Statistics for Sports Medicine

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Statistics for Sports Medicine"

Transcription

1 Statistics for Sports Medicine Suzanne Hecht, MD University of Minnesota Fellow s Research Conference July 2012: Philadelphia

2

3 GOALS Try not to bore you to death!! Try to teach you something useful Introduce concepts Give you a stats reference guide Encourage sports med research

4

5 QUIZ What is the appropriate stats test to apply?. 50 soccer players wore head gear & 40 did not. Players were followed for diagnosis of concussion over one season. 1. Paired two tailed t-test 2. ANOVA 3. Chi-square analysis 4. McNemar test

6 MY TOP 10 STATS TIP LIST

7 OVERVIEW Introduction Variables Normal distribution Hypothesis testing Comparing means Measuring association Scatterplots & Correlation Regression

8 PURPOSE Stats is just a tool to analyze data you collect Learn the basics Add to your foundation over time Lots of names of tests, just like Sports Medicine!! You wouldn t talk about a Jobe s test during a knee exam Mt Stats

9 PURPOSE Infer something about a population based on information from a sample of that population Use probability concepts Describe how reliable the conclusions are ie: You have all this data & is it useful in someway?

10 MY TOP 10 STATS TIP LIST

11 Variables Discrete Examples Gender (m/f); Fracture (y/n) Nominal or Ordinal Nominal: Set of categories, no ordering ie: m/f Ordinal: Ordering, but no meaning to differences in scores ie Compare 1 st & 2 nd place finishers (ranking) without using actual times Continuous Examples Weight, race time Differences between values has meaning

12 USE FOR FUTURE REFERENCE Variable Summary Statistics Comparing 2 groups Measuring Association Nominal Mode Chi-square Contingency Coefficient Ordinal Median Chi-square Nonparametric Kappa Spearman r Kendall s tao Continuous Mean Median & SD t-test Nonparametric Spearman r Pearson r

13 SAMPLE SIZE & POWER Important to calculate Do this prior to the study Avoid expenses, time, resources, etc. Calculations available in stats software Let s you know that you have enough subjects to detect a meaningful change

14 HYPOTHESIS TESTING Null hypothesis (H 0 ) No difference between groups (groups are the same) Alternative hypothesis (H 1 ) There is a difference between groups Type I error Saying groups are different when they aren t Type II error Saying groups are the same when they are different

15 MY TOP 10 STATS TIP LIST

16 Normal Distribution Applies to continuous variables Mean=median=mode Many stats tests assume nl distr t-test; ANOVA; regression Ways to test to see if a nl distribution Use non-parametric tests or transform data (ie log) if not a nl distribution Methods that assume nl distr Robust to moderate departures of nl distr assumption if n is large enough!

17 Normal Distribution Symmetrical about the mean BLUE= 68.2% of values w/in 1 SD BLUE+ BROWN= 95.4% of values w/in 2 SD BLUE + BROWN + GREEN= 99.7% of values w/in 3 SD

18 P-Value = the probability of obtaining results by chance alone p=0.05 (5% chance) May not tell whole story Statistically significant Clinically significant Small or large n s Small n: Type II error Give both: p-value & CI

19 MY TOP 10 STATS TIP LIST

20

21 Comparing 2 groups or rxs Type of Outcome Continuous Binary (y/n) Nl Distribution Paired Unpaired Paired t-test Yes Parametric Unpaired t-test Sign test No Nonparametric Paired Sign rank test McNemar s test Unpaired Wilcoxon rank sum test Yes Large Sample Size Chi-Squared No Fischer s Exact Test

22 Comparing 3 or > groups Type of Outcome Continuous Binary (y/n) Nl Distribution Yes Parametric No Nonparametric Frequency Tables Chi-squared Methods ANOVA Kruskal- Wallis Test

23 Comparing 2 groups or rxs Type of Outcome Continuous Binary (y/n) Nl Distribution Yes No Parametric Nonparametric Paired Unpaired Paired Unpaired t-test t-test Sign test Sign rank test Wilcoxon rank sum test

24 Comparing Group Means t-test ANOVA Assumptions Data is continuous & nl distributed Methods 2 indep samples: 2 sample t-test Paired data: Paired t-test >2 indep samples: ANOVA Includes Confidence intervals Hypothesis testing

25 3 types 2 sample t-test Student s t-test t-tests Independent samples t-test Paired samples t-test Paired data: 2 measurements on same subject or test unit One sample t-test Compare to a known (norm) value

26 t-tests One-tailed vs two-tailed Almost always use two-tailed Results could be higher or lower not just one way

27 95% CI Confidence Intervals 95% confident that the true value falls in the interval. Wide CI suggests uncertainty about data Does the CI contain a value that implies no change or no effect? Mean: 0 Odds ratio: 1 Does the confidence interval lie partly or entirely within a range of clinical indifference?

28 Example: Confidence Intervals Survey 19 millionaires Mean income donation=15% +/- 2 SD CI: +/- 2.4% Interpretation We are 95% confident that millionaires donate between % of their income.

29 Comparing 2 groups or rxs Type of Outcome Continuous Binary (y/n) Nl Distribution Yes No Parametric Nonparametric Paired Unpaired Paired Unpaired t-test t-test Sign test Sign rank test Wilcoxon rank sum test

30 SIGN TEST Non-parametric test Not a nl distribution Alternative to paired t-test Good for small sample size Test the difference for matched pairs on before & after data Method: Calculate diffs Throw-out zero diff Test for # of + diff H 1 is true: median does not = 0

31 WILCOXON SIGN RANK TEST Same application as Sign Test Uses the ranks & the signs of diff More powerful test than Sign Test Method: Calculate differences in pairs Throw away zero differences Rank from smallest to largest difference w/out regard to +/- Test: sum of ranks of + diff

32 Wilcoxon Rank Sum Test Also known as: Mann-Whitney U test Comparing 2 independent samples Not nl distribution Good for detecting changes in medians Method: Combine data from 2 gps Rank smallest to largest Add ranks in the gp with smaller sample size Add ranks in gp with larger N Test: sum of ranks for smaller gp compared to larger gp

33 EXAMPLE: Rank-Sum Test Team Cheetah 5 team members Team Impala 7 team members Results TC: 3, 4, 7, 12, 13 (min) Results TI: 2, 5, 6, 8, 9, 10, 11 (min) Combine data & then rank: 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 Sum ranks of smaller gp = 34 Test if sum ranks of smaller gp is the same or different from other group

34 MY TOP 10 STATS TIP LIST

35 Comparing 3 or > groups Type of Outcome Continuous Binary (y/n) Nl Distribution Yes Parametric No Nonparametric Frequency Tables Chi-squared Methods ANOVA Kruskal- Wallis Test

36 ANOVA Analysis of variance Comparing means of >2 groups Assumes Continuous Nl distrib Same variance w/in each group Benefits compared to t-tests Efficiency Avoids multiple testing problem Problem Sign F test tells you that at least 2 gps are different, but not which ones!

37 ANOVA-Problem Multiple Comparisons Procedures Used to tell which groups differ Stricter levels for accepting/rejecting that the means are the same 4 methods Bonferroni Tukey Neuman-Keuls Scheffe

38 Kruskal-Wallis Test Nonparametric test Use for comparing 3 or > independent groups Think of as a non-parametric ANOVA test Good for detecting changes in median

39 MY TOP 10 STATS TIP LIST

40 Comparing 2 groups or rxs Type of Outcome Continuous Binary (y/n) Paired Unpaired McNemar s test Yes Large Sample Size No Chi-Squared Fischer s Exact Test

41 Comparing Frequency Data Binary outcome (yes/no) Paired method McNemar s Test Non-paired methods Pearson s Chi-square Fisher s Exact Test

42 Assumes Pearson s Chi-square Random samples from 2 groups Compares expected with observed All samples sizes are large enough All frequencies must be > 5 2x2 table: Standard New Helmet Helmet Concussion No Concussion TOTAL n 1 =25 n 2 =19 p 1 =18/25 =0.72 (72%) p 2 =6/19 =0.32 (32%)

43 Pearson s Chi-square OBSERVED Standard Helmet New Helmet TOTAL Concussion No Concussion 7 13 TOTAL n 1 =25 n 2 = X 2 =7.1 (p=0.0077) EXPECTED (if not different) Concussion No Concussion Standard Helmet 24/44 x 25 = /44 x 25 =11.36 New Helmet 24/44 x 19 = /44 x 19 =8.64

44 Fisher s Exact Test Use this test when 1 or more of frequencies is < 5

45 McNemar s Test Use for paired binary data Same subject before & after rx Cross-over study

46 MY TOP 10 STATS TIP LIST

47 RISK Risk difference Absolute difference in risk proportions Can be difficult to interpret Relative Risk (RR) Also known as Risk Ratio Risk in 1 gp/risk in other gps Odds Ratio (OR) Probability or Odds of an event OR= odds of exposed gp/odds of control gp OR=1 means no difference

48 RELATIVE RISK Relative risk (RR) is the risk of an event relative to exposure. Risk of having a boy if mom took testosterone during pregnancy 75/100=75% Risk (probability) of having a boy= 51/100= 51% Risk Ratio=.75/.51=1.5 Easier to understand Risk ratio =0.5 =risk is half Risk ratio=2=risk is double

49 CALCULATING ODDS Odds of an event =# of events/# of nonevents 51 boys born for every 100 births Odds of any randomly chosen delivery being a boy=51/100-51=1.04 Odds>1: Event is more likely to happen than not Odds of certain event= Odds<1: Event is not likely to happen Odds of an impossible event=0

50 ODDS RATIO Testosterone example 75/ /100-51= 3/1.04= 2.9 The odds of having a boy is 2.9x higher in moms using testosterone vs mom s not using testosterone.

51 ODDS RATIO: Benefits No upper limit RR range varies depending on baseline prevalence When events are low (rare dz) OR approx RR OR ok to use with case control Don t use RR with case control

52 Calculating OR Cross Product Factor (Event) Group 1 Group 2 a b No Factor (No Event) c OR= a/c b/d d = a x d b x c Concussion No Concussion Standard New Helmet Helmet x 13 = x 7

53

54

55 MY TOP 10 STATS TIP LIST

56 SCATTERPLOT Can help answer the following Are variables X & Y related? Are X & Y linearly related? Are X & Y non-linearly related? Does the variation in Y change depending on X? Are there outliers? 1. Linear relationship 2. Small scatter (strong correlation) 3. + slope (+ correlation)

57 SCATTERPLOTS No relationship 1. Linear 2. Small scatter (strong correlation) 3. - slope (neg correlation)

58 SCATTERPLOTS Outlier Non-linear

59 CORRELATION: PEARSON Measures the strength of (linear) association between 2 variables Ranges from -1 to 1 1= -1= 0= Examples: r=0.8 r=0.3 r=-0.7 perfect + correlation perfect correlation no correlation strong + correlation weak + correlation moderate correlation

60 MY TOP 10 STATS TIP LIST

61 REGRESSION A straight line that describes the dependence of one variable on another is called a regression line Y=response variable ie finishing time X=explanatory variable ie body fat percentage Is finishing time predicted by body fat percentage?

62 Linear REGRESSION TYPES Data: Normal distribution Simple or Multiple Logistical Data: binary (y/n) Simple or Multiple Multiple Regression Models Allow estimation of the indep effect of each X after controlling for other variables in the model.

63 Simple LINEAR REGRESSION Use to predict Y given X Determine best fitting equation Test whether there is a relationship between X & Y

64 Linear Regression R 2 value =% of variance in Y explained by X If R 2 =1 then x can predict y 100% of the time F test for significance If p >0.05 then no significant relationship (slope of line =zero) exists between x & Y

65 Multiple Linear Regression Model that explains how a single dependent variable (Y) relates to several independent variables (x). Example: Test if age, gender, body fat %, prior triathlon competitions, & occupation predict finishing time.

66 Multiple Linear Regression How many variables to use? Recommend that you have 10-20x # of cases to variables tested. Test lots of variables Increase random chance of stat sign Model becomes unstable

67 Multiple Linear Regression Example cont: Model predicts 90% of variance in performance Now test for which variable or combinations of variables is most predictive Body fat %: 15% Age: 10% Gender: 30% Body fat & gender 35% Occupation 0% Prior triathlon 40%

68 MY TOP 10 STATS TIP LIST

69 QUIZ What is the appropriate stats test to apply?. 50 soccer players wore head gear & 40 did not. Players were followed for diagnosis of concussion over one season. 1. Paired two tailed t-test 2. ANOVA 3. Chi-square analysis 4. McNemar test

70 OTHER TIPS Stats support at Universities Usually charge per hour MS cheaper than PhD Authorship If stats person willing to: (International Committee of Medical Journal Editors (ICMJE) guidelines) Help design study Analyze data Format tables, graphs, etc Write a portion of article May be able to get small grant to cover $ of stats analysis On-line support

71

72 REFERENCES 1. Applied Biostatistics in Clinical Research Course Book; Case-Western Reserve General Clinical Research Center Biostatistics 100B Course Book; UCLA The Essentials of Clinical Investigation Course Book; UCLA Clinical Research Center Moore, McCabe, Craig (2009) Introduction to the Practice of Statistics, Sixth Edition. WH Freeman and Company, New York. ISBN-13:

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 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

More information

Descriptive Statistics

Descriptive Statistics Descriptive Statistics Primer Descriptive statistics Central tendency Variation Relative position Relationships Calculating descriptive statistics Descriptive Statistics Purpose to describe or summarize

More information

Analysing Questionnaires using Minitab (for SPSS queries contact -) Graham.Currell@uwe.ac.uk

Analysing Questionnaires using Minitab (for SPSS queries contact -) Graham.Currell@uwe.ac.uk Analysing Questionnaires using Minitab (for SPSS queries contact -) Graham.Currell@uwe.ac.uk Structure As a starting point it is useful to consider a basic questionnaire as containing three main sections:

More information

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

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

More information

The Dummy s Guide to Data Analysis Using SPSS

The Dummy s Guide to Data Analysis Using SPSS The Dummy s Guide to Data Analysis Using SPSS Mathematics 57 Scripps College Amy Gamble April, 2001 Amy Gamble 4/30/01 All Rights Rerserved TABLE OF CONTENTS PAGE Helpful Hints for All Tests...1 Tests

More information

UCLA STAT 13 Statistical Methods - Final Exam Review Solutions Chapter 7 Sampling Distributions of Estimates

UCLA STAT 13 Statistical Methods - Final Exam Review Solutions Chapter 7 Sampling Distributions of Estimates UCLA STAT 13 Statistical Methods - Final Exam Review Solutions Chapter 7 Sampling Distributions of Estimates 1. (a) (i) µ µ (ii) σ σ n is exactly Normally distributed. (c) (i) is approximately Normally

More information

Section 3 Part 1. Relationships between two numerical variables

Section 3 Part 1. Relationships between two numerical variables Section 3 Part 1 Relationships between two numerical variables 1 Relationship between two variables The summary statistics covered in the previous lessons are appropriate for describing a single variable.

More information

NONPARAMETRIC STATISTICS 1. depend on assumptions about the underlying distribution of the data (or on the Central Limit Theorem)

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

More information

Module 9: Nonparametric Tests. The Applied Research Center

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

More information

Biostatistics: Types of Data Analysis

Biostatistics: 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 information

Inferential Statistics

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

More information

Variables and Data A variable contains data about anything we measure. For example; age or gender of the participants or their score on a test.

Variables and Data A variable contains data about anything we measure. For example; age or gender of the participants or their score on a test. The Analysis of Research Data The design of any project will determine what sort of statistical tests you should perform on your data and how successful the data analysis will be. For example if you decide

More information

Non-parametric tests I

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,

More information

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

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

More information

II. DISTRIBUTIONS distribution normal distribution. standard scores

II. 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 information

X X X a) perfect linear correlation b) no correlation c) positive correlation (r = 1) (r = 0) (0 < r < 1)

X X X a) perfect linear correlation b) no correlation c) positive correlation (r = 1) (r = 0) (0 < r < 1) CORRELATION AND REGRESSION / 47 CHAPTER EIGHT CORRELATION AND REGRESSION Correlation and regression are statistical methods that are commonly used in the medical literature to compare two or more variables.

More information

Correlation Coefficient The correlation coefficient is a summary statistic that describes the linear relationship between two numerical variables 2

Correlation Coefficient The correlation coefficient is a summary statistic that describes the linear relationship between two numerical variables 2 Lesson 4 Part 1 Relationships between two numerical variables 1 Correlation Coefficient The correlation coefficient is a summary statistic that describes the linear relationship between two numerical variables

More information

Spearman s correlation

Spearman s correlation Spearman s correlation Introduction Before learning about Spearman s correllation it is important to understand Pearson s correlation which is a statistical measure of the strength of a linear relationship

More information

3. Nonparametric methods

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

More information

Lesson 4 Part 1. Relationships between. two numerical variables. Correlation Coefficient. Relationship between two

Lesson 4 Part 1. Relationships between. two numerical variables. Correlation Coefficient. Relationship between two Lesson Part Relationships between two numerical variables Correlation Coefficient The correlation coefficient is a summary statistic that describes the linear between two numerical variables Relationship

More information

The Statistics Tutor s

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

More information

Dr. Peter Tröger Hasso Plattner Institute, University of Potsdam. Software Profiling Seminar, Statistics 101

Dr. Peter Tröger Hasso Plattner Institute, University of Potsdam. Software Profiling Seminar, Statistics 101 Dr. Peter Tröger Hasso Plattner Institute, University of Potsdam Software Profiling Seminar, 2013 Statistics 101 Descriptive Statistics Population Object Object Object Sample numerical description Object

More information

Nonparametric Statistics

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

More information

Using Excel for inferential statistics

Using Excel for inferential statistics FACT SHEET Using Excel for inferential statistics Introduction When you collect data, you expect a certain amount of variation, just caused by chance. A wide variety of statistical tests can be applied

More information

Statistics and research

Statistics and research Statistics and research Usaneya Perngparn Chitlada Areesantichai Drug Dependence Research Center (WHOCC for Research and Training in Drug Dependence) College of Public Health Sciences Chulolongkorn University,

More information

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 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

More information

Introduction to Quantitative Methods

Introduction 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 information

EBM Cheat Sheet- Measurements Card

EBM Cheat Sheet- Measurements Card EBM Cheat Sheet- Measurements Card Basic terms: Prevalence = Number of existing cases of disease at a point in time / Total population. Notes: Numerator includes old and new cases Prevalence is cross-sectional

More information

Quantitative Data Analysis: Choosing a statistical test Prepared by the Office of Planning, Assessment, Research and Quality

Quantitative Data Analysis: Choosing a statistical test Prepared by the Office of Planning, Assessment, Research and Quality Quantitative Data Analysis: Choosing a statistical test Prepared by the Office of Planning, Assessment, Research and Quality 1 To help choose which type of quantitative data analysis to use either before

More information

SPSS Tests for Versions 9 to 13

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

More information

AMS7: WEEK 8. CLASS 1. Correlation Monday May 18th, 2015

AMS7: WEEK 8. CLASS 1. Correlation Monday May 18th, 2015 AMS7: WEEK 8. CLASS 1 Correlation Monday May 18th, 2015 Type of Data and objectives of the analysis Paired sample data (Bivariate data) Determine whether there is an association between two variables This

More information

SPSS Explore procedure

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,

More information

Data Analysis, Research Study Design and the IRB

Data Analysis, Research Study Design and the IRB Minding the p-values p and Quartiles: Data Analysis, Research Study Design and the IRB Don Allensworth-Davies, MSc Research Manager, Data Coordinating Center Boston University School of Public Health IRB

More information

Chapter 21 Section D

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

More information

The Statistics Tutor s Quick Guide to

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

More information

Projects Involving Statistics (& SPSS)

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,

More information

Come scegliere un test statistico

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

More information

UNIVERSITY OF NAIROBI

UNIVERSITY 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 information

Study Guide for the Final Exam

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

More information

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

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

More information

1. What is the critical value for this 95% confidence interval? CV = z.025 = invnorm(0.025) = 1.96

1. 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 1-propZint 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 information

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

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

More information

DATA INTERPRETATION AND STATISTICS

DATA 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 information

Analysis of numerical data S4

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:

More information

Statistical Significance and Bivariate Tests

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,

More information

THE KRUSKAL WALLLIS TEST

THE KRUSKAL WALLLIS TEST THE KRUSKAL WALLLIS TEST TEODORA H. MEHOTCHEVA Wednesday, 23 rd April 08 THE KRUSKAL-WALLIS TEST: The non-parametric alternative to ANOVA: testing for difference between several independent groups 2 NON

More information

Comparing Means in Two Populations

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

More information

Rank-Based Non-Parametric Tests

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

More information

Yiming Peng, Department of Statistics. February 12, 2013

Yiming Peng, Department of Statistics. February 12, 2013 Regression Analysis Using JMP Yiming Peng, Department of Statistics February 12, 2013 2 Presentation and Data http://www.lisa.stat.vt.edu Short Courses Regression Analysis Using JMP Download Data to Desktop

More information

Lecture 7: Binomial Test, Chisquare

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

More information

QUANTITATIVE METHODS BIOLOGY FINAL HONOUR SCHOOL NON-PARAMETRIC TESTS

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.

More information

BIOSTATISTICS QUIZ ANSWERS

BIOSTATISTICS QUIZ ANSWERS BIOSTATISTICS QUIZ ANSWERS 1. When you read scientific literature, do you know whether the statistical tests that were used were appropriate and why they were used? a. Always b. Mostly c. Rarely d. Never

More information

Introduction to Statistics and Quantitative Research Methods

Introduction 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 information

Nonparametric Statistics

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

More information

Statistics: revision

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

More information

DESCRIPTIVE STATISTICS. The purpose of statistics is to condense raw data to make it easier to answer specific questions; test hypotheses.

DESCRIPTIVE STATISTICS. The purpose of statistics is to condense raw data to make it easier to answer specific questions; test hypotheses. DESCRIPTIVE STATISTICS The purpose of statistics is to condense raw data to make it easier to answer specific questions; test hypotheses. DESCRIPTIVE VS. INFERENTIAL STATISTICS Descriptive To organize,

More information

Analysis of Variance ANOVA

Analysis 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 information

Section 13, Part 1 ANOVA. Analysis Of Variance

Section 13, Part 1 ANOVA. Analysis Of Variance Section 13, Part 1 ANOVA Analysis Of Variance Course Overview So far in this course we ve covered: Descriptive statistics Summary statistics Tables and Graphs Probability Probability Rules Probability

More information

Comparing two groups (t tests...)

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?

More information

We are often interested in the relationship between two variables. Do people with more years of full-time education earn higher salaries?

We are often interested in the relationship between two variables. Do people with more years of full-time education earn higher salaries? Statistics: Correlation Richard Buxton. 2008. 1 Introduction We are often interested in the relationship between two variables. Do people with more years of full-time education earn higher salaries? Do

More information

A Guide for a Selection of SPSS Functions

A Guide for a Selection of SPSS Functions A Guide for a Selection of SPSS Functions IBM SPSS Statistics 19 Compiled by Beth Gaedy, Math Specialist, Viterbo University - 2012 Using documents prepared by Drs. Sheldon Lee, Marcus Saegrove, Jennifer

More information

1. Why the hell do we need statistics?

1. Why the hell do we need statistics? 1. Why the hell do we need statistics? There are three kind of lies: lies, damned lies, and statistics, British Prime Minister Benjamin Disraeli (as credited by Mark Twain): It is easy to lie with statistics,

More information

Statistics Review PSY379

Statistics 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 information

Difference tests (2): nonparametric

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

More information

Basic Statistics and Data Analysis for Health Researchers from Foreign Countries

Basic Statistics and Data Analysis for Health Researchers from Foreign Countries Basic Statistics and Data Analysis for Health Researchers from Foreign Countries Volkert Siersma siersma@sund.ku.dk The Research Unit for General Practice in Copenhagen Dias 1 Content Quantifying association

More information

SPSS ADVANCED ANALYSIS WENDIANN SETHI SPRING 2011

SPSS 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 information

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

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

More information

Statistics. Measurement. Scales of Measurement 7/18/2012

Statistics. Measurement. Scales of Measurement 7/18/2012 Statistics Measurement Measurement is defined as a set of rules for assigning numbers to represent objects, traits, attributes, or behaviors A variableis something that varies (eye color), a constant does

More information

Permutation Tests for Comparing Two Populations

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

More information

Analyzing Research Data Using Excel

Analyzing Research Data Using Excel Analyzing Research Data Using Excel Fraser Health Authority, 2012 The Fraser Health Authority ( FH ) authorizes the use, reproduction and/or modification of this publication for purposes other than commercial

More information

Simple Predictive Analytics Curtis Seare

Simple Predictive Analytics Curtis Seare Using Excel to Solve Business Problems: Simple Predictive Analytics Curtis Seare Copyright: Vault Analytics July 2010 Contents Section I: Background Information Why use Predictive Analytics? How to use

More information

Research Methods 1 Handouts, Graham Hole,COGS - version 1.0, September 2000: Page 1:

Research Methods 1 Handouts, Graham Hole,COGS - version 1.0, September 2000: Page 1: Research Methods 1 Handouts, Graham Hole,COGS - version 1.0, September 000: Page 1: NON-PARAMETRIC TESTS: What are non-parametric tests? Statistical tests fall into two kinds: parametric tests assume that

More information

Principles of Hypothesis Testing for Public Health

Principles of Hypothesis Testing for Public Health Principles of Hypothesis Testing for Public Health Laura Lee Johnson, Ph.D. Statistician National Center for Complementary and Alternative Medicine johnslau@mail.nih.gov Fall 2011 Answers to Questions

More information

Business Statistics. Successful completion of Introductory and/or Intermediate Algebra courses is recommended before taking Business Statistics.

Business Statistics. Successful completion of Introductory and/or Intermediate Algebra courses is recommended before taking Business Statistics. Business Course Text Bowerman, Bruce L., Richard T. O'Connell, J. B. Orris, and Dawn C. Porter. Essentials of Business, 2nd edition, McGraw-Hill/Irwin, 2008, ISBN: 978-0-07-331988-9. Required Computing

More information

AP Statistics 2002 Scoring Guidelines

AP Statistics 2002 Scoring Guidelines AP Statistics 2002 Scoring Guidelines The materials included in these files are intended for use by AP teachers for course and exam preparation in the classroom; permission for any other use must be sought

More information

11/20/2014. Correlational research is used to describe the relationship between two or more naturally occurring variables.

11/20/2014. Correlational research is used to describe the relationship between two or more naturally occurring variables. Correlational research is used to describe the relationship between two or more naturally occurring variables. Is age related to political conservativism? Are highly extraverted people less afraid of rejection

More information

EPS 625 INTERMEDIATE STATISTICS FRIEDMAN TEST

EPS 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 repeated-measures data if participants are assessed on two occasions or conditions

More information

Types of Data, Descriptive Statistics, and Statistical Tests for Nominal Data. Patrick F. Smith, Pharm.D. University at Buffalo Buffalo, New York

Types of Data, Descriptive Statistics, and Statistical Tests for Nominal Data. Patrick F. Smith, Pharm.D. University at Buffalo Buffalo, New York Types of Data, Descriptive Statistics, and Statistical Tests for Nominal Data Patrick F. Smith, Pharm.D. University at Buffalo Buffalo, New York . NONPARAMETRIC STATISTICS I. DEFINITIONS A. Parametric

More information

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

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.

More information

Pearson s correlation

Pearson s correlation Pearson s correlation Introduction Often several quantitative variables are measured on each member of a sample. If we consider a pair of such variables, it is frequently of interest to establish if there

More information

Additional sources Compilation of sources: http://lrs.ed.uiuc.edu/tseportal/datacollectionmethodologies/jin-tselink/tselink.htm

Additional sources Compilation of sources: http://lrs.ed.uiuc.edu/tseportal/datacollectionmethodologies/jin-tselink/tselink.htm Mgt 540 Research Methods Data Analysis 1 Additional sources Compilation of sources: http://lrs.ed.uiuc.edu/tseportal/datacollectionmethodologies/jin-tselink/tselink.htm http://web.utk.edu/~dap/random/order/start.htm

More information

business statistics using Excel OXFORD UNIVERSITY PRESS Glyn Davis & Branko Pecar

business statistics using Excel OXFORD UNIVERSITY PRESS Glyn Davis & Branko Pecar business statistics using Excel Glyn Davis & Branko Pecar OXFORD UNIVERSITY PRESS Detailed contents Introduction to Microsoft Excel 2003 Overview Learning Objectives 1.1 Introduction to Microsoft Excel

More information

A correlation exists between two variables when one of them is related to the other in some way.

A correlation exists between two variables when one of them is related to the other in some way. Lecture #10 Chapter 10 Correlation and Regression The main focus of this chapter is to form inferences based on sample data that come in pairs. Given such paired sample data, we want to determine whether

More information

Non-Parametric Tests (I)

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

More information

Simple Linear 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 Statistical model for linear regression Estimating

More information

Simple Linear Regression in SPSS STAT 314

Simple Linear Regression in SPSS STAT 314 Simple Linear Regression in SPSS STAT 314 1. Ten Corvettes between 1 and 6 years old were randomly selected from last year s sales records in Virginia Beach, Virginia. The following data were obtained,

More information

Technology Step-by-Step Using StatCrunch

Technology Step-by-Step Using StatCrunch Technology Step-by-Step Using StatCrunch Section 1.3 Simple Random Sampling 1. Select Data, highlight Simulate Data, then highlight Discrete Uniform. 2. Fill in the following window with the appropriate

More information

Univariate Regression

Univariate Regression Univariate Regression Correlation and Regression The regression line summarizes the linear relationship between 2 variables Correlation coefficient, r, measures strength of relationship: the closer r is

More information

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

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:

More information

Research Methods & Experimental Design

Research 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 information

Bowerman, O'Connell, Aitken Schermer, & Adcock, Business Statistics in Practice, Canadian edition

Bowerman, O'Connell, Aitken Schermer, & Adcock, Business Statistics in Practice, Canadian edition 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

More information

The correlation coefficient

The correlation coefficient The correlation coefficient Clinical Biostatistics The correlation coefficient Martin Bland Correlation coefficients are used to measure the of the relationship or association between two quantitative

More information

Testing Hypotheses using SPSS

Testing Hypotheses using SPSS Is the mean hourly rate of male workers $2.00? T-Test One-Sample Statistics Std. Error N Mean Std. Deviation Mean 2997 2.0522 6.6282.2 One-Sample Test Test Value = 2 95% Confidence Interval Mean of the

More information

Study Design and Statistical Analysis

Study Design and Statistical Analysis Study Design and Statistical Analysis Anny H Xiang, PhD Department of Preventive Medicine University of Southern California Outline Designing Clinical Research Studies Statistical Data Analysis Designing

More information

Statistical tests for SPSS

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

More information

Nonparametric Two-Sample Tests. Nonparametric Tests. Sign Test

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

More information

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.

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

More information

CHAPTER 14 NONPARAMETRIC TESTS

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

More information

Erik Parner 14 September 2016. Basic Biostatistics - Day 2-21 September, 2016 1

Erik Parner 14 September 2016. Basic Biostatistics - Day 2-21 September, 2016 1 PhD course in Basic Biostatistics Day Erik Parner, Department of Biostatistics, Aarhus University Log-transformation of continuous data Exercise.+.4+Standard- (Triglyceride) Logarithms and exponentials

More information

STA-201-TE. 5. Measures of relationship: correlation (5%) Correlation coefficient; Pearson r; correlation and causation; proportion of common variance

STA-201-TE. 5. Measures of relationship: correlation (5%) Correlation coefficient; Pearson r; correlation and causation; proportion of common variance Principles of Statistics STA-201-TE This TECEP is an introduction to descriptive and inferential statistics. Topics include: measures of central tendency, variability, correlation, regression, hypothesis

More information