Statistical Analysis. NBAFB Metabolomics Masterclass. Mark Viant


 Collin Corey Morris
 3 years ago
 Views:
Transcription
1 Statistical Analysis NBAFB Metabolomics Masterclass Mark Viant
2 1. Introduction 2. Univariate analysis Overview of lecture 3. Unsupervised multivariate analysis Principal components analysis (PCA) Interpreting scores and loadings plots Statistical tests on PCA scores data 4. Supervised multivariate analysis Partial least squares discriminant analysis (PLSDA) Partial least squares regression (PLSR) 5. Data standards, databases, and NBAFB data analysis workflow
3 1. Introduction
4 peak 1 peak 2 peak 3 n bin 1 bin 2 bin 3 n Output from spectral processing (Jon & Ulf) sample 1 sample 2 sample 3 m X matrix of NMR signal intensities sample 1 sample 2 sample 3 X matrix of MS signal intensities m
5 peak 1 peak 2 peak 3 Output from spectral processing: X and Y matrices sample label X matrix of signal intensities EITHER Y matrix = treatment group labels = discrete variable OR Y matrix = separate nonmetabolic measurement for each sample = continuous variable
6 2. Univariate statistical analysis
7 peak 1 peak 2 peak 3 Univariate statistical analysis sample label X matrix of signal intensities Y matrix = treatment group labels = discrete variable ttest or ANOVA ttest or ANOVA with false discovery rate (FDR) correction
8 But what pvalue is significant? Yes, this is possible, but it must be done with caution! Typically if we conduct a single univariate statistical test then p<0.05 is considered a significant result. But this is associated with an error rate of 5% (1 in every 20 tests gives false result). Imagine we dataset contains 1000 metabolites; so we conduct 1000 univariate tests  if p<0.05 is significant, we will incorrectly say that 50 metabolites are significantly different when they are not Unacceptable error rate! Correction for multiple testing Adjustment for multiple testing False discovery rate (FDR) by Benjamini and Hochberg, Journal of the Royal Statistical Society, Series B 57: (1995). Controls the expected proportion of incorrectly rejected null hypotheses (type I errors)
9 Typical output for NBAFB MS dataset
10 peak 1 peak 2 peak 3 Multivariate statistical analysis sample label X matrix of signal intensities Y matrix = treatment group labels = discrete variable Analyse data in its entirety  unsupervised and supervised analyses
11 3. Unsupervised multivariate statistical analysis What is principal components analysis (PCA)? Scores plots and their interpretation Loadings plots and their interpretation Statistical tests on scores data
12 What is unsupervised multivariate statistics? Multivariate statistical analyses deals with large numbers of variables (e.g. metabolites) simultaneously Unsupervised means that the analysis algorithm has no knowledge of the identities of the samples; the algorithm looks at the innate variation in the dataset Many unsupervised methods; we focus on principal components analysis Widely used in omics analyses, including metabolomics, proteomics and transcriptomics
13 Multivariate data and PCA Common to find correlated variables in multivariate data redundancy in the information provided by these variables PCA exploits this redundancy enabling us to:  pick out patterns (relationships) in the variables  reduce the dimensionality of a data set without a significant loss of information PCA is a projection technique
14 Concept behind principal components analysis: Consider 50 different fish For each fish, measure length and breadth
15 breadth Principal components analysis  continued Plotting length vs. breadth shows clear relationship between these two variables Multivariate!!! Fish Length Breadth : : : : : : length
16 breadth Principal components analysis  continued Plotting length vs. breadth shows clear relationship between these two variables PC1 Create new axis (PC1) that accounts for the largest proportion of the data s variance PC1 = p1.length + p2.breadth length PC1 = principal component 1 For each data point, project the two original variables (length, breadth) onto the one new variable (PC1)
17 breadth Principal components analysis  continued Plotting length vs. breadth shows clear relationship between these two variables Simpler dataset!!! Fish PC1 PC : : length : : 50 6
18 Sample From dataset to variable space PCA step by step var. 3 (i) One sample in variable space var. 2 var. 1 The dataset (many samples) yields a swarm of points in "variable space"
19 var. 3 PCA step by step Mean centering move centre of swarm of points to the origin of variable space (0,0,0) var. 3 original mean (i) var. 2 new mean var. 2 var. 1 (i) var. 1
20 PCA step by step PC1 score var. 3 PC1 axis var. 2 (i) var. 1 The first principal component (PC1) is set to describe the largest variation in the data, which is the same as the direction in which the points spread most in the variable space. The Score value for point i is the distance from the projection of the point on the 1st component to the origin. PC1 is the first variable in a new coordinate system that describes the variation in the data.
21 PCA step by step var. 3 PC1 axis PC2 axis (i) var. 2 PC2 scores var. 1 The second principal component (PC2) is set to describe the largest variation in the data, perpendicular (orthogonal) to PC1. The Score value for point i is the distance from the projection of the point on the 2nd component to the origin.
22 GENDER DIFFERENCE PC2 axis PCA scores plot: Analysis of LCMS metabolomics data 100 Female Night 50 Female Day 050 Male Night Male Day PC1 axis DIURNAL DIFFERENCE The relative distances among individual samples in the scores plot represent the similarities/differences between those samples
23 PCA scores plots of 1 H NMR spectra of foot muscle Metabolic changes??? PC1 loadings
24 Loadings on PC 1 PCA loadings plot 0.03 Peaks/metabolites with positive PC1 loadings are diseased abalone ELEVATED in diseased abalone healthy abalone Peaks/metabolites with negative PC1 loadings are ELEVATED in healthy abalone Variable number (e.g. metabolites) Identify which metabolites (or peaks) are responsible for the pattern of samples in the scores plot
25 Loadings on PC 1 PCA loadings plot 0.03 homarine (p<0.001) diseased abalone formate (p<0.001) healthy abalone ATP (p<0.001) tryptophan (p<0.001) tyrosine (p<0.001) Variable number (e.g. metabolites) Identify which metabolites (or peaks) are responsible for the pattern of samples in the scores plot
26 Typical output for NBAFB MS dataset
27 Summary of PCA scores and loadings plots PCA scores plot shows relationship between samples shows major underlying unbiased structures in your data PCA loadings plot identifies which metabolites (or peaks) are responsible for the structures in the scores plot
28 Significance testing on PCA scores data (1) PC1 scores for healthy PC1 scores for diseased
29 Significance testing on PCA scores data (2) Sample PC1 score Healthy Healthy Healthy Healthy Healthy Healthy Diseased Diseased Diseased Diseased ttest on scores data (p<0.001 for abalone) Unsupervised analysis found significant separation of groups Diseased 5 7.3
30 Summary of Principal Components Analysis 1. PCA is a common unsupervised method for analysing metabolomics datasets. 2. Aim is to identify the metabolic similarities and differences between the samples. 3. Excellent initial approach for screening dataset, identifying outliers, and getting a feel of the structure of your data. 4. Can be used to determine which metabolites discriminate between different groups of samples (although not as powerful as supervised methods)
31 4. Supervised multivariate statistical analysis Partial least squares discriminant analysis (PLSDA) Partial least squares regression (PLSR)
32 What is supervised multivariate statistics? Supervised means that the analysis algorithm has prior knowledge of the identities (classification) or some other continuous property (regression) of the samples Used to build multivariate models that can predict identity of an unknown sample (classification) or predict continuous variable of that unknown sample (regression) Powerful tool for discovering biomarkers Many supervised methods exist; we focus on partial least squares (PLS) based methods Widely used in metabolomics
33 peak 1 peak 2 peak 3 Partial least squares discriminant analysis (PLSDA) sample label X matrix of signal intensities Y matrix = treatment group labels PLSDA seeks to discriminate different groups of samples (classification), and to discover the relevant biomarkers
34 Example of PLSDA Miniature Schnauzer (MS) dogs Labrador dogs known Labrador dogs Predict dog breed from urine known MS dogs
35 What are urinary metabolic differences between two dog breeds? Determined using partial least squares discriminant analysis (PLSDA)
36 peak 1 peak 2 peak 3 Partial least squares regression (PLSR) sample label X matrix of signal intensities Y matrix = separate nonmetabolic measurement for each sample = continuous variable PLSR seeks to discover relevant biomarkers that can predict the continuous variable (regression)
37 Total no. of neonates produced per daphnid Example dataset for PLSR (continuous variable = neonate production) 38 individual adult daphnids (in 5 treatment groups)
38 Example of PLSR (continuous variable = neonate production) r 2 (CV) = Optimal PLS model: 107 peaks in mass spectra (out of ca total)
39 5. Data standards, databases, and NBAFB data analysis workflow
40 Data standards in omics science Transcriptomics MIAME: Minimum information about a microarray experiment MAGE: Microarray gene expression  data exchange format Proteomics PSIOM: Proteomics standards initiative  object model Metabolomics
41 Transcriptomics Databases in omics science Proteomics Metabolomics?  no publically available databases to store metabolomics measurements (yet)
42 Median Relative Standard Deviation for QC No. of peaks RSD from 3 analytical reps (%) Median RSD is a simple measure of reproducibility
43 Typical NBAFB data analysis workflow NMR or MS spectral processing Initial PCA of dataset with QC samples is data of high technical quality? Initial PCA of dataset without QC samples are there biological outliers? Further multivariate statistics (PLSDA or PLSR, depending on biological question) Univariate statistics on NMR or MS data (with FDR) Metabolite identification using software tools (MIPack, Chenomx, etc.) Metabolite identification via further MS and/or NMR experiments
MarkerView Software 1.2.1 for Metabolomic and Biomarker Profiling Analysis
MarkerView Software 1.2.1 for Metabolomic and Biomarker Profiling Analysis Overview MarkerView software is a novel program designed for metabolomics applications and biomarker profiling workflows 1. Using
More informationGene expression analysis. Ulf Leser and Karin Zimmermann
Gene expression analysis Ulf Leser and Karin Zimmermann Ulf Leser: Bioinformatics, Wintersemester 2010/2011 1 Last lecture What are microarrays?  Biomolecular devices measuring the transcriptome of a
More informationA Streamlined Workflow for Untargeted Metabolomics
A Streamlined Workflow for Untargeted Metabolomics Employing XCMS plus, a Simultaneous Data Processing and Metabolite Identification Software Package for Rapid Untargeted Metabolite Screening Baljit K.
More informationTutorial for proteome data analysis using the Perseus software platform
Tutorial for proteome data analysis using the Perseus software platform Laboratory of Mass Spectrometry, LNBio, CNPEM Tutorial version 1.0, January 2014. Note: This tutorial was written based on the information
More informationTime series experiments
Time series experiments Time series experiments Why is this a separate lecture: The price of microarrays are decreasing more time series experiments are coming Often a more complex experimental design
More informationAGILENT S BIOINFORMATICS ANALYSIS SOFTWARE
ACCELERATING PROGRESS IS IN OUR GENES AGILENT S BIOINFORMATICS ANALYSIS SOFTWARE GENESPRING GENE EXPRESSION (GX) MASS PROFILER PROFESSIONAL (MPP) PATHWAY ARCHITECT (PA) See Deeper. Reach Further. BIOINFORMATICS
More informationOplAnalyzer: A Toolbox for MALDITOF Mass Spectrometry Data Analysis
OplAnalyzer: A Toolbox for MALDITOF Mass Spectrometry Data Analysis Thang V. Pham and Connie R. Jimenez OncoProteomics Laboratory, Cancer Center Amsterdam, VU University Medical Center De Boelelaan 1117,
More informationWhy Taking This Course? Course Introduction, Descriptive Statistics and Data Visualization. Learning Goals. GENOME 560, Spring 2012
Why Taking This Course? Course Introduction, Descriptive Statistics and Data Visualization GENOME 560, Spring 2012 Data are interesting because they help us understand the world Genomics: Massive Amounts
More informationData Clustering. Dec 2nd, 2013 Kyrylo Bessonov
Data Clustering Dec 2nd, 2013 Kyrylo Bessonov Talk outline Introduction to clustering Types of clustering Supervised Unsupervised Similarity measures Main clustering algorithms kmeans Hierarchical Main
More informationDimensionality Reduction: Principal Components Analysis
Dimensionality Reduction: Principal Components Analysis In data mining one often encounters situations where there are a large number of variables in the database. In such situations it is very likely
More informationQuantitative proteomics background
Proteomics data analysis seminar Quantitative proteomics and transcriptomics of anaerobic and aerobic yeast cultures reveals post transcriptional regulation of key cellular processes de Groot, M., Daran
More informationIntegrated Data Mining Strategy for Effective Metabolomic Data Analysis
The First International Symposium on Optimization and Systems Biology (OSB 07) Beijing, China, August 8 10, 2007 Copyright 2007 ORSC & APORC pp. 45 51 Integrated Data Mining Strategy for Effective Metabolomic
More informationDATA ANALYTICS USING R
DATA ANALYTICS USING R Duration: 90 Hours Intended audience and scope: The course is targeted at fresh engineers, practicing engineers and scientists who are interested in learning and understanding data
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 informationACTM State ExamStatistics
ACTM State ExamStatistics For the 25 multiplechoice questions, make your answer choice and record it on the answer sheet provided. Once you have completed that section of the test, proceed to the tiebreaker
More informationLecture 2: Descriptive Statistics and Exploratory Data Analysis
Lecture 2: Descriptive Statistics and Exploratory Data Analysis Further Thoughts on Experimental Design 16 Individuals (8 each from two populations) with replicates Pop 1 Pop 2 Randomly sample 4 individuals
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 informationBNG 202 Biomechanics Lab. Descriptive statistics and probability distributions I
BNG 202 Biomechanics Lab Descriptive statistics and probability distributions I Overview The overall goal of this short course in statistics is to provide an introduction to descriptive and inferential
More informationPrincipal Component Analysis
Principal Component Analysis ERS70D George Fernandez INTRODUCTION Analysis of multivariate data plays a key role in data analysis. Multivariate data consists of many different attributes or variables recorded
More informationRegression III: Dummy Variable Regression
Regression III: Dummy Variable Regression Tom Ilvento FREC 408 Linear Regression Assumptions about the error term Mean of Probability Distribution of the Error term is zero Probability Distribution of
More informationFunctional Data Analysis of MALDI TOF Protein Spectra
Functional Data Analysis of MALDI TOF Protein Spectra Dean Billheimer dean.billheimer@vanderbilt.edu. Department of Biostatistics Vanderbilt University Vanderbilt Ingram Cancer Center FDA for MALDI TOF
More informationAnomaly detection. Problem motivation. Machine Learning
Anomaly detection Problem motivation Machine Learning Anomaly detection example Aircraft engine features: = heat generated = vibration intensity Dataset: New engine: (vibration) (heat) Density estimation
More informationSimple 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 informationData, Measurements, Features
Data, Measurements, Features Middle East Technical University Dep. of Computer Engineering 2009 compiled by V. Atalay What do you think of when someone says Data? We might abstract the idea that data are
More informationCancer Biostatistics Workshop Science of Doing Science  Biostatistics
Cancer Biostatistics Workshop Science of Doing Science  Biostatistics Yu Shyr, PhD Jan. 18, 2008 Cancer Biostatistics Center VanderbiltIngram Cancer Center Yu.Shyr@vanderbilt.edu Aims Cancer Biostatistics
More informationExploratory data analysis for microarray data
Eploratory data analysis for microarray data Anja von Heydebreck Ma Planck Institute for Molecular Genetics, Dept. Computational Molecular Biology, Berlin, Germany heydebre@molgen.mpg.de Visualization
More informationAzure Machine Learning, SQL Data Mining and R
Azure Machine Learning, SQL Data Mining and R Daybyday Agenda Prerequisites No formal prerequisites. Basic knowledge of SQL Server Data Tools, Excel and any analytical experience helps. Best of all:
More informationNotes for STA 437/1005 Methods for Multivariate Data
Notes for STA 437/1005 Methods for Multivariate Data Radford M. Neal, 26 November 2010 Random Vectors Notation: Let X be a random vector with p elements, so that X = [X 1,..., X p ], where denotes transpose.
More informationAlignment and Preprocessing for Data Analysis
Alignment and Preprocessing for Data Analysis Preprocessing tools for chromatography Basics of alignment GC FID (D) data and issues PCA F Ratios GC MS (D) data and issues PCA F Ratios PARAFAC Piecewise
More information4.1 Exploratory Analysis: Once the data is collected and entered, the first question is: "What do the data look like?"
Data Analysis Plan The appropriate methods of data analysis are determined by your data types and variables of interest, the actual distribution of the variables, and the number of cases. Different analyses
More informationChapter 11: Linear Regression  Inference in Regression Analysis  Part 2
Chapter 11: Linear Regression  Inference in Regression Analysis  Part 2 Note: Whether we calculate confidence intervals or perform hypothesis tests we need the distribution of the statistic we will use.
More informationStatistical issues in the analysis of microarray data
Statistical issues in the analysis of microarray data Daniel Gerhard Institute of Biostatistics Leibniz University of Hannover ESNATS Summerschool, Zermatt D. Gerhard (LUH) Analysis of microarray data
More informationPractical Data Science with Azure Machine Learning, SQL Data Mining, and R
Practical Data Science with Azure Machine Learning, SQL Data Mining, and R Overview This 4day class is the first of the two data science courses taught by Rafal Lukawiecki. Some of the topics will be
More informationUsing multiple models: Bagging, Boosting, Ensembles, Forests
Using multiple models: Bagging, Boosting, Ensembles, Forests Bagging Combining predictions from multiple models Different models obtained from bootstrap samples of training data Average predictions or
More informationHypothesis Testing & Data Analysis. Statistics. Descriptive Statistics. What is the difference between descriptive and inferential statistics?
2 Hypothesis Testing & Data Analysis 5 What is the difference between descriptive and inferential statistics? Statistics 8 Tools to help us understand our data. Makes a complicated mess simple to understand.
More informationE205 Final: Version B
Name: Class: Date: E205 Final: Version B Multiple Choice Identify the choice that best completes the statement or answers the question. 1. The owner of a local nightclub has recently surveyed a random
More informationReview Jeopardy. Blue vs. Orange. Review Jeopardy
Review Jeopardy Blue vs. Orange Review Jeopardy Jeopardy Round Lectures 03 Jeopardy Round $200 How could I measure how far apart (i.e. how different) two observations, y 1 and y 2, are from each other?
More informationMIC  Detecting Novel Associations in Large Data Sets. by Nico Güttler, Andreas Ströhlein and Matt Huska
MIC  Detecting Novel Associations in Large Data Sets by Nico Güttler, Andreas Ströhlein and Matt Huska Outline Motivation Method Results Criticism Conclusions Motivation  Goal Determine important undiscovered
More informationHomework #3 is due Friday by 5pm. Homework #4 will be posted to the class website later this week. It will be due Friday, March 7 th, at 5pm.
Homework #3 is due Friday by 5pm. Homework #4 will be posted to the class website later this week. It will be due Friday, March 7 th, at 5pm. Political Science 15 Lecture 12: Hypothesis Testing Sampling
More informationExample: Credit card default, we may be more interested in predicting the probabilty of a default than classifying individuals as default or not.
Statistical Learning: Chapter 4 Classification 4.1 Introduction Supervised learning with a categorical (Qualitative) response Notation:  Feature vector X,  qualitative response Y, taking values in C
More informationProteinPilot Report for ProteinPilot Software
ProteinPilot Report for ProteinPilot Software Detailed Analysis of Protein Identification / Quantitation Results Automatically Sean L Seymour, Christie Hunter SCIEX, USA Pow erful mass spectrometers like
More informationChapter 13 Introduction to Linear Regression and Correlation Analysis
Chapter 3 Student Lecture Notes 3 Chapter 3 Introduction to Linear Regression and Correlation Analsis Fall 2006 Fundamentals of Business Statistics Chapter Goals To understand the methods for displaing
More informationHow to report the percentage of explained common variance in exploratory factor analysis
UNIVERSITAT ROVIRA I VIRGILI How to report the percentage of explained common variance in exploratory factor analysis Tarragona 2013 Please reference this document as: LorenzoSeva, U. (2013). How to report
More informationPHARMACOMETABOLOMICS IN BIPOLAR DISORDER
PHARMACOMETABOLOMICS IN BIPOLAR DISORDER V I C K I L. E L L I N G R O D, P H A R M. D., F C C P J O H N G I D E O N S E A R L E P R O F E S S O R O F C L I N I C A L A N D T R A N S L AT I O N A L P H
More informationUnivariate 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 informationChemometric Analysis for Spectroscopy
Chemometric Analysis for Spectroscopy Bridging the Gap between the State and Measurement of a Chemical System by Dongsheng Bu, PhD, Principal Scientist, CAMO Software Inc. Chemometrics is the use of mathematical
More information, then the form of the model is given by: which comprises a deterministic component involving the three regression coefficients (
Multiple regression Introduction Multiple regression is a logical extension of the principles of simple linear regression to situations in which there are several predictor variables. For instance if we
More informationLinear Models in STATA and ANOVA
Session 4 Linear Models in STATA and ANOVA Page Strengths of Linear Relationships 42 A Note on NonLinear Relationships 44 Multiple Linear Regression 45 Removal of Variables 48 Independent Samples
More informationClustering and Data Mining in R
Clustering and Data Mining in R Workshop Supplement Thomas Girke December 10, 2011 Introduction Data Preprocessing Data Transformations Distance Methods Cluster Linkage Hierarchical Clustering Approaches
More informationNCSS Statistical Software Principal Components Regression. In ordinary least squares, the regression coefficients are estimated using the formula ( )
Chapter 340 Principal Components Regression Introduction is a technique for analyzing multiple regression data that suffer from multicollinearity. When multicollinearity occurs, least squares estimates
More informationTechnology StepbyStep Using StatCrunch
Technology StepbyStep 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 informationANOVA MULTIPLE CHOICE QUESTIONS. In the following multiplechoice questions, select the best answer.
ANOVA MULTIPLE CHOICE QUESTIONS In the following multiplechoice questions, select the best answer. 1. Analysis of variance is a statistical method of comparing the of several populations. a. standard
More informationVariables 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 informationService courses for graduate students in degree programs other than the MS or PhD programs in Biostatistics.
Course Catalog In order to be assured that all prerequisites are met, students must acquire a permission number from the education coordinator prior to enrolling in any Biostatistics course. Courses are
More informationChapter 7: Simple linear regression Learning Objectives
Chapter 7: Simple linear regression Learning Objectives Reading: Section 7.1 of OpenIntro Statistics Video: Correlation vs. causation, YouTube (2:19) Video: Intro to Linear Regression, YouTube (5:18) 
More informationStatistics 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 informationMultivariate Tools for Modern Pharmaceutical Control FDA Perspective
Multivariate Tools for Modern Pharmaceutical Control FDA Perspective IFPAC Annual Meeting 22 January 2013 Christine M. V. Moore, Ph.D. Acting Director ONDQA/CDER/FDA Outline Introduction to Multivariate
More informationStatistics Graduate Courses
Statistics Graduate Courses STAT 7002Topics in StatisticsBiological/Physical/Mathematics (cr.arr.).organized study of selected topics. Subjects and earnable credit may vary from semester to semester.
More informationFrom Reads to Differentially Expressed Genes. The statistics of differential gene expression analysis using RNAseq data
From Reads to Differentially Expressed Genes The statistics of differential gene expression analysis using RNAseq data experimental design data collection modeling statistical testing biological heterogeneity
More information1. The standardised parameters are given below. Remember to use the population rather than sample standard deviation.
Kapitel 5 5.1. 1. The standardised parameters are given below. Remember to use the population rather than sample standard deviation. The graph of crossvalidated error versus component number is presented
More informationSPSS: Descriptive and Inferential Statistics. For Windows
For Windows August 2012 Table of Contents Section 1: Summarizing Data...3 1.1 Descriptive Statistics...3 Section 2: Inferential Statistics... 10 2.1 ChiSquare Test... 10 2.2 T tests... 11 2.3 Correlation...
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 informationIntroduction to Regression and Data Analysis
Statlab Workshop Introduction to Regression and Data Analysis with Dan Campbell and Sherlock Campbell October 28, 2008 I. The basics A. Types of variables Your variables may take several forms, and it
More informationSIMCA 14 MASTER YOUR DATA SIMCA THE STANDARD IN MULTIVARIATE DATA ANALYSIS
SIMCA 14 MASTER YOUR DATA SIMCA THE STANDARD IN MULTIVARIATE DATA ANALYSIS 02 Value From Data A NEW WORLD OF MASTERING DATA EXPLORE, ANALYZE AND INTERPRET Our world is increasingly dependent on data, and
More informationNonnegative Matrix Factorization (NMF) in Semisupervised Learning Reducing Dimension and Maintaining Meaning
Nonnegative Matrix Factorization (NMF) in Semisupervised Learning Reducing Dimension and Maintaining Meaning SAMSI 10 May 2013 Outline Introduction to NMF Applications Motivations NMF as a middle step
More informationModule 5: Statistical Analysis
Module 5: Statistical Analysis To answer more complex questions using your data, or in statistical terms, to test your hypothesis, you need to use more advanced statistical tests. This module reviews the
More informationMetabolic profile of veins and their implications in primary varicose veins Disease.
Metabolic profile of veins and their implications in primary varicose veins Disease. Anwar MA 1, Beckonert OP 2, Shalhoub J 1, Vorkas P 2, Lim CS 1, Want EJ 2, Nicholson JK 2, Holmes E 2, Davies AH 1 1
More informationMultivariate Normal Distribution
Multivariate Normal Distribution Lecture 4 July 21, 2011 Advanced Multivariate Statistical Methods ICPSR Summer Session #2 Lecture #47/21/2011 Slide 1 of 41 Last Time Matrices and vectors Eigenvalues
More informationPart 2: Analysis of Relationship Between Two Variables
Part 2: Analysis of Relationship Between Two Variables Linear Regression Linear correlation Significance Tests Multiple regression Linear Regression Y = a X + b Dependent Variable Independent Variable
More informationfifty Fathoms Statistics Demonstrations for Deeper Understanding Tim Erickson
fifty Fathoms Statistics Demonstrations for Deeper Understanding Tim Erickson Contents What Are These Demos About? How to Use These Demos If This Is Your First Time Using Fathom Tutorial: An Extended Example
More informationConcepts in Machine Learning, Unsupervised Learning & Astronomy Applications
Data Mining In Modern Astronomy Sky Surveys: Concepts in Machine Learning, Unsupervised Learning & Astronomy Applications ChingWa Yip cwyip@pha.jhu.edu; Bloomberg 518 Human are Great Pattern Recognizers
More informationBIG DATA What it is and how to use?
BIG DATA What it is and how to use? Lauri Ilison, PhD Data Scientist 21.11.2014 Big Data definition? There is no clear definition for BIG DATA BIG DATA is more of a concept than precise term 1 21.11.14
More informationChapter 16 Multiple Choice Questions (The answers are provided after the last question.)
Chapter 16 Multiple Choice Questions (The answers are provided after the last question.) 1. Which of the following symbols represents a population parameter? a. SD b. σ c. r d. 0 2. If you drew all possible
More informationExploratory data analysis (Chapter 2) Fall 2011
Exploratory data analysis (Chapter 2) Fall 2011 Data Examples Example 1: Survey Data 1 Data collected from a Stat 371 class in Fall 2005 2 They answered questions about their: gender, major, year in school,
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 informationt Tests in Excel The Excel Statistical Master By Mark Harmon Copyright 2011 Mark Harmon
ttests in Excel By Mark Harmon Copyright 2011 Mark Harmon No part of this publication may be reproduced or distributed without the express permission of the author. mark@excelmasterseries.com www.excelmasterseries.com
More informationPractice 3 SPSS. Partially based on Notes from the University of Reading:
Practice 3 SPSS Partially based on Notes from the University of Reading: http://www.reading.ac.uk Simple Linear Regression A simple linear regression model is fitted when you want to investigate whether
More informationDescribe what is meant by a placebo Contrast the doubleblind procedure with the singleblind procedure Review the structure for organizing a memo
Readings: Ha and Ha Textbook  Chapters 1 8 Appendix D & E (online) Plous  Chapters 10, 11, 12 and 14 Chapter 10: The Representativeness Heuristic Chapter 11: The Availability Heuristic Chapter 12: Probability
More informationApplied Multivariate Analysis
Neil H. Timm Applied Multivariate Analysis With 42 Figures Springer Contents Preface Acknowledgments List of Tables List of Figures vii ix xix xxiii 1 Introduction 1 1.1 Overview 1 1.2 Multivariate Models
More informationDr Alexander Henzing
Horizon 2020 Health, Demographic Change & Wellbeing EU funding, research and collaboration opportunities for 2016/17 Innovate UK funding opportunities in omics, bridging health and life sciences Dr Alexander
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 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 informationIntroduction to machine learning and pattern recognition Lecture 1 Coryn BailerJones
Introduction to machine learning and pattern recognition Lecture 1 Coryn BailerJones http://www.mpia.de/homes/calj/mlpr_mpia2008.html 1 1 What is machine learning? Data description and interpretation
More informationwhere b is the slope of the line and a is the intercept i.e. where the line cuts the y axis.
Least Squares Introduction We have mentioned that one should not always conclude that because two variables are correlated that one variable is causing the other to behave a certain way. However, sometimes
More informationCommon factor analysis
Common factor analysis This is what people generally mean when they say "factor analysis" This family of techniques uses an estimate of common variance among the original variables to generate the factor
More informationPsyc 250 Statistics & Experimental Design. Correlation Exercise
Psyc 250 Statistics & Experimental Design Correlation Exercise Preparation: Log onto Woodle and download the Class Data February 09 dataset and the associated Syntax to create scale scores Class Syntax
More informationMultivariate Analysis of Ecological Data
Multivariate Analysis of Ecological Data MICHAEL GREENACRE Professor of Statistics at the Pompeu Fabra University in Barcelona, Spain RAUL PRIMICERIO Associate Professor of Ecology, Evolutionary Biology
More informationPerformance Metrics for Graph Mining Tasks
Performance Metrics for Graph Mining Tasks 1 Outline Introduction to Performance Metrics Supervised Learning Performance Metrics Unsupervised Learning Performance Metrics Optimizing Metrics Statistical
More informationPREDA S4classes. Francesco Ferrari October 13, 2015
PREDA S4classes Francesco Ferrari October 13, 2015 Abstract This document provides a description of custom S4 classes used to manage data structures for PREDA: an R package for Position RElated Data Analysis.
More informationModel Selection. Introduction. Model Selection
Model Selection Introduction This user guide provides information about the Partek Model Selection tool. Topics covered include using a Down syndrome data set to demonstrate the usage of the Partek Model
More informationChapter 12 Discovering New Knowledge Data Mining
Chapter 12 Discovering New Knowledge Data Mining BecerraFernandez, et al.  Knowledge Management 1/e  2004 Prentice Hall Additional material 2007 Dekai Wu Chapter Objectives Introduce the student to
More information0BComparativeMarkerSelection Documentation
0BComparativeMarkerSelection Documentation Description: Author: Computes significance values for features using several metrics, including FDR(BH), Q Value, FWER, FeatureSpecific PValue, and Bonferroni.
More informationIncreasing the Multiplexing of High Resolution Targeted Peptide Quantification Assays
Increasing the Multiplexing of High Resolution Targeted Peptide Quantification Assays Scheduled MRM HR Workflow on the TripleTOF Systems Jenny Albanese, Christie Hunter AB SCIEX, USA Targeted quantitative
More informationPrincipal Components Analysis (PCA)
Principal Components Analysis (PCA) Janette Walde janette.walde@uibk.ac.at Department of Statistics University of Innsbruck Outline I Introduction Idea of PCA Principle of the Method Decomposing an Association
More informationUn (bref) aperçu des méthodes et outils de fouilles et de visualisation de données «omics»
Un (bref) aperçu des méthodes et outils de fouilles et de visualisation de données «omics» Workshop «Protéomique & Maladies rares» 25 th September 2012, Paris yves.vandenbrouck@cea.fr CEA Grenoble irtsv
More informationDoing Quantitative Research 26E02900, 6 ECTS Lecture 2: Measurement Scales. OlliPekka Kauppila Rilana Riikkinen
Doing Quantitative Research 26E02900, 6 ECTS Lecture 2: Measurement Scales OlliPekka Kauppila Rilana Riikkinen Learning Objectives 1. Develop the ability to assess a quality of measurement instruments
More informationGene Expression Analysis
Gene Expression Analysis Jie Peng Department of Statistics University of California, Davis May 2012 RNA expression technologies Highthroughput technologies to measure the expression levels of thousands
More informationUnit 26: Small Sample Inference for One Mean
Unit 26: Small Sample Inference for One Mean Prerequisites Students need the background on confidence intervals and significance tests covered in Units 24 and 25. Additional Topic Coverage Additional coverage
More informationEnvironmental Remote Sensing GEOG 2021
Environmental Remote Sensing GEOG 2021 Lecture 4 Image classification 2 Purpose categorising data data abstraction / simplification data interpretation mapping for land cover mapping use land cover class
More informationDidacticiel  Études de cas
1 Topic Linear Discriminant Analysis Data Mining Tools Comparison (Tanagra, R, SAS and SPSS). Linear discriminant analysis is a popular method in domains of statistics, machine learning and pattern recognition.
More information