmetric. Test Procedure: Compute the differences as observations minus hypothesized value or as the differences (given a specific subtraction order) if paired. Count the number of positive differences - that is the test statistic. An equal number of positive and negative differences is expected if the null hypothesis is true. Compute the p-value as the probability you observe your number of positive differences or more extreme using binomial probabilities. Function in R: No direct function, but can be done using binomial probabilities. Adjustments do need to be made for upper/lower/two-tailed tests. Benefits/Issues: Simplistic idea. Not used often because it has low relative efficiency compared to parametric test. You lose all information about the magnitude of the differences, which can be very important. The Signed-Rank test is a better choice. For example, for the sign test, both of the following data sets would have the same test statistic of 3. But you lose all information about spread. Data set 1: -1, -.5, -.25, 1, 2, 3 Data set 2: -1, -.5, -.25, 2, 6, Wilcoxon Signed-Rank Test for a Population Median Can use as paired test on the differences Situation: You observe n observations from a population or 2n observations which are paired leaving you with n differences after the differences have been computed. Hypotheses: Same forms as for µ (or µ d ) except µ is replaced by median - θ (or θ d ). 1. The n observations or n differences are independent. 2. The observations or differences come from a continuous population which has a median θ and which is symmetric. Test Procedure: If dealing with observations, the test computes observations minus hypothesized θ to get differences. Starting with the differences (if the median really is θ, these differences should be symmetric around 0), compute their absolute values. Rank each difference by absolute value 3

4 (small to large) and add up the ranks of the differences which are positive as your test statistic. Example: If your observations are 4, 14, 19, 30, 59 and θ is hypothesized to be 25, the test first computes the differences 4-25, 14-25, 19-25, 30-25, Those differences are -21, -11, -6, 5, 34. The ranked absolute values of the differences are 4,3,2,1, and 5 respectively. The sums of the ranks for the positive differences are 1+5=6. The test then finds the probability of getting that test statistic or something more extreme. Function in R: wilcox.test(x,y,paired=f or T,alternative=,mu=hypothesized value (default 0)) If doing a one-sample test for µ, you would run wilcox.test(x,mu=hyp value, alternative = two.sided ) and fill in the value for hypothesized value and change alternative to match what you have. If doing a one-sample test for µ d, you would run wilcox.test(x,y,paired=t,alternative = two.sided ) and change the alternative to match what you have. x and y are the before/after scores or whatever that you want the differences computed between. Benefits: Does not lose all information about magnitude of differences. Has high relative efficiency compared to parametric test. Example: The paired example we did in class on spending amounts comparing actual and budgeted amounts did not satisfy the normal distribution assumption for the population. In that situation, you might try to do a nonparametric test due to assumption worries (even with n=42). Below is another example paired test where the qq-plot looked very bad, but also had a very small sample size, n=15. For this example, the p-value in the parametric test was.04934, but there are major concerns about assumptions being violated. x=firm, y=audit wilcox.test(x, y, paired = TRUE, alternative = greater ) Wilcoxon signed rank test with continuity correction data: x and y V = 97.5, p-value = alternative hypothesis: true location shift is greater than 0 Warning message: In wilcox.test.default(x, y, paired = TRUE, alternative = greater ) : cannot compute exact p-value with ties There are some ties with ranks that appear here, and the output lets you know that the p-values are therefore approximate. 5 Wilcoxon Rank-Sum Test for a difference in two Population Means Can also be done using the Mann-Whitney U statistic Situation: You obtain n+m observations from two groups and you want to compare their medians. Hypotheses: This is a little different than anything we have seen. In probability, there is something called a distribution function and this test tests for equality of the distribution functions 4

5 explicitly. However, it is equivalent to say that it tests for the equality of population medians instead of means (which was the parametric test), with hypotheses now in terms of medians as θ 1 θ The samples from each populations were random samples. 2. The samples were independent. 3. Both populations are continuous. Test Procedure: Sort the combined observations and compute their ranks. The test statistic is the sum of ranks of observations from the second sample. Compute p-value accordingly. Note that the expected value of the test statistic here depends on the sample sizes - you would expect different values depending on how many observations were in each sample. This is less intuitive than expecting a zero difference like in the sign test. Function in R: wilcox.test(x,y,alternative = ) x and y are the two sets of observations (do not need to be same length), and set alternative as appropriate. Benefits: Does not require parametric assumptions. Keeps information about magnitude by using combined rank values. Has high relative efficiency compared to parametric test. Example: Salamander data: Assume instead of 35 male and 42 female salamanders as before we only had 4 males and 6 females with length measurements as below. We perform a test to see if females are longer than males based on medians (note, putting females first means > in the alternative). females=c(59.66,71.64,61.38,67.96,63.56,64.23) males=c(62.49,59.04,58.49,62.39) wilcox.test(females,males,alternative= greater ) Wilcoxon rank sum test data: females and males W = 20, p-value = alternative hypothesis: true location shift is greater than 0 Here is the parametric test on just these 10 combined observations, just so you can see the difference: t.test(females,males,alternative= greater ) Welch Two Sample t-test data: females and males t = , df = 7.579, p-value = alternative hypothesis: true difference in means is greater than 0 95 percent confidence interval: Inf sample estimates: mean of x mean of y

6 6 Nonparametric ANOVA - Kruskal-Wallis for General Alternatives Situation: You have n total observations from k populations (i.e. k samples) and you want to compare their medians. (It s actually a bit more general than that but that is enough detail to get the gist of it). Hypotheses: Same forms as ANOVA, just with µ i replaced by θ i for medians. 1. The k samples were independent. 2. Each sample was a random sample. 3. The populations are related by at most a shift in distribution function (this means the populations differ at most by their medians but other characteristics are the same). Test Procedure: Combine all samples. Rank all observations. Compute the sum of ranks for each sample. Compute average rank of each sample. Combine that information into a test statistic and compute p-value. Function in R: For an example with k = 3, let x, y, z be the list of observations in each sample. Then run kruskal.test(list(x,y,z)) No information about alternatives is required since this is like an ANOVA. Benefits: You don t need the requirement that all populations are normally distributed, though you still need spreads to be somewhat similar. More advanced versions for directed alternatives (called umbrella hypotheses) exist. Has pretty high relative efficiency compared to ANOVA, but less efficient than either of the Wilcoxon methods compared to their parametric counterparts. Example: Flammability study from class Five labs are being compared based on a clothing flammability test. Each lab tested 11 samples of the same fabric. lab1=c(2.9,3.1,3.1,3.7,3.1,4.2,3.7,3.9,3.1,3.0,2.9) lab2=c(2.7,3.4,3.6,3.2,4.0,4.1,3.8,3.8,4.3,3.4,3.3) lab3=c(3.3,3.3,3.5,3.5,2.8,2.8,3.2,2.8,3.8,3.5,3.8) lab4=c(3.3,3.2,3.4,2.7,2.7,3.3,2.9,3.2,2.9,2.6,2.8) lab5=c(4.1,4.1,3.7,4.2,3.1,3.5,2.8,3.5,3.7,3.5,3.9) kruskal.test(list(lab1,lab2,lab3,lab4,lab5)) Kruskal-Wallis rank sum test data: list(lab1, lab2, lab3, lab4, lab5) Kruskal-Wallis chi-squared = , df = 4, p-value =

3. Nonparametric methods

3. Nonparametric methods If the probability distributions of the statistical variables are unknown or are not as required (e.g. normality assumption violated), then we may still apply nonparametric tests

Nonparametric Statistics

1 14.1 Using the Binomial Table Nonparametric Statistics In this chapter, we will survey several methods of inference from Nonparametric Statistics. These methods will introduce us to several new tables

Chapter 16 Appendix. Nonparametric Tests with Excel, JMP, Minitab, SPSS, CrunchIt!, R, and TI-83-/84 Calculators

The Wilcoxon Rank Sum Test Chapter 16 Appendix Nonparametric Tests with Excel, JMP, Minitab, SPSS, CrunchIt!, R, and TI-83-/84 Calculators These nonparametric tests make no assumption about Normality.

QUANTITATIVE METHODS BIOLOGY FINAL HONOUR SCHOOL NON-PARAMETRIC TESTS

QUANTITATIVE METHODS BIOLOGY FINAL HONOUR SCHOOL NON-PARAMETRIC 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.

NONPARAMETRIC 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 p-values classical significance testing depend on assumptions

Nonparametric tests these test hypotheses that are not statements about population parameters (e.g.,

CHAPTER 13 Nonparametric and Distribution-Free Statistics Nonparametric tests these test hypotheses that are not statements about population parameters (e.g., 2 tests for goodness of fit and independence).

Wilcoxon Rank Sum or Mann-Whitney Test Chapter 7.11

STAT Non-Parametric tests /0/0 Here s a summary of the tests we will look at: Setting Normal test NonParametric Test One sample One-sample t-test Sign Test Wilcoxon signed-rank test Matched pairs Apply

T adult = 96 T child = 114.

Homework Solutions Do all tests at the 5% level and quote p-values when possible. When answering each question uses sentences and include the relevant JMP output and plots (do not include the data in your

Outline of Topics. Statistical Methods I. Types of Data. Descriptive Statistics

Statistical Methods I Tamekia L. Jones, Ph.D. (tjones@cog.ufl.edu) Research Assistant Professor Children s Oncology Group Statistics & Data Center Department of Biostatistics Colleges of Medicine and Public

Non-Parametric Tests (I)

Lecture 5: Non-Parametric 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 Distribution-Free Tests (ii) Median Test for Two Independent

Analysis of numerical data S4

Basic medical statistics for clinical and experimental research Analysis of numerical data S4 Katarzyna Jóźwiak k.jozwiak@nki.nl 3rd November 2015 1/42 Hypothesis tests: numerical and ordinal data 1 group:

Statistiek I. t-tests. John Nerbonne. CLCG, Rijksuniversiteit Groningen. John Nerbonne 1/35

Statistiek I t-tests John Nerbonne CLCG, Rijksuniversiteit Groningen http://wwwletrugnl/nerbonne/teach/statistiek-i/ John Nerbonne 1/35 t-tests To test an average or pair of averages when σ is known, we

Rank-Based Non-Parametric Tests

Rank-Based Non-Parametric 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

Hypothesis Testing. Dr. Bob Gee Dean Scott Bonney Professor William G. Journigan American Meridian University

Hypothesis Testing Dr. Bob Gee Dean Scott Bonney Professor William G. Journigan American Meridian University 1 AMU / Bon-Tech, LLC, Journi-Tech Corporation Copyright 2015 Learning Objectives Upon successful

SCHOOL 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

Statistical Significance and Bivariate Tests

Statistical Significance and Bivariate Tests BUS 735: Business Decision Making and Research 1 1.1 Goals Goals Specific goals: Re-familiarize ourselves with basic statistics ideas: sampling distributions,

Module 9: Nonparametric Tests. The Applied Research Center

Module 9: Nonparametric Tests The Applied Research Center Module 9 Overview } Nonparametric Tests } Parametric vs. Nonparametric Tests } Restrictions of Nonparametric Tests } One-Sample Chi-Square Test

Structure of the Data. Paired Samples. Overview. The data from a paired design can be tabulated in this form. Individual Y 1 Y 2 d i = Y 1 Y

Structure of the Data Paired Samples Bret Larget Departments of Botany and of Statistics University of Wisconsin Madison Statistics 371 11th November 2005 The data from a paired design can be tabulated

1/22/2016. What are paired data? Tests of Differences: two related samples. What are paired data? Paired Example. Paired Data.

Tests of Differences: two related samples What are paired data? Frequently data from ecological work take the form of paired (matched, related) samples Before and after samples at a specific site (or individual)

Nonparametric Two-Sample Tests. Nonparametric Tests. Sign Test

Nonparametric Two-Sample Tests Sign test Mann-Whitney U-test (a.k.a. Wilcoxon two-sample test) Kolmogorov-Smirnov Test Wilcoxon Signed-Rank Test Tukey-Duckworth Test 1 Nonparametric Tests Recall, nonparametric

Chapter 3: Nonparametric Tests

B. Weaver (15-Feb-00) Nonparametric Tests... 1 Chapter 3: Nonparametric Tests 3.1 Introduction Nonparametric, or distribution free tests are so-called because the assumptions underlying their use are fewer

CHAPTER 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

Hypothesis Testing Level I Quantitative Methods. IFT Notes for the CFA exam

Hypothesis Testing 2014 Level I Quantitative Methods IFT Notes for the CFA exam Contents 1. Introduction... 3 2. Hypothesis Testing... 3 3. Hypothesis Tests Concerning the Mean... 10 4. Hypothesis Tests

Supplement on the Kruskal-Wallis test. So what do you do if you don t meet the assumptions of an ANOVA?

Supplement on the Kruskal-Wallis test So what do you do if you don t meet the assumptions of an ANOVA? {There are other ways of dealing with things like unequal variances and non-normal data, but we won

StatCrunch 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

Comparing 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

MAT X Hypothesis Testing - Part I

MAT 2379 3X Hypothesis Testing - Part I Definition : A hypothesis is a conjecture concerning a value of a population parameter (or the shape of the population). The hypothesis will be tested by evaluating

NCSS Statistical Software. One-Sample T-Test

Chapter 205 Introduction This procedure provides several reports for making inference about a population mean based on a single sample. These reports include confidence intervals of the mean or median,

Permutation & Non-Parametric Tests

Permutation & Non-Parametric 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

Non-Parametric Two-Sample Analysis: The Mann-Whitney U Test

Non-Parametric Two-Sample Analysis: The Mann-Whitney U Test When samples do not meet the assumption of normality parametric tests should not be used. To overcome this problem, non-parametric tests can

Statistics. One-two sided test, Parametric and non-parametric test statistics: one group, two groups, and more than two groups samples

Statistics One-two sided test, Parametric and non-parametric test statistics: one group, two groups, and more than two groups samples February 3, 00 Jobayer Hossain, Ph.D. & Tim Bunnell, Ph.D. Nemours

NCSS Statistical Software

Chapter 06 Introduction This procedure provides several reports for the comparison of two distributions, including confidence intervals for the difference in means, two-sample t-tests, the z-test, the

SPSS 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

CHAPTER 11 CHI-SQUARE: NON-PARAMETRIC COMPARISONS OF FREQUENCY

CHAPTER 11 CHI-SQUARE: NON-PARAMETRIC COMPARISONS OF FREQUENCY The hypothesis testing statistics detailed thus far in this text have all been designed to allow comparison of the means of two or more samples

Nonparametric 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

Non-parametric tests I

Non-parametric tests I Objectives Mann-Whitney Wilcoxon Signed Rank Relation of Parametric to Non-parametric tests 1 the problem Our testing procedures thus far have relied on assumptions of independence,

Contents 1. Contents

Contents 1 Contents 3 K-sample Methods 2 3.1 Setup............................ 2 3.2 Classic Method Based on Normality Assumption..... 3 3.3 Permutation F -test.................... 5 3.4 Kruskal-Wallis

Nonparametric tests, Bootstrapping

Nonparametric tests, Bootstrapping http://www.isrec.isb-sib.ch/~darlene/embnet/ Hypothesis testing review 2 competing theories regarding a population parameter: NULL hypothesis H ( straw man ) ALTERNATIVEhypothesis

Stat 371, Cecile Ane Practice problems Midterm #2, Spring 2012

Stat 371, Cecile Ane Practice problems Midterm #2, Spring 2012 The first 3 problems are taken from previous semesters exams, with solutions at the end of this document. The other problems are suggested

Lecture 7: Binomial Test, Chisquare

Lecture 7: Binomial Test, Chisquare Test, and ANOVA May, 01 GENOME 560, Spring 01 Goals ANOVA Binomial test Chi square test Fisher s exact test Su In Lee, CSE & GS suinlee@uw.edu 1 Whirlwind Tour of One/Two

SPSS Explore procedure

SPSS Explore procedure One useful function in SPSS is the Explore procedure, which will produce histograms, boxplots, stem-and-leaf plots and extensive descriptive statistics. To run the Explore procedure,

Suggested solution for exam in MSA830: Statistical Analysis and Experimental Design October 2009

Petter Mostad Matematisk Statistik Chalmers Suggested solution for exam in MSA830: Statistical Analysis and Experimental Design October 2009 1. (a) To use a t-test, one must assume that both groups of

Hypothesis testing. c 2014, Jeffrey S. Simonoff 1

Hypothesis testing So far, we ve talked about inference from the point of estimation. We ve tried to answer questions like What is a good estimate for a typical value? or How much variability is there

Chapter 21 Section D

Chapter 21 Section D Statistical Tests for Ordinal Data The rank-sum test. You can perform the rank-sum test in SPSS by selecting 2 Independent Samples from the Analyze/ Nonparametric Tests menu. The first

Nonparametric 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

We know from STAT.1030 that the relevant test statistic for equality of proportions is:

2. Chi 2 -tests for equality of proportions Introduction: Two Samples Consider comparing the sample proportions p 1 and p 2 in independent random samples of size n 1 and n 2 out of two populations which

STA218 Introduction to Hypothesis Testing

STA218 Introduction to Hypothesis Testing Al Nosedal. University of Toronto. Fall 2015 October 29, 2015 Who wants to be a millionaire? Let s say that one of you is invited to this popular show. As you

Projects 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,

Once saved, if the file was zipped you will need to unzip it.

1 Commands in SPSS 1.1 Dowloading data from the web The data I post on my webpage will be either in a zipped directory containing a few files or just in one file containing data. Please learn how to unzip

Testing Group Differences using T-tests, ANOVA, and Nonparametric Measures

Testing Group Differences using T-tests, ANOVA, and Nonparametric Measures Jamie DeCoster Department of Psychology University of Alabama 348 Gordon Palmer Hall Box 870348 Tuscaloosa, AL 35487-0348 Phone:

Tests of relationships between variables Chi-square Test Binomial Test Run Test for Randomness One-Sample Kolmogorov-Smirnov Test.

N. Uttam Singh, Aniruddha Roy & A. K. Tripathi ICAR Research Complex for NEH Region, Umiam, Meghalaya uttamba@gmail.com, aniruddhaubkv@gmail.com, aktripathi2020@yahoo.co.in Non Parametric Tests: Hands

Business Statistics. Lecture 8: More Hypothesis Testing

Business Statistics Lecture 8: More Hypothesis Testing 1 Goals for this Lecture Review of t-tests Additional hypothesis tests Two-sample tests Paired tests 2 The Basic Idea of Hypothesis Testing Start

Difference tests (2): nonparametric

NST 1B Experimental Psychology Statistics practical 3 Difference tests (): nonparametric Rudolf Cardinal & Mike Aitken 10 / 11 February 005; Department of Experimental Psychology University of Cambridge

Tutorial 5: Hypothesis Testing

Tutorial 5: Hypothesis Testing Rob Nicholls nicholls@mrc-lmb.cam.ac.uk MRC LMB Statistics Course 2014 Contents 1 Introduction................................ 1 2 Testing distributional assumptions....................

Bowerman, O'Connell, Aitken Schermer, & Adcock, Business Statistics in Practice, Canadian edition Online Learning Centre Technology Step-by-Step - Excel Microsoft Excel is a spreadsheet software application

How to choose a statistical test. Francisco J. Candido dos Reis DGO-FMRP University of São Paulo

How to choose a statistical test Francisco J. Candido dos Reis DGO-FMRP University of São Paulo Choosing the right test One of the most common queries in stats support is Which analysis should I use There

Statistical 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

Come scegliere un test statistico

Come scegliere un test statistico Estratto dal Capitolo 37 of Intuitive Biostatistics (ISBN 0-19-508607-4) by Harvey Motulsky. Copyright 1995 by Oxfd University Press Inc. (disponibile in Iinternet) Table

Once 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

Univariate and Bivariate Tests

Univariate and BUS 230: Business and Economics Research and Communication Univariate and Goals Hypotheses Tests Goals 1/ 20 Specific goals: Be able to distinguish different types of data and prescribe

Module 5 Hypotheses Tests: Comparing Two Groups

Module 5 Hypotheses Tests: Comparing Two Groups Objective: In medical research, we often compare the outcomes between two groups of patients, namely exposed and unexposed groups. At the completion of this

Paired T-Test. Chapter 208. Introduction. Technical Details. Research Questions

Chapter 208 Introduction This procedure provides several reports for making inference about the difference between two population means based on a paired sample. These reports include confidence intervals

Chi Square Analysis. When do we use chi square?

Chi Square Analysis When do we use chi square? More often than not in psychological research, we find ourselves collecting scores from participants. These data are usually continuous measures, and might

Formulas and Tables by Mario F. Triola

Formulas and Tables by Mario F. Triola Copyright 010 Pearson Education, Inc. Ch. 3: Descriptive Statistics x Mean f # x x f Mean (frequency table) 1x - x s B n - 1 Standard deviation n 1 x - 1 x Standard

Lecture 1: t tests and CLT

Lecture 1: t tests and CLT http://www.stats.ox.ac.uk/ winkel/phs.html Dr Matthias Winkel 1 Outline I. z test for unknown population mean - review II. Limitations of the z test III. t test for unknown population

ISyE 2028 Basic Statistical Methods - Fall 2015 Bonus Project: Big Data Analytics Final Report: Time spent on social media

ISyE 2028 Basic Statistical Methods - Fall 2015 Bonus Project: Big Data Analytics Final Report: Time spent on social media Abstract: The growth of social media is astounding and part of that success was

Hypothesis testing. Null hypothesis H 0 and alternative hypothesis H 1.

Hypothesis testing Null hypothesis H 0 and alternative hypothesis H 1. Hypothesis testing Null hypothesis H 0 and alternative hypothesis H 1. Simple and compound hypotheses. Simple : the probabilistic

Inferential Statistics. Probability. From Samples to Populations. Katie Rommel-Esham Education 504

Inferential Statistics Katie Rommel-Esham Education 504 Probability Probability is the scientific way of stating the degree of confidence we have in predicting something Tossing coins and rolling dice

One-Way Analysis of Variance (ANOVA) Example Problem

One-Way Analysis of Variance (ANOVA) Example Problem Introduction Analysis of Variance (ANOVA) is a hypothesis-testing technique used to test the equality of two or more population (or treatment) means

For example, enter the following data in three COLUMNS in a new View window.

Statistics with Statview - 18 Paired t-test A paired t-test compares two groups of measurements when the data in the two groups are in some way paired between the groups (e.g., before and after on the

PROBLEM SET 1 For the first three answer true or false and explain your answer. A picture is often helpful. 1. Suppose the significance level of a hypothesis test is α=0.05. If the p-value of the test

Statistics: revision

NST 1B Experimental Psychology Statistics practical 5 Statistics: revision Rudolf Cardinal & Mike Aitken 3 / 4 May 2005 Department of Experimental Psychology University of Cambridge Slides at pobox.com/~rudolf/psychology

1. Rejecting a true null hypothesis is classified as a error. 2. Failing to reject a false null hypothesis is classified as a error.

1. Rejecting a true null hypothesis is classified as a error. 2. Failing to reject a false null hypothesis is classified as a error. 8.5 Goodness of Fit Test Suppose we want to make an inference about

1 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

Study 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

Part 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

Non-Inferiority Tests for One Mean

Chapter 45 Non-Inferiority ests for One Mean Introduction his module computes power and sample size for non-inferiority tests in one-sample designs in which the outcome is distributed as a normal random

ANOVA Analysis of Variance

ANOVA Analysis of Variance What is ANOVA and why do we use it? Can test hypotheses about mean differences between more than 2 samples. Can also make inferences about the effects of several different IVs,

Comparing two groups (t tests...)

Page 1 of 33 Comparing two groups (t tests...) You've measured a variable in two groups, and the means (and medians) are distinct. Is that due to chance? Or does it tell you the two groups are really different?

Recall this chart that showed how most of our course would be organized:

Chapter 4 One-Way ANOVA Recall this chart that showed how most of our course would be organized: Explanatory Variable(s) Response Variable Methods Categorical Categorical Contingency Tables Categorical

Parametric 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

Data Analysis. Lecture Empirical Model Building and Methods (Empirische Modellbildung und Methoden) SS Analysis of Experiments - Introduction

Data Analysis Lecture Empirical Model Building and Methods (Empirische Modellbildung und Methoden) Prof. Dr. Dr. h.c. Dieter Rombach Dr. Andreas Jedlitschka SS 2014 Analysis of Experiments - Introduction

Inferential Statistics

Inferential Statistics Sampling and the normal distribution Z-scores Confidence levels and intervals Hypothesis testing Commonly used statistical methods Inferential Statistics Descriptive statistics are

LAB 4 INSTRUCTIONS CONFIDENCE INTERVALS AND HYPOTHESIS TESTING

LAB 4 INSTRUCTIONS CONFIDENCE INTERVALS AND HYPOTHESIS TESTING In this lab you will explore the concept of a confidence interval and hypothesis testing through a simulation problem in engineering setting.

Testing: is my coin fair?

Testing: is my coin fair? Formally: we want to make some inference about P(head) Try it: toss coin several times (say 7 times) Assume that it is fair ( P(head)= ), and see if this assumption is compatible

A) to D) to B) to E) to C) to Rate of hay fever per 1000 population for people under 25

Unit 0 Review #3 Name: Date:. Suppose a random sample of 380 married couples found that 54 had two or more personality preferences in common. In another random sample of 573 married couples, it was found

Nonparametric statistics and model selection

Chapter 5 Nonparametric statistics and model selection In Chapter, we learned about the t-test and its variations. These were designed to compare sample means, and relied heavily on assumptions of normality.

Some Critical Information about SOME Statistical Tests and Measures of Correlation/Association

Some Critical Information about SOME Statistical Tests and Measures of Correlation/Association This information is adapted from and draws heavily on: Sheskin, David J. 2000. Handbook of Parametric and

Non-Inferiority Tests for Two Means using Differences

Chapter 450 on-inferiority Tests for Two Means using Differences Introduction This procedure computes power and sample size for non-inferiority tests in two-sample designs in which the outcome is a continuous

General Method: Difference of Means. 3. Calculate df: either Welch-Satterthwaite 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 Welch-Satterthwaite formula or simpler df = min(n

The Statistics Tutor s

statstutor community project encouraging academics to share statistics support resources All stcp resources are released under a Creative Commons licence Stcp-marshallowen-7 The Statistics Tutor s www.statstutor.ac.uk

CHAPTER 12 TESTING DIFFERENCES WITH ORDINAL DATA: MANN WHITNEY U

CHAPTER 12 TESTING DIFFERENCES WITH ORDINAL DATA: MANN WHITNEY U Previous chapters of this text have explained the procedures used to test hypotheses using interval data (t-tests and ANOVA s) and nominal

Nonparametric Methods for Two Samples. Nonparametric Methods for Two Samples

Nonparametric Methods for Two Samples An overview In the independent two-sample t-test, we assume normality, independence, and equal variances. This t-test is robust against nonnormality, but is sensitive

Permutation Tests for Comparing Two Populations

Permutation Tests for Comparing Two Populations Ferry Butar Butar, Ph.D. Jae-Wan Park Abstract Permutation tests for comparing two populations could be widely used in practice because of flexibility of

Overview of Non-Parametric Statistics PRESENTER: ELAINE EISENBEISZ OWNER AND PRINCIPAL, OMEGA STATISTICS

Overview of Non-Parametric Statistics PRESENTER: ELAINE EISENBEISZ OWNER AND PRINCIPAL, OMEGA STATISTICS About Omega Statistics Private practice consultancy based in Southern California, Medical and Clinical

Biostatistics Lab Notes

Biostatistics Lab Notes Page 1 Lab 1: Measurement and Sampling Biostatistics Lab Notes Because we used a chance mechanism to select our sample, each sample will differ. My data set (GerstmanB.sav), looks

Statistics for Management II-STAT 362-Final Review

Statistics for Management II-STAT 362-Final Review Multiple Choice Identify the letter of the choice that best completes the statement or answers the question. 1. The ability of an interval estimate to

Biodiversity Data Analysis: Testing Statistical Hypotheses By Joanna Weremijewicz, Simeon Yurek, Steven Green, Ph. D. and Dana Krempels, Ph. D.

Biodiversity Data Analysis: Testing Statistical Hypotheses By Joanna Weremijewicz, Simeon Yurek, Steven Green, Ph. D. and Dana Krempels, Ph. D. In biological science, investigators often collect biological