The Association Design and a Continuous Phenotype

Size: px
Start display at page:

Download "The Association Design and a Continuous Phenotype"

Transcription

1 PSYC 5102: Association Design & Continuous Phenotypes (4/4/07) 1 The Association Design and a Continuous Phenotype The purpose of this note is to demonstrate how to perform a population-based association study with a continuous phenotype. Although the example used is with knockout mice, the logic applies equally well to studies with humans. Mathematical Model The model used here assumes two alleles per locus (which we designate as A and a), giving three genotypes AA, Aa, and aa. The overall notation is similar to that used in Falconer and Mackay (1996) and is presented in Table 1. Table 1. Notation for the single-gene model. Genotype Frequency Expected Mean Variance within Genotype aa f aa m α σ 2 Aa f Aa m + δ σ 2 AA f AA m + α σ 2 Here m is the midpoint between the two homozygotes. The quantity α is the additive genetic effect and has the following interpretation: if we were to substitute allele A for allele a in a genotype, then we expect, on average, a phenotypic change of α units. The quantity δ is the parameter for dominance. It measures the extent to which the mean of the heterozygote Aa deviates from the average of the two homozygotes. When δ = 0, there is complete additivity. Data Arrangement The arrangement of data for the analysis is illustrated in Table 2. In addition to a column for genotype and one for phenotypic scores (the values of which are fictitious in this table), two new quantitative variables are created. The first of these is called alpha in Table 2 and it is used to obtain an estimate of the additive effect of an allelic substitution and also an estimate of narrow-sense (i.e., additive) heritability. The rule for constructing variable alpha is simple. Alpha equals 1 for one homozygote, equals 1 for the other homozygote, and equals 0 for the heterozygote. (Hint: let alpha equal 1 for the homozygote with the lower mean.) The second variable is called delta and it is used to assess the presence of dominance. If the genotype is a heterozygote, then the value of delta is 1; otherwise, delta equals 0.

2 PSYC 5102: Association Design & Continuous Phenotypes (4/4/07) 2 Table 2. Example of a data set arranged for single-gene analysis. Phenotype Genotype alpha delta 8.3 AA Aa aa aa Aa AA 1 0 Sequence of Analysis After variables alpha and delta are constructed, two regressions are performed. The first regression, referred to by some authors as the compact model (Judd & McClelland, 1989), uses the phenotypic score as the dependent variable and variable alpha as the independent variable. The second, termed the augmented model, uses both variables alpha and delta as the independent variables. Interpretation of the Output The squared multiple correlation (R 2 ) from the first regression is an estimate of the narrow sense heritability or the proportion of additive genetic variance to phenotypic variance for the locus. Multiplying this R 2 by the phenotypic variance gives the additive genetic variance that this locus contributes to the trait. If there is no dominance (discussed below), then the regression coefficient for the variable alpha is a direct estimate of the additive effect of an allelic substitution (i.e., the quantity α in Table 1). Also, the test of significant for this coefficient is always the most powerful statistical test for genetic effects provided dominance is not strong. The regression for the augmented model tests for dominance. If we reject the null hypothesis of no dominance, then this regression gives additional important quantities; otherwise, we return to the first regression and present and interpret those results. The intercept from this multiple regression model equals the midpoint between the two homozygotes (i.e., the quantity m in Table 1). The regression coefficient for variable alpha equals the additive effect of an allelic substitution (i.e., the quantity α in Table 1). The regression coefficient for variable delta equals the deviation of the heterozygote mean from the midpoint (i.e., the quantity δ in Table 1). The F statistic from augmented model is an omnibus F that assesses the fit of the whole model. It, along with its p value, will be identical to the F (and that F s p value) from a oneway ANOVA. For the types of sample sizes available for neuroscience research, the t test for the regression coefficient of variable alpha in either the first or second regression is almost always a more powerful statistic for testing the presence of genetic effects at the locus than the omnibus F. For those few cases in which the F test is more powerful (complete dominance, large additive effect, and large sample sizes), the maximal difference in power is about.03. However, in the rest of the parameter space, the difference in power favoring the t statistic can be appreciable up to.20.

3 PSYC 5102: Association Design & Continuous Phenotypes (4/4/07) 3 The appropriate test for dominance is the significance of the t statistic for the regression coefficient of variable delta. The p level for this t statistic will be identical to that of an F statistic that tests whether adding variable delta significantly increased R 2 over the first regression. This test for dominance will always be less powerful than the t test for variable alpha s regression coefficient. The squared multiple correlation from the second regression is an estimate of broad sense heritability or the proportion of phenotypic variance attributable to total genetic variance (additive plus dominance variance) at the gene. Thus, the proportion of phenotype variance attributable to dominance variance can be calculated by subtracting the R 2 from this regression from the R 2 of the first regression. Multiplying this quantity by the phenotypic standard deviation gives dominance variance in raw score units. A numerical example As an example, we analyze data collected and reported by Bowers et al. (2000) on behavior on an elevated plus-maze for mice lacking the gene for the γ isoform of protein kinase C (PKCγ knockouts) and their heterozygous and wild-type littermates. Two phenotypes are analyzed, both derived from a principal components analysis of the original variables presented in Table 1 of Bowers et al. (2000). These factors agree almost perfectly with those reported by Rodgers & Johnson (1995) using a different population of mice. The first phenotype is activity in a novel environment which is measured by the total number of entrances, and entrances into the closed arms of the maze. The second phenotype is anxiety. Here, high scores are marked by a high percentage of time and of entrances into the closed arm while low scores are indexed by a high percentage of time and entrances into the open arms. Descriptive statistics for these two phenotypes are presented in Table 3. Table 3. Means and standard deviations for activity and anxiety measures on an elevated plus-maze for mice lacking the gene for PKCγ (knock outs) and their heterozygous and wild-type littermates. Activity Anxiety Genotype N Mean St. Dev. Mean St. Dev. Knock Out Heterozygote Wild Type The values of alpha were assigned so that the PKCγ knock out mice were given the value of 1, heterozygotes a value of 0, and the wild type homozygotes, a value of 1. An example program in the Statistical Analysis System for the analyses of these data is given in the Appendix. The activity phenotype illustrates how the method operates for a system with only additive gene action. The results from the first regression, presented in Table 4, should be used to interpret whether or not the PKCγ locus has an effect on activity. Here, one could interpret either the F statistic from the ANOVA table or the t statistic testing whether the parameter estimate for variable alpha is significantly different from 0. (Both

4 PSYC 5102: Association Design & Continuous Phenotypes (4/4/07) 4 statistics are equivalent because with only one independent variable the F statistic is the square of the t statistic and both will have identical p values.) Here, t = (p =.037), so we reject the null hypothesis of no genetic effect and conclude that the PKCγ gene has an influence on overall activity in the elevated plus-maze. The value of the coefficient for variable alpha (i.e., our estimate of α) is -.42 indicating that, on average, a substitution of one wild type allele for null (i.e., knock out) allele reduces activity by.42 units. Here, the estimate of α may be viewed as an effect size expressed in the metric of the original data. Table 4. Output from SAS PROC REG on the activity phenotype: Compact (additive only) model. Bowers et al (2000) data on PKC-gamma and activity first model The REG Procedure Model: additive Dependent Variable: activity Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model Error Corrected Total Root MSE R-Square Dependent Mean Adj R-Sq Coeff Var Parameter Estimates Parameter Standard Variable DF Estimate Error t Value Pr > t Intercept alpha This effect size may be standardized in one of two ways. First, the estimate of α may be divided by the error standard deviation (i.e., the square root of the error mean square). This gives a measure of effect size favored by statisticians such as Cohen (1988). In the present case, this gives.42 /.90 =.44. Hence, the average effect of an allelic substitution is to change activity by.44 standard deviation units. The second way to standardize is to divide α by the phenotypic standard deviation. Because we used scores from a principal components analysis, the phenotypic standard deviations are 1.0, leaving α unchanged.

5 PSYC 5102: Association Design & Continuous Phenotypes (4/4/07) 5 A second way of expressing effect size is in terms of the proportion of variance explained. The statistic here is R 2, the squared multiple correlation that will be calculated and printed in any output. It just so happens that this quantity also equals narrow-sense heritability or the ratio of additive genetic variance to phenotypic variance. For this regression, the R 2 is.12, implying that 12% of phenotypic variance is attributable to additive genetic variance. The next step is to test for dominance by regressing the activity phenotype on both variables alpha and delta. Results are presented in Table 5. The critical statistic is the t statistic that tests whether the parameter estimate for delta is significantly difference from 0. Here, the value of t is.08 and its associated p value is.937. Hence, there is no evidence for dominance on activity, and we would return and interpret the first regression as the best model to explain the data. Table 5. Output from SAS PROC REG on the activity phenotype: Augmented (additive plus dominance) model. Bowers et al (2000) data on PKC-gamma and activity 2 second model The REG Procedure Model: total Dependent Variable: activity Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model Error Corrected Total Root MSE R-Square Dependent Mean Adj R-Sq Coeff Var Parameter Estimates Parameter Standard Variable DF Estimate Error t Value Pr > t Intercept alpha delta The results on activity also illustrate a specific instance in which the regression method could lead to different results than that of a oneway ANOVA. The ANOVA table from a oneway ANOVA is identical to that presented in Table 5. Here, the F value

6 PSYC 5102: Association Design & Continuous Phenotypes (4/4/07) 6 is 2.28 and its p value is.118, so one would not reject the null hypothesis. The typical conclusion would be that there is no evidence that the PKCγ locus influences activity in the elevated plus-maze. On the other hand, we have seen that testing whether the coefficient for alpha differs from 0 results in a statistically significant finding. In summary, there is good evidence that the PKCγ locus influences activity in a novel environment. All gene action appears to be additive and the estimate of both narrow and broad-sense heritability for the locus is.12. Whether an effect size of this magnitude is something that is worthwhile pursuing is, of course, a matter that should be determined by the substance of the problem and not the statistics. The anxiety phenotype is used to illustrate the method when dominance is important. The results of regressing anxiety on variable alpha are presented in Table 6. Here, the t statistic testing whether the coefficient for alpha equals is 3.09 (p =.004), so we conclude that there is evidence that the PKCγ locus also influences anxiety. The R 2 from this regression (.22) equals the estimate of narrow sense heritability for anxiety. Table 6. Output from SAS PROC REG on the activity phenotype: Compact (additive only) model. Bowers et al (2000) data on PKC-gamma and anxiety first model The REG Procedure Model: additive Dependent Variable: anxiety Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model Error Corrected Total Root MSE R-Square Dependent Mean E-17 Adj R-Sq Coeff Var E18 Parameter Estimates Parameter Standard Variable DF Estimate Error t Value Pr > t Intercept E alpha The results of the second regression are given in Table 7. The t statistic for the coefficient for variable delta equals 3.25 (p =.003), so we reject the null hypothesis of no

7 PSYC 5102: Association Design & Continuous Phenotypes (4/4/07) 7 dominance. Because there is evidence for dominance, we favor the parameter estimate for alpha using this regression instead of that from the first regression. (The two estimates are the same in the present case because there are equal sample sizes for the genotypes; when sample sizes differ, the estimates of alpha may be different in the two regressions). Here, the value of the coefficient for variable alpha is.56, implying that substituting one wild-type allele for a null PKCγ allele has the average effect of increasing anxiety by.56 units. The value of the coefficient for variable delta (i.e., our estimate of δ) is.91. This is larger than the value for α, so we might suspect heterosis. Let us postpone discussion of this topic to focus on interpretation of heritability. Table 7. Output from SAS PROC REG on the anxiety phenotype: Compact (additive and dominance) model. Bowers et al (2000) data on PKC-gamma and anxiety second model The REG Procedure Model: total Dependent Variable: anxiety Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model Error Corrected Total Root MSE R-Square Dependent Mean E-17 Adj R-Sq Coeff Var E18 Parameter Estimates Parameter Standard Variable DF Estimate Error t Value Pr > t Intercept alpha delta The R 2 for this second regression is.41. This is our estimate of broad sense heritability for anxiety. In short, variation in the PKCγ locus accounts for about 41% of the variability in this anxiety measure in this population of mice. Because the R 2 from the first regression is an estimate of narrow-sense heritability, the contribution of dominance to broad sense heritability may be found by subtracting the R 2 from the first regression from that in the second regression. This gives =.19.

8 PSYC 5102: Association Design & Continuous Phenotypes (4/4/07) 8 Should we interpret the large estimate of δ as overdominance? Certainly the mean of the heterozygote is consistent with this possibility. Most but not all modern regression software allows for a direct test of this hypothesis. When there is heterosis, then the value for δ should be significantly greater than the value of α (or significantly less than the value of α, depending on which allele is dominant). One can test for this by constraining the regression coefficients for variables alpha and delta to be equal and then testing the significance of this model against the second regression given above. One simple SAS statement is sufficient for this test (see Appendix 1). For the present case, the test is not significant (F(1,33) = 1.14, p =.29). Hence, the value of δ is not significantly greater than that for α, and there is no evidence for overdominance.

9 PSYC 5102: Association Design & Continuous Phenotypes (4/4/07) 9 Appendix: SAS Code for the input of data, construction of contrast codes, and analysis of the anxiety phenotype. data plusmaze; input genotype activity anxiety; if genotype=1 then alpha = -1; else if genotype=2 then alpha = 0; else alpha = 1; delta = 0; if genotype=2 then delta = 1; datalines; run;

10 PSYC 5102: Association Design & Continuous Phenotypes (4/4/07) 10 title Bowers et al (2000) data on PKC-gamma and anxiety; proc reg data=plusmaze; var anxiety alpha delta; title2 first model; additive: model anxiety = alpha; run; title2 second model; total: model anxiety = alpha delta; run; title3 test for overdominance; test alpha = delta; run; quit;

Analysis of single gene effects 1. Quantitative analysis of single gene effects. Gregory Carey, Barbara J. Bowers, Jeanne M.

Analysis of single gene effects 1. Quantitative analysis of single gene effects. Gregory Carey, Barbara J. Bowers, Jeanne M. Analysis of single gene effects 1 Quantitative analysis of single gene effects Gregory Carey, Barbara J. Bowers, Jeanne M. Wehner From the Department of Psychology (GC, JMW) and Institute for Behavioral

More information

HZAU MULTIVARIATE HOMEWORK #2 MULTIPLE AND STEPWISE LINEAR REGRESSION

HZAU MULTIVARIATE HOMEWORK #2 MULTIPLE AND STEPWISE LINEAR REGRESSION HZAU MULTIVARIATE HOMEWORK #2 MULTIPLE AND STEPWISE LINEAR REGRESSION Using the malt quality dataset on the class s Web page: 1. Determine the simple linear correlation of extract with the remaining variables.

More information

ANOVA. Thomas Elliott. January 29, 2013

ANOVA. Thomas Elliott. January 29, 2013 ANOVA Thomas Elliott January 29, 2013 ANOVA stands for analysis of variance and is one of the basic statistical tests we can use to find relationships between two or more variables. ANOVA compares the

More information

Decomposition of the Genotypic Value

Decomposition of the Genotypic Value Decomposition of the Genotypic Value 1 / 17 Partitioning of Phenotypic Values We introduced the general model of Y = G + E in the first lecture, where Y is the phenotypic value, G is the genotypic value,

More information

Introduction to Quantitative Genetics

Introduction to Quantitative Genetics Introduction to Quantitative Genetics 1 / 17 Historical Background Quantitative genetics is the study of continuous or quantitative traits and their underlying mechanisms. The main principals of quantitative

More information

Chapter 9. Factorial ANOVA with Two Between-Group Factors 10/22/ Factorial ANOVA with Two Between-Group Factors

Chapter 9. Factorial ANOVA with Two Between-Group Factors 10/22/ Factorial ANOVA with Two Between-Group Factors Chapter 9 Factorial ANOVA with Two Between-Group Factors 10/22/2001 1 Factorial ANOVA with Two Between-Group Factors Recall that in one-way ANOVA we study the relation between one criterion variable and

More information

Use the above variables and any you might need to construct to specify the MODEL A/C comparisons you would use to ask the following questions.

Use the above variables and any you might need to construct to specify the MODEL A/C comparisons you would use to ask the following questions. Fall, 2002 Grad Stats Final Exam There are four questions on this exam, A through D, and each question has multiple sub-questions. Unless otherwise indicated, each sub-question is worth 3 points. Question

More information

One-Way ANOVAs t-test two statistically significant Type I error alpha null hypothesis dependant variable Independent variable three levels;

One-Way ANOVAs t-test two statistically significant Type I error alpha null hypothesis dependant variable Independent variable three levels; 1 One-Way ANOVAs We have already discussed the t-test. The t-test is used for comparing the means of two groups to determine if there is a statistically significant difference between them. The t-test

More information

General Example: Gas Mileage (Stat 5044 Schabenberger & J.P.Morgen)

General Example: Gas Mileage (Stat 5044 Schabenberger & J.P.Morgen) General Example: Gas Mileage (Stat 5044 Schabenberger & J.P.Morgen) From Motor Trend magazine data were obtained for n=32 cars on the following variables: Y= Gas Mileage (miles per gallon, MPG) X1= Engine

More information

3 CONCEPTUAL FOUNDATIONS OF STATISTICS

3 CONCEPTUAL FOUNDATIONS OF STATISTICS 3 CONCEPTUAL FOUNDATIONS OF STATISTICS In this chapter, we examine the conceptual foundations of statistics. The goal is to give you an appreciation and conceptual understanding of some basic statistical

More information

HERITABILITY AND ITS GENETIC WORTH FOR PLANT BREEDING

HERITABILITY AND ITS GENETIC WORTH FOR PLANT BREEDING HERITABILITY AND ITS GENETIC WORTH FOR PLANT BREEDING Author: Prasanta Kumar Majhi M. Sc. (Agri.), Junior Research Scholar, Department of Genetics and Plant Breeding, College of Agriculture, UAS, Dharwad,

More information

Roadmap. Inbreeding How inbred is a population? What are the consequences of inbreeding?

Roadmap. Inbreeding How inbred is a population? What are the consequences of inbreeding? 1 Roadmap Quantitative traits What kinds of variation can selection work on? How much will a population respond to selection? Heritability How can response be restored? Inbreeding How inbred is a population?

More information

Hungry Mice. NP: Mice in this group ate as much as they pleased of a non-purified, standard diet for laboratory mice.

Hungry Mice. NP: Mice in this group ate as much as they pleased of a non-purified, standard diet for laboratory mice. Hungry Mice When laboratory mice (and maybe other animals) are fed a nutritionally adequate but near-starvation diet, they may live longer on average than mice that eat a normal amount of food. In this

More information

An Introduction to Quantitative Genetics I. Heather A Lawson Advanced Genetics Spring2018

An Introduction to Quantitative Genetics I. Heather A Lawson Advanced Genetics Spring2018 An Introduction to Quantitative Genetics I Heather A Lawson Advanced Genetics Spring2018 Outline What is Quantitative Genetics? Genotypic Values and Genetic Effects Heritability Linkage Disequilibrium

More information

Lab 5: Testing Hypotheses about Patterns of Inheritance

Lab 5: Testing Hypotheses about Patterns of Inheritance Lab 5: Testing Hypotheses about Patterns of Inheritance How do we talk about genetic information? Each cell in living organisms contains DNA. DNA is made of nucleotide subunits arranged in very long strands.

More information

Your DNA extractions! 10 kb

Your DNA extractions! 10 kb Your DNA extractions! 10 kb Quantitative characters: polygenes and environment Most ecologically important quantitative traits (QTs) vary. Distributions are often unimodal and approximately normal. Offspring

More information

Stat Wk 9: Hypothesis Tests and Analysis

Stat Wk 9: Hypothesis Tests and Analysis Stat 342 - Wk 9: Hypothesis Tests and Analysis Crash course on ANOVA, proc glm Stat 342 Notes. Week 9 Page 1 / 57 Crash Course: ANOVA AnOVa stands for Analysis Of Variance. Sometimes it s called ANOVA,

More information

d =.20 which means females earn 2/10 a standard deviation more than males

d =.20 which means females earn 2/10 a standard deviation more than males Sampling Using Cohen s (1992) Two Tables (1) Effect Sizes, d and r d the mean difference between two groups divided by the standard deviation for the data Mean Cohen s d 1 Mean2 Pooled SD r Pearson correlation

More information

Multiple Linear Regression Analysis

Multiple Linear Regression Analysis Revised July 2018 Multiple Linear Regression Analysis This set of notes shows how to use Stata in multiple regression analysis. It assumes that you have set Stata up on your computer (see the Getting Started

More information

Business Statistics Probability

Business Statistics Probability Business Statistics The following was provided by Dr. Suzanne Delaney, and is a comprehensive review of Business Statistics. The workshop instructor will provide relevant examples during the Skills Assessment

More information

Homework Exercises for PSYC 3330: Statistics for the Behavioral Sciences

Homework Exercises for PSYC 3330: Statistics for the Behavioral Sciences Homework Exercises for PSYC 3330: Statistics for the Behavioral Sciences compiled and edited by Thomas J. Faulkenberry, Ph.D. Department of Psychological Sciences Tarleton State University Version: July

More information

Population Genetics Simulation Lab

Population Genetics Simulation Lab Name Period Assignment # Pre-lab: annotate each paragraph Population Genetics Simulation Lab Evolution occurs in populations of organisms and involves variation in the population, heredity, and differential

More information

Effect of Source and Level of Protein on Weight Gain of Rats

Effect of Source and Level of Protein on Weight Gain of Rats Effect of Source and Level of Protein on of Rats 1 * two factor analysis of variance with interaction; 2 option ls=120 ps=75 nocenter nodate; 3 4 title Effect of Source of Protein and Level of Protein

More information

(b) What is the allele frequency of the b allele in the new merged population on the island?

(b) What is the allele frequency of the b allele in the new merged population on the island? 2005 7.03 Problem Set 6 KEY Due before 5 PM on WEDNESDAY, November 23, 2005. Turn answers in to the box outside of 68-120. PLEASE WRITE YOUR ANSWERS ON THIS PRINTOUT. 1. Two populations (Population One

More information

MENDELIAN GENETICS. MENDEL RULE AND LAWS Please read and make sure you understand the following instructions and knowledge before you go on.

MENDELIAN GENETICS. MENDEL RULE AND LAWS Please read and make sure you understand the following instructions and knowledge before you go on. MENDELIAN GENETICS Objectives Upon completion of this lab, students should: 1. Understand the principles and terms used in Mendelian genetics. 2. Know how to complete a Punnett square to estimate phenotypic

More information

HARDY- WEINBERG PRACTICE PROBLEMS

HARDY- WEINBERG PRACTICE PROBLEMS HARDY- WEINBERG PRACTICE PROBLEMS PROBLEMS TO SOLVE: 1. The proportion of homozygous recessives of a certain population is 0.09. If we assume that the gene pool is large and at equilibrium and all genotypes

More information

Pedigree Analysis Why do Pedigrees? Goals of Pedigree Analysis Basic Symbols More Symbols Y-Linked Inheritance

Pedigree Analysis Why do Pedigrees? Goals of Pedigree Analysis Basic Symbols More Symbols Y-Linked Inheritance Pedigree Analysis Why do Pedigrees? Punnett squares and chi-square tests work well for organisms that have large numbers of offspring and controlled mating, but humans are quite different: Small families.

More information

Using SAS to Conduct Pilot Studies: An Instructors Guide

Using SAS to Conduct Pilot Studies: An Instructors Guide Using SAS to Conduct Pilot Studies: An Instructors Guide Sean W. Mulvenon, University of Arkansas, Fayetteville, AR Ronna C. Turner, University of Arkansas, Fayetteville, AR ABSTRACT An important component

More information

For more information about how to cite these materials visit

For more information about how to cite these materials visit Author(s): Kerby Shedden, Ph.D., 2010 License: Unless otherwise noted, this material is made available under the terms of the Creative Commons Attribution Share Alike 3.0 License: http://creativecommons.org/licenses/by-sa/3.0/

More information

CHAPTER - 6 STATISTICAL ANALYSIS. This chapter discusses inferential statistics, which use sample data to

CHAPTER - 6 STATISTICAL ANALYSIS. This chapter discusses inferential statistics, which use sample data to CHAPTER - 6 STATISTICAL ANALYSIS 6.1 Introduction This chapter discusses inferential statistics, which use sample data to make decisions or inferences about population. Populations are group of interest

More information

Confidence Intervals On Subsets May Be Misleading

Confidence Intervals On Subsets May Be Misleading Journal of Modern Applied Statistical Methods Volume 3 Issue 2 Article 2 11-1-2004 Confidence Intervals On Subsets May Be Misleading Juliet Popper Shaffer University of California, Berkeley, shaffer@stat.berkeley.edu

More information

additive genetic component [d] = rded

additive genetic component [d] = rded Heredity (1976), 36 (1), 31-40 EFFECT OF GENE DISPERSION ON ESTIMATES OF COMPONENTS OF GENERATION MEANS AND VARIANCES N. E. M. JAYASEKARA* and J. L. JINKS Department of Genetics, University of Birmingham,

More information

APPENDIX N. Summary Statistics: The "Big 5" Statistical Tools for School Counselors

APPENDIX N. Summary Statistics: The Big 5 Statistical Tools for School Counselors APPENDIX N Summary Statistics: The "Big 5" Statistical Tools for School Counselors This appendix describes five basic statistical tools school counselors may use in conducting results based evaluation.

More information

Statistical Tests for X Chromosome Association Study. with Simulations. Jian Wang July 10, 2012

Statistical Tests for X Chromosome Association Study. with Simulations. Jian Wang July 10, 2012 Statistical Tests for X Chromosome Association Study with Simulations Jian Wang July 10, 2012 Statistical Tests Zheng G, et al. 2007. Testing association for markers on the X chromosome. Genetic Epidemiology

More information

Analysis of Variance (ANOVA)

Analysis of Variance (ANOVA) Research Methods and Ethics in Psychology Week 4 Analysis of Variance (ANOVA) One Way Independent Groups ANOVA Brief revision of some important concepts To introduce the concept of familywise error rate.

More information

Chapter 12: Introduction to Analysis of Variance

Chapter 12: Introduction to Analysis of Variance Chapter 12: Introduction to Analysis of Variance of Variance Chapter 12 presents the general logic and basic formulas for the hypothesis testing procedure known as analysis of variance (ANOVA). The purpose

More information

Investigating the robustness of the nonparametric Levene test with more than two groups

Investigating the robustness of the nonparametric Levene test with more than two groups Psicológica (2014), 35, 361-383. Investigating the robustness of the nonparametric Levene test with more than two groups David W. Nordstokke * and S. Mitchell Colp University of Calgary, Canada Testing

More information

MULTIPLE REGRESSION OF CPS DATA

MULTIPLE REGRESSION OF CPS DATA MULTIPLE REGRESSION OF CPS DATA A further inspection of the relationship between hourly wages and education level can show whether other factors, such as gender and work experience, influence wages. Linear

More information

SPSS output for 420 midterm study

SPSS output for 420 midterm study Ψ Psy Midterm Part In lab (5 points total) Your professor decides that he wants to find out how much impact amount of study time has on the first midterm. He randomly assigns students to study for hours,

More information

When bad things happen to good genes: mutation vs. selection

When bad things happen to good genes: mutation vs. selection When bad things happen to good genes: mutation vs. selection Selection tends to increase the frequencies of alleles with higher marginal fitnesses. Does this mean that genes are perfect? No, mutation can

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

Estimating genetic variation within families

Estimating genetic variation within families Estimating genetic variation within families Peter M. Visscher Queensland Institute of Medical Research Brisbane, Australia peter.visscher@qimr.edu.au 1 Overview Estimation of genetic parameters Variation

More information

Evolution II.2 Answers.

Evolution II.2 Answers. Evolution II.2 Answers. 1. (4 pts) Contrast the predictions of blending inheritance for F1 and F2 generations with those observed under Mendelian inheritance. Blending inheritance predicts both F1 and

More information

An Introduction to Quantitative Genetics

An Introduction to Quantitative Genetics An Introduction to Quantitative Genetics Mohammad Keramatipour MD, PhD Keramatipour@tums.ac.ir ac ir 1 Mendel s work Laws of inheritance Basic Concepts Applications Predicting outcome of crosses Phenotype

More information

Psych 5741/5751: Data Analysis University of Boulder Gary McClelland & Charles Judd. Exam #2, Spring 1992

Psych 5741/5751: Data Analysis University of Boulder Gary McClelland & Charles Judd. Exam #2, Spring 1992 Exam #2, Spring 1992 Question 1 A group of researchers from a neurobehavioral institute are interested in the relationships that have been found between the amount of cerebral blood flow (CB FLOW) to the

More information

12/31/2016. PSY 512: Advanced Statistics for Psychological and Behavioral Research 2

12/31/2016. PSY 512: Advanced Statistics for Psychological and Behavioral Research 2 PSY 512: Advanced Statistics for Psychological and Behavioral Research 2 Introduce moderated multiple regression Continuous predictor continuous predictor Continuous predictor categorical predictor Understand

More information

Still important ideas

Still important ideas Readings: OpenStax - Chapters 1 13 & Appendix D & E (online) Plous Chapters 17 & 18 - Chapter 17: Social Influences - Chapter 18: Group Judgments and Decisions Still important ideas Contrast the measurement

More information

8/28/2017. If the experiment is successful, then the model will explain more variance than it can t SS M will be greater than SS R

8/28/2017. If the experiment is successful, then the model will explain more variance than it can t SS M will be greater than SS R PSY 5101: Advanced Statistics for Psychological and Behavioral Research 1 If the ANOVA is significant, then it means that there is some difference, somewhere but it does not tell you which means are different

More information

Georgina Salas. Topics EDCI Intro to Research Dr. A.J. Herrera

Georgina Salas. Topics EDCI Intro to Research Dr. A.J. Herrera Homework assignment topics 51-63 Georgina Salas Topics 51-63 EDCI Intro to Research 6300.62 Dr. A.J. Herrera Topic 51 1. Which average is usually reported when the standard deviation is reported? The mean

More information

Using SAS to Calculate Tests of Cliff s Delta. Kristine Y. Hogarty and Jeffrey D. Kromrey

Using SAS to Calculate Tests of Cliff s Delta. Kristine Y. Hogarty and Jeffrey D. Kromrey Using SAS to Calculate Tests of Cliff s Delta Kristine Y. Hogarty and Jeffrey D. Kromrey Department of Educational Measurement and Research, University of South Florida ABSTRACT This paper discusses a

More information

SPSS output for 420 midterm study

SPSS output for 420 midterm study Ψ Psy Midterm Part In lab (5 points total) Your professor decides that he wants to find out how much impact amount of study time has on the first midterm. He randomly assigns students to study for hours,

More information

Regression Including the Interaction Between Quantitative Variables

Regression Including the Interaction Between Quantitative Variables Regression Including the Interaction Between Quantitative Variables The purpose of the study was to examine the inter-relationships among social skills, the complexity of the social situation, and performance

More information

Dr. Kelly Bradley Final Exam Summer {2 points} Name

Dr. Kelly Bradley Final Exam Summer {2 points} Name {2 points} Name You MUST work alone no tutors; no help from classmates. Email me or see me with questions. You will receive a score of 0 if this rule is violated. This exam is being scored out of 00 points.

More information

Testing Means. Related-Samples t Test With Confidence Intervals. 6. Compute a related-samples t test and interpret the results.

Testing Means. Related-Samples t Test With Confidence Intervals. 6. Compute a related-samples t test and interpret the results. 10 Learning Objectives Testing Means After reading this chapter, you should be able to: Related-Samples t Test With Confidence Intervals 1. Describe two types of research designs used when we select related

More information

HERITABILITY INTRODUCTION. Objectives

HERITABILITY INTRODUCTION. Objectives 36 HERITABILITY In collaboration with Mary Puterbaugh and Larry Lawson Objectives Understand the concept of heritability. Differentiate between broad-sense heritability and narrowsense heritability. Learn

More information

Model of an F 1 and F 2 generation

Model of an F 1 and F 2 generation Mendelian Genetics Casual observation of a population of organisms (e.g. cats) will show variation in many visible characteristics (e.g. color of fur). While members of a species will have the same number

More information

Chapter 19: Quantitative II Estimation & Testing

Chapter 19: Quantitative II Estimation & Testing 2000, Gregory Carey Chapter 19: Quantitative II - 1 Chapter 19: Quantitative II Estimation & Testing Introduction The previous chapter presented quantitative genetics from a conceptual view. We learned

More information

MODEL I: DRINK REGRESSED ON GPA & MALE, WITHOUT CENTERING

MODEL I: DRINK REGRESSED ON GPA & MALE, WITHOUT CENTERING Interpreting Interaction Effects; Interaction Effects and Centering Richard Williams, University of Notre Dame, https://www3.nd.edu/~rwilliam/ Last revised February 20, 2015 Models with interaction effects

More information

Describe what is meant by a placebo Contrast the double-blind procedure with the single-blind procedure Review the structure for organizing a memo

Describe what is meant by a placebo Contrast the double-blind procedure with the single-blind procedure Review the structure for organizing a memo Business Statistics The following was provided by Dr. Suzanne Delaney, and is a comprehensive review of Business Statistics. The workshop instructor will provide relevant examples during the Skills Assessment

More information

Effects of Nutrients on Shrimp Growth

Effects of Nutrients on Shrimp Growth Data Set 5: Effects of Nutrients on Shrimp Growth Statistical setting This Handout is an example of extreme collinearity of the independent variables, and of the methods used for diagnosing this problem.

More information

Mendelian Genetics using Fast Plants Report due Sept. 15/16. Readings: Mendelian genetics: Hartwell Chapter 2 pp , Chapter 5 pp

Mendelian Genetics using Fast Plants Report due Sept. 15/16. Readings: Mendelian genetics: Hartwell Chapter 2 pp , Chapter 5 pp 1 Biology 423L Sept. 1/2 Mendelian Genetics using Fast Plants Report due Sept. 15/16. Readings: Mendelian genetics: Hartwell Chapter 2 pp. 13-27, Chapter 5 pp. 127-130. FASTPLANTS: Williams et al. (1986)

More information

Discontinuous Traits. Chapter 22. Quantitative Traits. Types of Quantitative Traits. Few, distinct phenotypes. Also called discrete characters

Discontinuous Traits. Chapter 22. Quantitative Traits. Types of Quantitative Traits. Few, distinct phenotypes. Also called discrete characters Discontinuous Traits Few, distinct phenotypes Chapter 22 Also called discrete characters Quantitative Genetics Examples: Pea shape, eye color in Drosophila, Flower color Quantitative Traits Phenotype is

More information

CHAPTER ONE CORRELATION

CHAPTER ONE CORRELATION CHAPTER ONE CORRELATION 1.0 Introduction The first chapter focuses on the nature of statistical data of correlation. The aim of the series of exercises is to ensure the students are able to use SPSS to

More information

CHAPTER 3 DATA ANALYSIS: DESCRIBING DATA

CHAPTER 3 DATA ANALYSIS: DESCRIBING DATA Data Analysis: Describing Data CHAPTER 3 DATA ANALYSIS: DESCRIBING DATA In the analysis process, the researcher tries to evaluate the data collected both from written documents and from other sources such

More information

Name: emergency please discuss this with the exam proctor. 6. Vanderbilt s academic honor code applies.

Name: emergency please discuss this with the exam proctor. 6. Vanderbilt s academic honor code applies. Name: Biostatistics 1 st year Comprehensive Examination: Applied in-class exam May 28 th, 2015: 9am to 1pm Instructions: 1. There are seven questions and 12 pages. 2. Read each question carefully. Answer

More information

CRITERIA FOR USE. A GRAPHICAL EXPLANATION OF BI-VARIATE (2 VARIABLE) REGRESSION ANALYSISSys

CRITERIA FOR USE. A GRAPHICAL EXPLANATION OF BI-VARIATE (2 VARIABLE) REGRESSION ANALYSISSys Multiple Regression Analysis 1 CRITERIA FOR USE Multiple regression analysis is used to test the effects of n independent (predictor) variables on a single dependent (criterion) variable. Regression tests

More information

Readings: Textbook readings: OpenStax - Chapters 1 13 (emphasis on Chapter 12) Online readings: Appendix D, E & F

Readings: Textbook readings: OpenStax - Chapters 1 13 (emphasis on Chapter 12) Online readings: Appendix D, E & F Readings: Textbook readings: OpenStax - Chapters 1 13 (emphasis on Chapter 12) Online readings: Appendix D, E & F Plous Chapters 17 & 18 Chapter 17: Social Influences Chapter 18: Group Judgments and Decisions

More information

Hypothesis Testing. Richard S. Balkin, Ph.D., LPC-S, NCC

Hypothesis Testing. Richard S. Balkin, Ph.D., LPC-S, NCC Hypothesis Testing Richard S. Balkin, Ph.D., LPC-S, NCC Overview When we have questions about the effect of a treatment or intervention or wish to compare groups, we use hypothesis testing Parametric statistics

More information

Mendelian Genetics: Patterns of Inheritance

Mendelian Genetics: Patterns of Inheritance Mendelian Genetics: Patterns of Inheritance A Bit on Gregor Mendel Born to a poor farming family in what is now part of Czech Republic Attended Augustinian monastery (1843) Became an excellent teacher

More information

Sheila Barron Statistics Outreach Center 2/8/2011

Sheila Barron Statistics Outreach Center 2/8/2011 Sheila Barron Statistics Outreach Center 2/8/2011 What is Power? When conducting a research study using a statistical hypothesis test, power is the probability of getting statistical significance when

More information

INTENDED LEARNING OUTCOMES

INTENDED LEARNING OUTCOMES FACTORIAL ANOVA INTENDED LEARNING OUTCOMES Revise factorial ANOVA (from our last lecture) Discuss degrees of freedom in factorial ANOVA Recognise main effects and interactions Discuss simple effects QUICK

More information

Problem #1 Neurological signs and symptoms of ciguatera poisoning as the start of treatment and 2.5 hours after treatment with mannitol.

Problem #1 Neurological signs and symptoms of ciguatera poisoning as the start of treatment and 2.5 hours after treatment with mannitol. Ho (null hypothesis) Ha (alternative hypothesis) Problem #1 Neurological signs and symptoms of ciguatera poisoning as the start of treatment and 2.5 hours after treatment with mannitol. Hypothesis: Ho:

More information

Mating Systems. 1 Mating According to Index Values. 1.1 Positive Assortative Matings

Mating Systems. 1 Mating According to Index Values. 1.1 Positive Assortative Matings Mating Systems After selecting the males and females that will be used to produce the next generation of animals, the next big decision is which males should be mated to which females. Mating decisions

More information

Basic Statistics and Data Analysis in Work psychology: Statistical Examples

Basic Statistics and Data Analysis in Work psychology: Statistical Examples Basic Statistics and Data Analysis in Work psychology: Statistical Examples WORK PSYCHOLOGY INTRODUCTION In this chapter we examine a topic which is given too little coverage in most texts of this kind,

More information

Bio 1M: Evolutionary processes

Bio 1M: Evolutionary processes Bio 1M: Evolutionary processes Evolution by natural selection Is something missing from the story I told last chapter? Heritable variation in traits Selection (i.e., differential reproductive success)

More information

Lab #7: Confidence Intervals-Hypothesis Testing (2)-T Test

Lab #7: Confidence Intervals-Hypothesis Testing (2)-T Test A. Objectives: Lab #7: Confidence Intervals-Hypothesis Testing (2)-T Test 1. Subsetting based on variable 2. Explore Normality 3. Explore Hypothesis testing using T-Tests Confidence intervals and initial

More information

Simple Sensitivity Analyses for Matched Samples Thomas E. Love, Ph.D. ASA Course Atlanta Georgia https://goo.

Simple Sensitivity Analyses for Matched Samples Thomas E. Love, Ph.D. ASA Course Atlanta Georgia https://goo. Goal of a Formal Sensitivity Analysis To replace a general qualitative statement that applies in all observational studies the association we observe between treatment and outcome does not imply causation

More information

bivariate analysis: The statistical analysis of the relationship between two variables.

bivariate analysis: The statistical analysis of the relationship between two variables. bivariate analysis: The statistical analysis of the relationship between two variables. cell frequency: The number of cases in a cell of a cross-tabulation (contingency table). chi-square (χ 2 ) test for

More information

Two-Way Independent Samples ANOVA with SPSS

Two-Way Independent Samples ANOVA with SPSS Two-Way Independent Samples ANOVA with SPSS Obtain the file ANOVA.SAV from my SPSS Data page. The data are those that appear in Table 17-3 of Howell s Fundamental statistics for the behavioral sciences

More information

Pedigree Construction Notes

Pedigree Construction Notes Name Date Pedigree Construction Notes GO TO à Mendelian Inheritance (http://www.uic.edu/classes/bms/bms655/lesson3.html) When human geneticists first began to publish family studies, they used a variety

More information

Simple Linear Regression the model, estimation and testing

Simple Linear Regression the model, estimation and testing Simple Linear Regression the model, estimation and testing Lecture No. 05 Example 1 A production manager has compared the dexterity test scores of five assembly-line employees with their hourly productivity.

More information

Mendelian Genetics. Gregor Mendel. Father of modern genetics

Mendelian Genetics. Gregor Mendel. Father of modern genetics Mendelian Genetics Gregor Mendel Father of modern genetics Objectives I can compare and contrast mitosis & meiosis. I can properly use the genetic vocabulary presented. I can differentiate and gather data

More information

A SAS Macro to Investigate Statistical Power in Meta-analysis Jin Liu, Fan Pan University of South Carolina Columbia

A SAS Macro to Investigate Statistical Power in Meta-analysis Jin Liu, Fan Pan University of South Carolina Columbia Paper 109 A SAS Macro to Investigate Statistical Power in Meta-analysis Jin Liu, Fan Pan University of South Carolina Columbia ABSTRACT Meta-analysis is a quantitative review method, which synthesizes

More information

Systems of Mating: Systems of Mating:

Systems of Mating: Systems of Mating: 8/29/2 Systems of Mating: the rules by which pairs of gametes are chosen from the local gene pool to be united in a zygote with respect to a particular locus or genetic system. Systems of Mating: A deme

More information

EXERCISE: HOW TO DO POWER CALCULATIONS IN OPTIMAL DESIGN SOFTWARE

EXERCISE: HOW TO DO POWER CALCULATIONS IN OPTIMAL DESIGN SOFTWARE ...... EXERCISE: HOW TO DO POWER CALCULATIONS IN OPTIMAL DESIGN SOFTWARE TABLE OF CONTENTS 73TKey Vocabulary37T... 1 73TIntroduction37T... 73TUsing the Optimal Design Software37T... 73TEstimating Sample

More information

Mendel s Methods: Monohybrid Cross

Mendel s Methods: Monohybrid Cross Mendel s Methods: Monohybrid Cross Mendel investigated whether the white-flowered form disappeared entirely by breeding the F1 purple flowers with each other. Crossing two purple F1 monohybrid plants is

More information

4Stat Wk 10: Regression

4Stat Wk 10: Regression 4Stat 342 - Wk 10: Regression Loading data with datalines Regression (Proc glm) - with interactions - with polynomial terms - with categorical variables (Proc glmselect) - with model selection (this is

More information

Applied Statistical Analysis EDUC 6050 Week 4

Applied Statistical Analysis EDUC 6050 Week 4 Applied Statistical Analysis EDUC 6050 Week 4 Finding clarity using data Today 1. Hypothesis Testing with Z Scores (continued) 2. Chapters 6 and 7 in Book 2 Review! = $ & '! = $ & ' * ) 1. Which formula

More information

Statistical Techniques. Meta-Stat provides a wealth of statistical tools to help you examine your data. Overview

Statistical Techniques. Meta-Stat provides a wealth of statistical tools to help you examine your data. Overview 7 Applying Statistical Techniques Meta-Stat provides a wealth of statistical tools to help you examine your data. Overview... 137 Common Functions... 141 Selecting Variables to be Analyzed... 141 Deselecting

More information

BIOL 458 BIOMETRY Lab 7 Multi-Factor ANOVA

BIOL 458 BIOMETRY Lab 7 Multi-Factor ANOVA BIOL 458 BIOMETRY Lab 7 Multi-Factor ANOVA PART 1: Introduction to Factorial ANOVA ingle factor or One - Way Analysis of Variance can be used to test the null hypothesis that k or more treatment or group

More information

Lessons in biostatistics

Lessons in biostatistics Lessons in biostatistics The test of independence Mary L. McHugh Department of Nursing, School of Health and Human Services, National University, Aero Court, San Diego, California, USA Corresponding author:

More information

12 MENDEL, GENES, AND INHERITANCE

12 MENDEL, GENES, AND INHERITANCE 12 MENDEL, GENES, AND INHERITANCE Chapter Outline 12.1 THE BEGINNINGS OF GENETICS: MENDEL S GARDEN PEAS Mendel chose true-breeding garden peas for his experiments Mendel first worked with single-character

More information

The Making of the Fittest: Natural Selection in Humans

The Making of the Fittest: Natural Selection in Humans MENDELIAN GENETICS, PROBABILITY, PEDIGREES, AND CHI-SQUARE STATISTICS INTRODUCTION Hemoglobin is a protein found in red blood cells that transports oxygen throughout the body. The hemoglobin protein consists

More information

Final Exam PS 217, Fall 2010

Final Exam PS 217, Fall 2010 Final Exam PS 27, Fall 200. Farzin, et al. (200) wrote an article that appeared in Psychological Science titled: Spatial resolution of conscious visual perception in infants. The abstract read: Humans

More information

Chapter 2 Interactions Between Socioeconomic Status and Components of Variation in Cognitive Ability

Chapter 2 Interactions Between Socioeconomic Status and Components of Variation in Cognitive Ability Chapter 2 Interactions Between Socioeconomic Status and Components of Variation in Cognitive Ability Eric Turkheimer and Erin E. Horn In 3, our lab published a paper demonstrating that the heritability

More information

Ch. 23 The Evolution of Populations

Ch. 23 The Evolution of Populations Ch. 23 The Evolution of Populations 1 Essential question: Do populations evolve? 2 Mutation and Sexual reproduction produce genetic variation that makes evolution possible What is the smallest unit of

More information

BIOL 364 Population Biology Fairly testing the theory of evolution by natural selection with playing cards

BIOL 364 Population Biology Fairly testing the theory of evolution by natural selection with playing cards BIOL 364 Population Biology Fairly testing the theory of evolution by natural selection with playing cards Game I: The Basics Scenario: Our classroom is now a closed population (no immigration or emigration)

More information

MULTIPLE LINEAR REGRESSION 24.1 INTRODUCTION AND OBJECTIVES OBJECTIVES

MULTIPLE LINEAR REGRESSION 24.1 INTRODUCTION AND OBJECTIVES OBJECTIVES 24 MULTIPLE LINEAR REGRESSION 24.1 INTRODUCTION AND OBJECTIVES In the previous chapter, simple linear regression was used when you have one independent variable and one dependent variable. This chapter

More information

Lecture 7: Introduction to Selection. September 14, 2012

Lecture 7: Introduction to Selection. September 14, 2012 Lecture 7: Introduction to Selection September 14, 2012 Announcements Schedule of open computer lab hours on lab website No office hours for me week. Feel free to make an appointment for M-W. Guest lecture

More information

The Making of the Fittest: Natural Selection in Humans

The Making of the Fittest: Natural Selection in Humans INTRODUCTION MENDELIAN GENETICS, PROBABILITY, PEDIGREES, AND CHI-SQUARE STATISTICS Hemoglobin is a protein found in red blood cells (RBCs) that transports oxygen throughout the body. The hemoglobin protein

More information