# Microarray Data Analysis. Statistical methods to detect differentially expressed genes

Save this PDF as:

Size: px
Start display at page:

Download "Microarray Data Analysis. Statistical methods to detect differentially expressed genes"

## Transcription

1 Microarray Data Analysis Statistical methods to detect differentially expressed genes

2 Outline The class comparison problem Statistical tests Calculation of p-values Permutations tests The volcano plot Multiple testing Extensions Examples 2

3 Class comparison: Identifying differentially expressed genes Identify genes differentially expressed between different conditions such as Treatment, cell type,... (qualitative covariates) Dose, time,... (quantitative covariate) Survival, infection time,...! Estimate effects/differences between groups probably using log-ratios, i.e. the difference on log scale log(x)-log(y) [=log(x/y)] 3

4 What is a significant change? Depends on the variability within groups, which may be different from gene to gene. To assess the statistical significance of differences, conduct a statistical test for each gene. 4

5 Different settings for statistical tests Indirect comparisons: 2 groups, 2 samples, unpaired E.g. 10 individuals: 5 suffer diabetes, 5 healthy One sample fro each individual Typically: Two sample t-test or similar Direct comparisons: Two groups, two samples, paired E.g. 6 individuals with brain stroke. Two samples from each: one from healthy (region 1) and one from affected (region 2). Typically: One sample t-test (also called paired t-test) or similar based on the individual differences between conditions. 5

6 Different ways to do the experiment An experiment use cdna arrays ( two-colour ) or affy ( one-colour). Depending on the technology used allocation of conditions to slides changes. Type of chip Experiment 10 indiv. Diab (5) Heal (5) 6 indiv. Region 1 Region 2 cdna (2-col) Reference design. (5) Diab/Ref (5) Heal/Ref 6 slides 1 individual per slide (6) reg1/reg2 Affy (1-col) Comparison design. (5) Diab vs (5) Heal 12 slides (6) Paired differences 6

7 Natural measures of discrepancy For Direct comparisons in two colour or paired-one colour. 1 Mean (log) ratio = n T n T i= 1 i, (R or M used indistinctly) Classical t-test = t = ( R) SE, ( SE estimates standard error of R) Robust t-test = Use robust estimates of location &scale For Indirect comparisons in two colour or Direct comparisons in one colour. R n 1 T n 1 C Mean difference = T Ci = T C n T i i= 1 nc i= 1 Classical t-test = t = ( T C) s 1/ n + 1/ n p T C Robust t-test = Use robust estimates of location &scale 7

8 Some Issues Can we trust average effect sizes (average difference of means) alone? Can we trust the t statistic alone? Here is evidence that the answer is no. Gene M1 M2 M3 M4 M5 M6 Mean SD t A B C D E Courtesy of Y.H. Yang 8

9 Some Issues Can we trust average effect sizes (average difference of means) alone? Can we trust the t statistic alone? Here is evidence that the answer is no. Gene M1 M2 M3 M4 M5 M6 Mean SD t A B C D E Averages can be driven by outliers. Courtesy of Y.H. Yang 9

10 Some Issues Can we trust average effect sizes (average difference of means) alone? Can we trust the t statistic alone? Here is evidence that the answer is no. Gene M1 M2 M3 M4 M5 M6 Mean SD t A B C D E t s can be driven by tiny variances. Courtesy of Y.H. Yang 10

11 Variations in t-tests (1) Let R g mean observed log ratio SE g standard error of R g estimated from data on gene g. SE standard error of R g estimated from data across all genes. Global t-test: t=r g /SE Gene-specific t-test t=r g /SE g 11

12 Some pro s and con s of t-test Test Pro s Con s Global t-test: t=r g /SE Gene-specific: t=r g /SE g Yields stable variance estimate Robust to variance heterogeneity Assumes variance homogeneity biased if false Low power Yields unstable variance estimates (due to few data) 12

13 T-tests extensions SAM (Tibshirani, 2001) Regularized-t (Baldi, 2001) EB-moderated t (Smyth, 2003) S t = t = Rg = c + SE 0 g vse + ( n 1) SE 2 2 g v 0 R g + n R 2 d SE + d SE g d 0 g + d 13

14 Up to here : Can we generate a list of candidate genes? With the tools we have, the reasonable steps to generate a list of candidate genes may be: Gene 1: M 11, M 12,., M 1k Gene 2: M 21, M 22,., M 2k. Gene G: M G1, M G2,., M Gk For every gene, calculate S i =t(m i1, M i2,., M ik ), e.g. t-statistics, S, B,? Statistics of interest S 1, S 2,., S G A list of candidate DE genes We need an idea of how significant are these values We d like to assign them p-values 14

15 Significance testing

16 Nominal p-values After a test statistic is computed, it is convenient to convert it to a p-value: The probability that a test statistic, say S(X), takes values equal or greater than that taken on the observed sample, say S(X 0 ), under the assumption that the null hypothesis is true p=p{s(x)>=s(x 0 ) H 0 true} 16

17 Significance testing Test of significance at the α level: Reject the null hypothesis if your p-value is smaller than the significance level It has advantages but not free from criticisms Genes with p-values falling below a prescribed level may be regarded as significant 17

18 Hypothesis testing overview for a single gene Reported decision H 0 is Rejected (gene is Selected) H 0 is Accepted (gene not Selected) State of the nature ("Truth") H 0 is false (Affected) H 0 is true (Not Affected) TP, prob: 1-α FP, P[Rej H 0 H 0 ]<= α Type I error FN, prob: 1-β Type II error TN, prob: β Sensitiviy TP/[TP+FN] Specificity TN/[TN+FP] Positive predictive value Negative predictive value TP/[TP+FP] TN/[TN+FN] 18

19 Calculation of p-values Standard methods for calculating p- values: (i) Refer to a statistical distribution table (Normal, t, F, ) or (ii) Perform a permutation analysis 19

20 (i) Tabulated p-values Tabulated p-values can be obtained for standard test statistics (e.g.the t-test) They often rely on the assumption of normally distributed errors in the data This assumption can be checked (approximately) using a Histogram Q-Q plot 20

21 Example Golub data, 27 ALL vs 11 AML samples, 3051 genes A t-test yields 1045 genes with p<

22 (ii) Permutations tests Based on data shuffling. No assumptions Random interchange of labels between samples Estimate p-values for each comparison (gene) by using the permutation distribution of the t-statistics Repeat for every possible permutation, b=1 B Permute the n data points for the gene (x). The first n1 are referred to as treatments, the second n2 as controls For each gene, calculate the corresponding two sample t-statistic, tb After all the B permutations are done put p = #{b: tb tobserved }/B 22

23 Permutation tests (2) 23

24 The volcano plot: fold change vs log(odds) 1 Significant change detected No change detected 24

25 Multiple testing

26 How far can we trust the decision? The test: "Reject H 0 if p-val α" issaidtocontrol the type I error because, under a certain set of assumptions, the probability of falsely rejecting H 0 is less than a fixed small threshold P[Reject H 0 H 0 true]=p[fp] α Nothing is warranted about P[FN] Optimal tests are built trying to minimize this probability In practical situations it is often high 26

27 What if we wish to test more than one gene at once? (1) Consider more than one test at once Two tests each at 5% level. Now probability of getting a false positive is *0.95 = Three tests = n tests n Converge towards 1 as n increases Small p-values don t necessarily imply significance!!! We are not controlling the probability of type I error anymore 27

28 What if we wish to test more than one gene at once? (2): a simulation Simulation of this process for 6,000 genes with 8 treatments and 8 controls All the gene expression values were simulated i.i.d from a N (0,1) distribution, i.e. NOTHING is differentially expressed in our simulation The number of genes falsely rejected will be on the average of (6000 α), i.e. if we wanted to reject all genes with a p-value of less than 1% we would falsely reject around 60 genes See example 28

29 Multiple testing: Counting errors State of the nature ("Truth") H 0 is false (Affected) H 0 is true (Not Affected) H 0 is Rejected (Genes Selected) Decision reported H 0 is accepted (Genes not Selected) Total (m-m m α αm 0 (S) o )- (T) m-m (m α αm o 0) αm 0 (V) m o -αm0 (U) m o Total M α (R) m-m α (m-r) m V = # Type I errors [false positives] T = # Type II errors [false negatives] All these quantities could be known if m 0 was known 29

30 How does type I error control extend to multiple testing situations? Selecting genes with a p-value less than α doesn t control for P[FP] anymore What can be done? Extend the idea of type I error FWER and FDR are two such extensions Look for procedures that control the probability for these extended error types Mainly adjust raw p-values 30

31 Two main error rate extensions Family Wise Error Rate (FWER) FWER is probability of at least one false positive FWER= Pr(# of false discoveries >0) = Pr(V>0) False Discovery Rate (FDR) FDR is expected value of proportion of false positives among rejected null hypotheses FDR = E[V/R; R>0] = E[V/R R>0] P[R>0] 31

32 FWER FDR and FWER controlling procedures Bonferroni (adj Pvalue = min{n*pvalue,1}) Holm (1979) Hochberg (1986) Westfall & Young (1993) maxt and minp FDR Benjamini & Hochberg (1995) Benjamini & Yekutieli (2001) 32

33 Difference between controlling FWER or FDR FWER Controls for no (0) false positives gives many fewer genes (false positives), but you are likely to miss many adequate if goal is to identify few genes that differ between two groups FDR Controls the proportion of false positives if you can tolerate more false positives you will get many fewer false negatives adequate if goal is to pursue the study e.g. to determine functional relationships among genes 33

34 Steps to generate a list of candidate genes revisited (2) Gene 1: M 11, M 12,., M 1k Gene 2: M 21, M 22,., M 2k. Gene G: M G1, M G2,., M Gk For every gene, calculate S i =t(m i1, M i2,., M ik ), e.g. t-statistics, S, B, Statistics of interest S 1, S 2,., S G Assumption on the null distribution: data normality Nominal p-values P 1, P 2,, P G Adjusted p-values ap 1, ap 2,, ap G A list of candidate DE genes Select genes with adjusted P-values smaller than α 34

35 Example Golub data, 27 ALL vs 11 AML samples, 3051 genes Bonferroni adjustment: 98 genes with p adj < 0.05 (p raw < ) 35

36 Extensions Some issues we have not dealt with Replicates within and between slides Several effects: use a linear model ANOVA: are the effects equal? Time series: selecting genes for trends Different solutions have been suggested for each problem Still many open questions 36

37 Examples

38 Ex. 1- Swirl zebrafish experiment Swirl is a point mutation causing defects in the organization of the developing embryo along its ventral-dorsal axis As a result some cell types are reduced and others are expanded A goal of this experiment was to identify genes with altered expression in the swirl mutant compared to the wild zebrafish 38

39 Example 1: Experimental design Each microarray contained 8848 cdna probes (either genes or EST sequences) 4 replicate slides: 2 sets of dye-swap pairs For each pair, target cdna of the swirl mutant was labeled using one of Cy5 or Cy3 and the target cdna of the wild type mutant was labeled using the other dye Wild type 2 2 Swirl 39

40 Example 1. Data analysis Gene expression data on 8848 genes for 4 samples (slides): Each hybridixed with Mutant and Wild type On a gene-per-gene basis this is a onesample problem Hypothesis to be tested for each gene: H 0 : log 2 (R/G)=0 The decision will be based on average log-ratios 40

41 Example 2. Scanvenger receptor BI (SR-BI) experiment Callow et al. (2000). A study of lipid metabolism and atherosclerosis susceptibility in mice. Transgenic mice with SR-BI gene overexpressed have low HDL cholesterol levels. Goal: To identify genes with altered expression in the livers of transgenic mice with SR-BI gene overexpressed mice (T) compared to normal FVB control mice (C). 41

42 Example 2. Experimental design 8 treatment mice (T i ) and 8 control ones (C i ). 16 hybridizations: liver mrna from each of the 16 mice (T i, C i ) is labelled with Cy5, while pooled liver mrna from the control mice (C*) is labelled with Cy3. Probes: ~ 6,000 cdnas (genes), including 200 related to pathogenicity. T C 8 8 C* 42

43 Example 2. Data analysis Gene expression data on 6348 genes for 16 samples: 8 for treatment (log T/C*) and 8 for control (log (C/C*)) On a gene-per-gene basis this is a 2 sample problem Hypothesis to be tested for each gene: H 0 : [log (R 1 /G)-log (R 2 /G)]=0 Decision will be based on average difference of log ratios 43

### Multiple testing with gene expression array data

Multiple testing with gene expression array data Anja von Heydebreck Max Planck Institute for Molecular Genetics, Dept. Computational Molecular Biology, Berlin, Germany heydebre@molgen.mpg.de Slides partly

### 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

### Multiple One-Sample or Paired T-Tests

Chapter 610 Multiple One-Sample or Paired T-Tests Introduction This chapter describes how to estimate power and sample size (number of arrays) for paired and one sample highthroughput studies using the.

### The microarray block. Outline. Microarray experiments. Microarray Technologies. Outline

The microarray block Bioinformatics 13-17 March 006 Microarray data analysis John Gustafsson Mathematical statistics Chalmers Lectures DNA microarray technology overview (KS) of microarray data (JG) How

### Basics of microarrays. Petter Mostad 2003

Basics of microarrays Petter Mostad 2003 Why microarrays? Microarrays work by hybridizing strands of DNA in a sample against complementary DNA in spots on a chip. Expression analysis measure relative amounts

### Course on Microarray Gene Expression Analysis

Course on Microarray Gene Expression Analysis ::: Differential Expression Analysis Daniel Rico drico@cnio.es Bioinformatics Unit CNIO Upregulation or No Change Downregulation Image analysis comparison

### Bootstrapping p-value estimations

Bootstrapping p-value estimations In microarray studies it is common that the the sample size is small and that the distribution of expression values differs from normality. In this situations, permutation

### Statistical 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

### Quantitative Biology Lecture 5 (Hypothesis Testing)

15 th Oct 2015 Quantitative Biology Lecture 5 (Hypothesis Testing) Gurinder Singh Mickey Atwal Center for Quantitative Biology Summary Classification Errors Statistical significance T-tests Q-values (Traditional)

### Statistical foundations of machine learning

Machine learning p. 1/45 Statistical foundations of machine learning INFO-F-422 Gianluca Bontempi Département d Informatique Boulevard de Triomphe - CP 212 http://www.ulb.ac.be/di Machine learning p. 2/45

### Gene Expression Analysis

Gene Expression Analysis Jie Peng Department of Statistics University of California, Davis May 2012 RNA expression technologies High-throughput technologies to measure the expression levels of thousands

### Design and Analysis of Comparative Microarray Experiments

CHAPTER 2 Design and Analysis of Comparative Microarray Experiments Yee Hwa Yang and Terence P. Speed 2.1 Introduction This chapter discusses the design and analysis of relatively simple comparative experiments

### From Reads to Differentially Expressed Genes. The statistics of differential gene expression analysis using RNA-seq data

From Reads to Differentially Expressed Genes The statistics of differential gene expression analysis using RNA-seq data experimental design data collection modeling statistical testing biological heterogeneity

### False Discovery Rates

False Discovery Rates John D. Storey Princeton University, Princeton, USA January 2010 Multiple Hypothesis Testing In hypothesis testing, statistical significance is typically based on calculations involving

### 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

### 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

### Tutorial 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

### 0BComparativeMarkerSelection Documentation

0BComparativeMarkerSelection Documentation Description: Author: Computes significance values for features using several metrics, including FDR(BH), Q Value, FWER, Feature-Specific P-Value, and Bonferroni.

### 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

### Gene 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

### An example ANOVA situation. 1-Way ANOVA. Some notation for ANOVA. Are these differences significant? Example (Treating Blisters)

An example ANOVA situation Example (Treating Blisters) 1-Way ANOVA MATH 143 Department of Mathematics and Statistics Calvin College Subjects: 25 patients with blisters Treatments: Treatment A, Treatment

### One-sample normal hypothesis Testing, paired t-test, two-sample normal inference, normal probability plots

1 / 27 One-sample normal hypothesis Testing, paired t-test, two-sample normal inference, normal probability plots Timothy Hanson Department of Statistics, University of South Carolina Stat 704: Data Analysis

### Comparative genomic hybridization Because arrays are more than just a tool for expression analysis

Microarray Data Analysis Workshop MedVetNet Workshop, DTU 2008 Comparative genomic hybridization Because arrays are more than just a tool for expression analysis Carsten Friis ( with several slides from

### Simple Linear Regression Chapter 11

Simple Linear Regression Chapter 11 Rationale Frequently decision-making situations require modeling of relationships among business variables. For instance, the amount of sale of a product may be related

### Statistical Inference and t-tests

1 Statistical Inference and t-tests Objectives Evaluate the difference between a sample mean and a target value using a one-sample t-test. Evaluate the difference between a sample mean and a target value

### Test Volume 12, Number 1. June 2003

Sociedad Española de Estadística e Investigación Operativa Test Volume 12, Number 1. June 2003 Resampling-based Multiple Testing for Microarray Data Analysis Yongchao Ge Department of Statistics University

### Power and Sample Size. In epigenetic epidemiology studies

Power and Sample Size In epigenetic epidemiology studies Overview Pros and cons Working examples Concerns for epigenetic epidemiology Definition Power is the probability of detecting an effect, given that

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

### Null and Alternative Hypotheses. Lecture # 3. Steps in Conducting a Hypothesis Test (Cont d) Steps in Conducting a Hypothesis Test

Lecture # 3 Significance Testing Is there a significant difference between a measured and a standard amount (that can not be accounted for by random error alone)? aka Hypothesis testing- H 0 (null hypothesis)

### Principles of Hypothesis

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

### Inference for two Population Means

Inference for two Population Means Bret Hanlon and Bret Larget Department of Statistics University of Wisconsin Madison October 27 November 1, 2011 Two Population Means 1 / 65 Case Study Case Study Example

### Descriptive Statistics

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

### Two-Way ANOVA tests. I. Definition and Applications...2. II. Two-Way ANOVA prerequisites...2. III. How to use the Two-Way ANOVA tool?...

Two-Way ANOVA tests Contents at a glance I. Definition and Applications...2 II. Two-Way ANOVA prerequisites...2 III. How to use the Two-Way ANOVA tool?...3 A. Parametric test, assume variances equal....4

### Analysis of gene expression data. Ulf Leser and Philippe Thomas

Analysis of gene expression data Ulf Leser and Philippe Thomas This Lecture Protein synthesis Microarray Idea Technologies Applications Problems Quality control Normalization Analysis next week! Ulf Leser:

### Using CrunchIt (http://bcs.whfreeman.com/crunchit/bps4e) or StatCrunch (www.calvin.edu/go/statcrunch)

Using CrunchIt (http://bcs.whfreeman.com/crunchit/bps4e) or StatCrunch (www.calvin.edu/go/statcrunch) 1. In general, this package is far easier to use than many statistical packages. Every so often, however,

### 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

### 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:

### 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....................

### Chapter 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 One-way ANOVA To test the null hypothesis that several population means are equal,

### 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

### MS&E 226: Small Data. Lecture 17: Additional topics in inference (v1) Ramesh Johari

MS&E 226: Small Data Lecture 17: Additional topics in inference (v1) Ramesh Johari ramesh.johari@stanford.edu 1 / 34 Warnings 2 / 34 Modeling assumptions: Regression Remember that most of the inference

### 7. Tests of association and Linear Regression

7. Tests of association and Linear Regression In this chapter we consider 1. Tests of Association for 2 qualitative variables. 2. Measures of the strength of linear association between 2 quantitative variables.

### Null Hypothesis Significance Testing Signifcance Level, Power, t-tests Spring 2014 Jeremy Orloff and Jonathan Bloom

Null Hypothesis Significance Testing Signifcance Level, Power, t-tests 18.05 Spring 2014 Jeremy Orloff and Jonathan Bloom Simple and composite hypotheses Simple hypothesis: the sampling distribution is

### CHAPTERS 4-6: Hypothesis Tests Read sections 4.3, 4.5, 5.1.5, Confidence Interval vs. Hypothesis Test (4.3):

CHAPTERS 4-6: Hypothesis Tests Read sections 4.3, 4.5, 5.1.5, 6.1.3 Confidence Interval vs. Hypothesis Test (4.3): The purpose of a confidence interval is to estimate the value of a parameter. The purpose

### Hypothesis testing S2

Basic medical statistics for clinical and experimental research Hypothesis testing S2 Katarzyna Jóźwiak k.jozwiak@nki.nl 2nd November 2015 1/43 Introduction Point estimation: use a sample statistic to

### MAANOVA: A Software Package for the Analysis of Spotted cdna Microarray Experiments

MAANOVA: A Software Package for the Analysis of Spotted cdna Microarray Experiments i Hao Wu 1, M. Kathleen Kerr 2, Xiangqin Cui 1, and Gary A. Churchill 1 1 The Jackson Laboratory, Bar Harbor, ME 2 The

### PASS Sample Size Software. Linear Regression

Chapter 855 Introduction Linear regression is a commonly used procedure in statistical analysis. One of the main objectives in linear regression analysis is to test hypotheses about the slope (sometimes

### Inferences About Differences Between Means Edpsy 580

Inferences About Differences Between Means Edpsy 580 Carolyn J. Anderson Department of Educational Psychology University of Illinois at Urbana-Champaign Inferences About Differences Between Means Slide

### Experimental Design Part I

Experimental Design Part I Yi-Ju Li, Ph.D. Department of Biostatistics & Bioinformatics Duke University Medical Center July 13, 2015 Outline Definition of DOE 7/13 (Monday) Part I Definition of Design

### 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

### 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

### 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

### The scatterplot indicates a positive linear relationship between waist size and body fat percentage:

STAT E-150 Statistical Methods Multiple Regression Three percent of a man's body is essential fat, which is necessary for a healthy body. However, too much body fat can be dangerous. For men between the

### MINITAB ASSISTANT WHITE PAPER

MINITAB ASSISTANT WHITE PAPER This paper explains the research conducted by Minitab statisticians to develop the methods and data checks used in the Assistant in Minitab 17 Statistical Software. 2-Sample

### Classical and Bayesian mixed model analysis of microarray data for detecting gene expression and DNA differences

Graduate Theses and Dissertations Graduate College 2009 Classical and Bayesian mixed model analysis of microarray data for detecting gene expression and DNA differences Cumhur Yusuf Demirkale Iowa State

### 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

### Measuring gene expression (Microarrays) Ulf Leser

Measuring gene expression (Microarrays) Ulf Leser This Lecture Gene expression Microarrays Idea Technologies Problems Quality control Normalization Analysis next week! 2 http://learn.genetics.utah.edu/content/molecules/transcribe/

### Do the following using Mintab (1) Make a normal probability plot for each of the two curing times.

SMAM 314 Computer Assignment 4 1. An experiment was performed to determine the effect of curing time on the comprehensive strength of concrete blocks. Two independent random samples of 14 blocks were prepared

### SELF-TEST: SIMPLE REGRESSION

ECO 22000 McRAE SELF-TEST: SIMPLE REGRESSION Note: Those questions indicated with an (N) are unlikely to appear in this form on an in-class examination, but you should be able to describe the procedures

### 1.2 Statistical testing by permutation

Statistical testing by permutation 17 Excerpt (pp. 17-26) Ch. 13), from: McBratney & Webster (1981), McBratney et al. (1981), Webster & Burgess (1984), Borgman & Quimby (1988), and François-Bongarçon (1991).

### Microarray Analysis Using R/Bioconductor

Microarray Analysis Using R/Bioconductor Reddy Gali, Ph.D. rgali@hms.harvard.edu h"p://catalyst.harvard.edu Agenda Introduction to microarrays Workflow of a gene expression microarray experiment Publishing

### Interpreting Multiple Regression

Fall Semester, 2001 Statistics 621 Lecture 5 Robert Stine 1 Preliminaries Interpreting Multiple Regression Project and assignments Hope to have some further information on project soon. Due date for Assignment

### Statistical Foundations:

Statistical Foundations: Hypothesis Testing Psychology 790 Lecture #9 9/19/2006 Today sclass Hypothesis Testing. General terms and philosophy. Specific Examples Hypothesis Testing Rules of the NHST Game

### Simple Linear Regression Inference

Simple Linear Regression Inference 1 Inference requirements The Normality assumption of the stochastic term e is needed for inference even if it is not a OLS requirement. Therefore we have: Interpretation

### Statistical Foundations:

Statistical Foundations: Hypothesis Testing Psychology 790 Lecture #10 9/26/2006 Today sclass Hypothesis Testing. An Example. Types of errors illustrated. Misconceptions about hypothesis testing. Upcoming

### Machine Learning. Topic: Evaluating Hypotheses

Machine Learning Topic: Evaluating Hypotheses Bryan Pardo, Machine Learning: EECS 349 Fall 2011 How do you tell something is better? Assume we have an error measure. How do we tell if it measures something

### Hypothesis Testing. Jungmo Yoon CMC, Claremont McKeena College. Jungmo Yoon (CMC) Testing CMC, / 7

Hypothesis Testing Jungmo Yoon Claremont McKeena College CMC, 2009 Jungmo Yoon (CMC) Testing CMC, 2009 1 / 7 Concepts of Hypothesis Testing A criminal trial as an example of hypothesis testing. A jury

### QVALUE: The Manual Version 1.0

QVALUE: The Manual Version 1.0 Alan Dabney and John D. Storey Department of Biostatistics University of Washington Email: jstorey@u.washington.edu March 2003; Updated June 2003; Updated January 2004 Table

### AP: LAB 8: THE CHI-SQUARE TEST. Probability, Random Chance, and Genetics

Ms. Foglia Date AP: LAB 8: THE CHI-SQUARE TEST Probability, Random Chance, and Genetics Why do we study random chance and probability at the beginning of a unit on genetics? Genetics is the study of inheritance,

### 6. Statistical Inference: Significance Tests

6. Statistical Inference: Significance Tests Goal: Use statistical methods to check hypotheses such as Women's participation rates in elections in France is higher than in Germany. (an effect) Ethnic divisions

### Some Considerations for the Design of Microarray Experiments

Some Considerations for the Design of Microarray Experiments John H. Maindonald, Yvonne E. Pittelkow and Susan R. Wilson Abstract Issues relevant for the design of gene expression experiments using spotted

### 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

### Resampling: Bootstrapping and Randomization. Presented by: Jenn Fortune, Alayna Gillespie, Ivana Pejakovic, and Anne Bergen

Resampling: Bootstrapping and Randomization Presented by: Jenn Fortune, Alayna Gillespie, Ivana Pejakovic, and Anne Bergen Outline 1. The logic of resampling and bootstrapping 2. Bootstrapping: confidence

### ANOVA - Analysis of Variance

ANOVA - Analysis of Variance ANOVA - Analysis of Variance Extends independent-samples t test Compares the means of groups of independent observations Don t be fooled by the name. ANOVA does not compare

### PREPROCESSING MICROARRAY DATA. Background correction Normalization Summarization Transforms

PREPROCESSING MICROARRAY DATA Background correction Normalization Summarization Transforms Microarray studies life cycle Biological question Experimental design Failed Microarray experiment Quality Measurement

### In Chapter 2, we used linear regression to describe linear relationships. The setting for this is a

Math 143 Inference on Regression 1 Review of Linear Regression In Chapter 2, we used linear regression to describe linear relationships. The setting for this is a bivariate data set (i.e., a list of cases/subjects

### Gene expression: Microarray data analysis

Gene expression: Microarray data analysis Compare gene expression in this cell type after viral infection relative to a knockout in samples from patients after drug treatment at a later developmental time

### Design of microarray experiments

Practical microarray analysis experimental design Design of microarray experiments Ulrich Mansmann mansmann@imbi.uni-heidelberg.de Practical microarray analysis October 2003 Heidelberg Heidelberg, October

### For eg:- The yield of a new paddy variety will be 3500 kg per hectare scientific hypothesis. In Statistical language if may be stated as the random

Lecture.9 Test of significance Basic concepts null hypothesis alternative hypothesis level of significance Standard error and its importance steps in testing Test of Significance Objective To familiarize

### The calculations lead to the following values: d 2 = 46, n = 8, s d 2 = 4, s d = 2, SEof d = s d n s d n

EXAMPLE 1: Paired t-test and t-interval DBP Readings by Two Devices The diastolic blood pressures (DBP) of 8 patients were determined using two techniques: the standard method used by medical personnel

### The Variability of P-Values. Summary

The Variability of P-Values Dennis D. Boos Department of Statistics North Carolina State University Raleigh, NC 27695-8203 boos@stat.ncsu.edu August 15, 2009 NC State Statistics Departement Tech Report

### Planned Contrasts and Post Hoc Tests in MANOVA Made Easy Chii-Dean Joey Lin, SDSU, San Diego, CA

Planned Contrasts and Post Hoc Tests in MANOVA Made Easy Chii-Dean Joey Lin, SDSU, San Diego, CA ABSTRACT Multivariate analysis of variance (MANOVA) is a multivariate version of analysis of variance (ANOVA).

### 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

### ΔCT c-myc- GAPDH. untreated 30.49± ± ± ± ( ) 27.03± ± ± ± (5.3-6.

Analyzing your QRT-PCR Data The Comparative CT Method (ΔΔCT Method): Data Analysis Example The following table presents data from an experiment where the expression levels of a target (cmyc) and an endogenous

### reductio ad absurdum null hypothesis, alternate hypothesis

Chapter 10 s Using a Single Sample 10.1: Hypotheses & Test Procedures Basics: In statistics, a hypothesis is a statement about a population characteristic. s are based on an reductio ad absurdum form of

### Hypothesis Testing. April 21, 2009

Hypothesis Testing April 21, 2009 Your Claim is Just a Hypothesis I ve never made a mistake. Once I thought I did, but I was wrong. Your Claim is Just a Hypothesis Confidence intervals quantify how sure

### 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:

### RNR / ENTO Assumptions for Simple Linear Regression

74 RNR / ENTO 63 --Assumptions for Simple Linear Regression Statistical statements (hypothesis tests and CI estimation) with least squares estimates depends on 4 assumptions:. Linearity of the mean responses

### fifty 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

### Tukey s HSD (Honestly Significant Difference).

Agenda for Week 4 (Tuesday, Jan 26) Week 4 Hour 1 AnOVa review. Week 4 Hour 2 Multiple Testing Tukey s HSD (Honestly Significant Difference). Week 4 Hour 3 (Thursday) Two-way AnOVa. Sometimes you ll need

### 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

### Two-sample inference: Continuous data

Two-sample inference: Continuous data Patrick Breheny April 5 Patrick Breheny STA 580: Biostatistics I 1/32 Introduction Our next two lectures will deal with two-sample inference for continuous data As

### 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

### Hypothesis tests: the t-tests

Hypothesis tests: the t-tests Introduction Invariably investigators wish to ask whether their data answer certain questions that are germane to the purpose of the investigation. It is often the case that

### Chapter 8 Hypothesis Testing

Chapter 8 Hypothesis Testing Chapter problem: Does the MicroSort method of gender selection increase the likelihood that a baby will be girl? MicroSort: a gender-selection method developed by Genetics

### 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

### MCQ TESTING OF HYPOTHESIS

MCQ TESTING OF HYPOTHESIS MCQ 13.1 A statement about a population developed for the purpose of testing is called: (a) Hypothesis (b) Hypothesis testing (c) Level of significance (d) Test-statistic MCQ

### Statistics 104: Section 7

Statistics 104: Section 7 Section Overview Reminders Comments on Midterm Common Mistakes on Problem Set 6 Statistical Week in Review Comments on Midterm Overall, the midterms were good with one notable