ANOVA ANOVA. TwoWay ANOVA. OneWay ANOVA. When to use ANOVA ANOVA. Analysis of Variance. Chapter 16. A procedure for comparing more than two groups


 Roy Pierce Wilcox
 2 years ago
 Views:
Transcription
1 ANOVA ANOVA Analysis of Variance Chapter 6 A procedure for comparing more than two groups independent variable: smoking status nonsmoking one pack a day > two packs a day dependent variable: number of coughs per day k number of conditions (in this case, 3) OneWay ANOVA OneWay ANOVA has one independent variable ( factor) with > conditions conditions levels treatments e.g., for a brand of cola factor, the levels are: Coke, Pepsi, RC Cola Independent variables factors TwoWay ANOVA TwoWay ANOVA has independent variables (factors) each can have multiple conditions Example Two Independent Variables (IV s) IV: Brand; and IV: Calories Three levels of Brand: Coke, Pepsi, RC Cola Two levels of Calories: Regular, Diet When to use ANOVA Oneway ANOVA: you have more than two levels (conditions) of a single IV EXAMPLE: studying effectiveness of three types of pain reliever aspirin vs. tylenol vs. ibuprofen Twoway ANOVA: you have more than one IV (factor) EXAMPLE: studying pain relief based on pain reliever and type of pain Factor A: Pain reliever (aspirin vs. tylenol) Factor B: type of pain (headache vs. back pain) ANOVA When a factor uses independent samples in all conditions, it is called a betweensubjects factor betweensubjects ANOVA When a factor uses related samples in all conditions, it is called a withinsubjects factor withinsubjects ANOVA PASW: referred to as repeated measures
2 ANOVA & PASW Why bother with ANOVA? 5 Independent Samples Related Samples samples Independent Samples ttest Paired Samples ttest or more samples Between Subjects ANOVA Repeated Measures ANOVA Mean Pain level 4 3 Tylenol Aspirin Ibuprofen Gin Pain Reliever Would require six ttests, each with an associated Type I (false alarm) rate. Familywise rate Overall probability of making a Type I (false alarm) somewhere in an experiment One ttest, familywise rate is equal to α (e.g.,.05) Multiple ttests result in a familywise rate much larger than the α we selected ANOVA keeps the familywise rate equal to α Posthoc Tests If the ANOVA is significant at least one significant difference between conditions In that case, we follow the ANOVA with posthoc tests that compare two conditions at a time posthoc comparisons identify the specific significant differences between each pair Mean Pain level Tylenol Aspirin Ibuprofen Gin Pain Reliever ANOVA Assumptions Partitioning Variance Homogeneity of variance σ σ σ 3 σ 4 σ 5 Normality scores in each population are normally distributed Mean Pain level Tylenol Aspirin Ibuprofen Gin Pain Reliever
3 Partitioning Variance Total Variance in Scores Partitioning Variance Total Variance in Scores Variance Within Groups () Variance Between Groups group (chance variance) (systematic variance: treatment effect) Mean Square; short for mean squared deviation Similar to variance (s x ) t obt F obt X X s X X difference between sample means difference expected by chance (standard ) variance between sample means variance expected by chance () systematic variance chance variance is an estimate of the variability as measured by differences within the conditions sometimes called the within group variance or the term chance variance (random + individual differences) Tylenol Aspirin Ibuprofen 5 Gin systematic variance.9.7 chance variance 3.3. Mean:.4.8. Pain level variance (within groups) Tylenol Aspirin Ibuprofen Gin Pain Reliever group is an estimate of the differences in scores that occurs between the levels in a factor also called between Treatment effect (systematic variance) Total Variance (variability among all the scores in the data set) X: Tylenol Aspirin Ibuprofen Gin Overall X. Between Groups Variance. Treatment effect (systematic). Chance (random + individual differences) Error Variance (within groups). Chance (random + individual differences) group variance between groups 3
4 FRatio When H 0 is TRUE (there is no treatment effect): F between group variance variance (within groups) Treatment effect + Chance FRatio Chance 0 + Chance Chance In ANOVA, variance Mean Square () between group variance FRatio variance (within groups) group When H 0 is FALSE (there is a treatment effect): F Treatment effect + Chance Chance > Signalto Noise Ratio ANOVA is about looking at the signal relative to noise group is the signal is the noise We want to see if the betweengroup variance (signal), is comparable to the withingroup variance (noise) Logic Behind ANOVA If there is no true difference between groups at the population level: the only differences we get between groups in the sample should be due to. if that s the case, differences between groups should be about the same as differences among individual scores within groups (). group and will be about the same. Logic Behind ANOVA If there are true differences between groups: variance between groups will exceed variance (within groups) F obt will be much greater than F obt F obt can also deviate from by chance alone we need a sampling distribution to tell how high F obt needs to be before we reject the H 0 compare F obt to critical value (e.g., F.05 ) group Logic Behind ANOVA The critical value (F.05 ) depends on degrees of freedom between groups: df group k  (within): df k ( n  ) Total: df total N  alpha (α) e.g.,.05,.0 4
5 ANOVA Example: Cell phones Research Question: Is your reaction time when driving slowed by a cell phone? Does it matter if it s a handsfree phone? Twelve participants went into a driving simulator.. A random subset of 4 drove while listening to the radio (control group).. Another 4 drove while talking on a cell phone. 3. Remaining 4 drove while talking on a handsfree cell phone. Every so often, participants would approach a traffic light that was turning red. The time it took for participants to hit the breaks was measured. A 6 Step Program for Hypothesis Testing. State your research question. Choose a statistical test 3. Select alpha which determines the critical value (F.05 ) 4. State your statistical hypotheses (as equations) 5. Collect data and calculate test statistic (F obt ) 6. Interpret results in terms of hypothesis Report results Explain in plain language A 6 Step Program for Hypothesis Testing. State your research question Is your reaction time when driving influenced by cellphone usage?. Choose a statistical test three levels of a single independent variable (cell; handsfree; control) OneWay ANOVA, between subjects 3. Select α, which determines the critical value α.05 in this case See Ftables (page 543 in the Appendix) df group k 3 (numerator) df k (n  ) 3(4) 9 (denominator) F.05? 4.6 F Distribution critical values (alpha.05) df group k 3 (numerator) 4. State Hypotheses df k (n  ) 3(4) 9 (denominator) H 0 : μ μ μ 3 H : not all μ s are equal referred to as the omnibus null hypothesis When rejecting the Null in ANOVA, we can only conclude that there is at least one significant difference among conditions. If ANOVA significant pinpoint the actual difference(s), with posthoc comparisons 5
6 Examine Data and Calculate F obt DV: Response time (seconds) X Control Is there at least one significant difference between conditions? X Normal Cell X 3 Handsfree Cell A Reminder about Variance Variance: the average squared deviation from the mean X, 4, 6 X 4 Sample Variance Definitional Formula s X (X  X) N Sum of the squared deviation scores X XX (XX) (X  X) 8 s X 8/ 4 ANOVA Summary Table Source Sum of df Mean F Squares Squares Group SS group df group group F obt Error SS df Total SS total df total SS Sum of squared deviations or Sum of Squares ANOVA Summary Table Source Sum of df Mean F Squares Squares Group.07 df group group F obt Error.050 df Total. df total SS total SS + SS group SS total ANOVA Summary Table Source Sum of df Mean F Squares Squares Group.07 group F obt Error Total. df between groups k  df (within groups ) k (n ) df total N (the sum of df group and df ) Examine Data and Calculate F obt Compute the mean squares SS group df SS df group group
7 Examine Data and Calculate F obt ANOVA Summary Table Compute F obt F obt group Source Sum of df Mean F Squares Squares Group Error Total. ANOVA Example: Cell phones Interpret results in terms of hypothesis 6.45 > 4.6; Reject H 0 and accept H Report results F(, 9) 6.45, p <.05 Explain in plain language Among those three groups, there is at least one significant difference X Interpret F obt Figure 6.3 Probability of a Type I as a function of the number of pairwise comparisons where α.05 for any one comparison Posthoc Comparisons Fisher s Least Signficant Difference Test (LSD) uses ttests to perform all pairwise comparisons between group means. good with three groups, risky with > 3 this is a liberal test; i.e., it gives you high power to detect a difference if there is one, but at an increased risk of a Type I 7
8 Posthoc Comparisons Bonferroni procedure uses ttests to perform pairwise comparisons between group means, but controls overall rate by setting the rate for each test to the familywise rate divided by the total number of tests. Hence, the observed significance level is adjusted for the fact that multiple comparisons are being made. e.g., if six comparisons are being made (all possibilities for four groups), then alpha.05/ Posthoc Comparisons Tukey HSD (Honestly Significant Difference) sets the familywise rate at the rate for the collection for all pairwise comparisons. very common test Other posthoc tests also seen: e.g., NewmanKeuls, Duncan, Scheffe Effect Size: Partial Eta Squared Partial Eta squared (η ) indicates the proportion of variance attributable to a factor 0.0 small effect 0.50 medium effect 0.80 large effect Calculation: PASW Effect Size: Omega Squared A less biased indicator of variance explained in the population by a predictor variable SSgroup ( k ) ω SS total +.07 (3 )(.0056) ω % of the variability in response times can be attributed to group membership (medium effect) PASW: OneWay ANOVA (Between Subjects) Setup a oneway between subjects ANOVA as you would an independent samples ttest: Create two variables one variable contains levels of your independent variable (here called group ). there are three groups in this case numbered 3. second variable contains the scores of your dependent variable (here called time ) PASW : OneWay ANOVA (Between Subjects) 8
9 Label the numbers you used to differentiate groups: Go to Variable View, then click on the Values box, then the gray box labeled Enter Value (in this case, or 3) and the Value Label (in this case: control, cell, hands) Click Add, and then add the next two variables. Performing Test Select from Menu: Analyze > General Linear Model > Univariate Select your dependent variable (here: time ) in the Dependent Variable box Select your independent variable (here: group ) in the Fixed Factor(s) box Click Options button, checkdescriptives (this will print the means for each of your levels) check Estimates of effect size for Partial Eta Squared Click the Post Hoc button for post hoc comparisons; move factor to Post Hoc Tests for box; then check LSD, Bonferroni, or Tukey Click OK Dependent Variable: rt Tukey HSD control and cell groups are significantly different if p <.05, then significant effect (I) condition control cell hands (J) condition cell hands control hands control cell *. The mean difference is significant at the.05 level. Mean Difference 95% Confidence Interval (IJ) Std. Error Sig. Lower Bound Upper Bound * * * * hands and cell groups are NOT significantly different Complete explanation Any kind of cell phone conversation can cause a longer reaction time compared to listening to the radio. There is no significant difference between reaction times in the normal cell phone and handsfree conditions. PASW and Effect Size Click Options menu; then check Estimates of effect size box This option produces partial eta squared Partial Eta Squared 9
10 PASW Data Example ANOVA Summary Three groups with three in each group (N 9) Fast Medium Slow X if p <.05, then significant effect Effect size Post Hoc Comparisons slow and medium groups are not significantly different slow and fast groups are significantly different ShamayTsoory SG, Tomer R, AharonPeretz J. (005) The neuroanatomical basis of understanding sarcasm and its relationship to social cognition. Neuropsychology. 9(3), A Sarcastic Version Item Joe came to work, and instead of beginning to work, he sat down to rest. His boss noticed his behavior and said, Joe, don t work too hard! A Neutral Version Item Joe came to work and immediately began to work. His boss noticed his behavior and said, Joe, don t work too hard! Following each story, participants were asked: Did the manager believe Joe was working hard? 0
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 Oneway ANOVA To test the null hypothesis that several population means are equal,
More informationINTERPRETING THE ONEWAY ANALYSIS OF VARIANCE (ANOVA)
INTERPRETING THE ONEWAY ANALYSIS OF VARIANCE (ANOVA) As with other parametric statistics, we begin the oneway ANOVA with a test of the underlying assumptions. Our first assumption is the assumption of
More informationANOVA Analysis of Variance
ANOVA Analysis of Variance What is ANOVA and why do we use it? Can test hypotheses about mean differences between more than 2 samples. Can also make inferences about the effects of several different IVs,
More informationAnalysis of Data. Organizing Data Files in SPSS. Descriptive Statistics
Analysis of Data Claudia J. Stanny PSY 67 Research Design Organizing Data Files in SPSS All data for one subject entered on the same line Identification data Betweensubjects manipulations: variable to
More informationSection 13, Part 1 ANOVA. Analysis Of Variance
Section 13, Part 1 ANOVA Analysis Of Variance Course Overview So far in this course we ve covered: Descriptive statistics Summary statistics Tables and Graphs Probability Probability Rules Probability
More informationOneWay Analysis of Variance
OneWay Analysis of Variance Note: Much of the math here is tedious but straightforward. We ll skim over it in class but you should be sure to ask questions if you don t understand it. I. Overview A. We
More informationStudy 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 informationOneWay Analysis of Variance (ANOVA) Example Problem
OneWay Analysis of Variance (ANOVA) Example Problem Introduction Analysis of Variance (ANOVA) is a hypothesistesting technique used to test the equality of two or more population (or treatment) means
More informationEPS 625 ANALYSIS OF COVARIANCE (ANCOVA) EXAMPLE USING THE GENERAL LINEAR MODEL PROGRAM
EPS 6 ANALYSIS OF COVARIANCE (ANCOVA) EXAMPLE USING THE GENERAL LINEAR MODEL PROGRAM ANCOVA One Continuous Dependent Variable (DVD Rating) Interest Rating in DVD One Categorical/Discrete Independent Variable
More informationA Basic Guide to Analyzing Individual Scores Data with SPSS
A Basic Guide to Analyzing Individual Scores Data with SPSS Step 1. Clean the data file Open the Excel file with your data. You may get the following message: If you get this message, click yes. Delete
More informationRandomized Block Analysis of Variance
Chapter 565 Randomized Block Analysis of Variance Introduction This module analyzes a randomized block analysis of variance with up to two treatment factors and their interaction. It provides tables of
More informationOneWay ANOVA using SPSS 11.0. SPSS ANOVA procedures found in the Compare Means analyses. Specifically, we demonstrate
1 OneWay ANOVA using SPSS 11.0 This section covers steps for testing the difference between three or more group means using the SPSS ANOVA procedures found in the Compare Means analyses. Specifically,
More informationChapter 7. Oneway ANOVA
Chapter 7 Oneway ANOVA Oneway ANOVA examines equality of population means for a quantitative outcome and a single categorical explanatory variable with any number of levels. The ttest of Chapter 6 looks
More informationIntroduction to Analysis of Variance (ANOVA) Limitations of the ttest
Introduction to Analysis of Variance (ANOVA) The Structural Model, The Summary Table, and the One Way ANOVA Limitations of the ttest Although the ttest is commonly used, it has limitations Can only
More informationCOMPARISONS OF CUSTOMER LOYALTY: PUBLIC & PRIVATE INSURANCE COMPANIES.
277 CHAPTER VI COMPARISONS OF CUSTOMER LOYALTY: PUBLIC & PRIVATE INSURANCE COMPANIES. This chapter contains a full discussion of customer loyalty comparisons between private and public insurance companies
More informationTwo Related Samples t Test
Two Related Samples t Test In this example 1 students saw five pictures of attractive people and five pictures of unattractive people. For each picture, the students rated the friendliness of the person
More informationExperimental Designs (revisited)
Introduction to ANOVA Copyright 2000, 2011, J. Toby Mordkoff Probably, the best way to start thinking about ANOVA is in terms of factors with levels. (I say this because this is how they are described
More informationBasic Statistcs Formula Sheet
Basic Statistcs Formula Sheet Steven W. ydick May 5, 0 This document is only intended to review basic concepts/formulas from an introduction to statistics course. Only meanbased procedures are reviewed,
More informationFactor B: Curriculum New Math Control Curriculum (B (B 1 ) Overall Mean (marginal) Females (A 1 ) Factor A: Gender Males (A 2) X 21
1 Factorial ANOVA The ANOVA designs we have dealt with up to this point, known as simple ANOVA or oneway ANOVA, had only one independent grouping variable or factor. However, oftentimes a researcher has
More information13: Additional ANOVA Topics. Post hoc Comparisons
13: Additional ANOVA Topics Post hoc Comparisons ANOVA Assumptions Assessing Group Variances When Distributional Assumptions are Severely Violated KruskalWallis Test Post hoc Comparisons In the prior
More informationStatistiek II. John Nerbonne. October 1, 2010. Dept of Information Science j.nerbonne@rug.nl
Dept of Information Science j.nerbonne@rug.nl October 1, 2010 Course outline 1 Oneway ANOVA. 2 Factorial ANOVA. 3 Repeated measures ANOVA. 4 Correlation and regression. 5 Multiple regression. 6 Logistic
More informationContrasts ask specific questions as opposed to the general ANOVA null vs. alternative
Chapter 13 Contrasts and Custom Hypotheses Contrasts ask specific questions as opposed to the general ANOVA null vs. alternative hypotheses. In a oneway ANOVA with a k level factor, the null hypothesis
More informationData Analysis in SPSS. February 21, 2004. If you wish to cite the contents of this document, the APA reference for them would be
Data Analysis in SPSS Jamie DeCoster Department of Psychology University of Alabama 348 Gordon Palmer Hall Box 870348 Tuscaloosa, AL 354870348 Heather Claypool Department of Psychology Miami University
More informationUsing Microsoft Excel to Analyze Data
Entering and Formatting Data Using Microsoft Excel to Analyze Data Open Excel. Set up the spreadsheet page (Sheet 1) so that anyone who reads it will understand the page. For the comparison of pipets:
More informationRecall this chart that showed how most of our course would be organized:
Chapter 4 OneWay ANOVA Recall this chart that showed how most of our course would be organized: Explanatory Variable(s) Response Variable Methods Categorical Categorical Contingency Tables Categorical
More informationDescriptive Statistics
Descriptive Statistics Primer Descriptive statistics Central tendency Variation Relative position Relationships Calculating descriptive statistics Descriptive Statistics Purpose to describe or summarize
More informationUNDERSTANDING THE ONEWAY ANOVA
UNDERSTANDING The Oneway Analysis of Variance (ANOVA) is a procedure for testing the hypothesis that K population means are equal, where K >. The Oneway ANOVA compares the means of the samples or groups
More informationAn analysis method for a quantitative outcome and two categorical explanatory variables.
Chapter 11 TwoWay ANOVA An analysis method for a quantitative outcome and two categorical explanatory variables. If an experiment has a quantitative outcome and two categorical explanatory variables that
More informationTwosample hypothesis testing, II 9.07 3/16/2004
Twosample hypothesis testing, II 9.07 3/16/004 Small sample tests for the difference between two independent means For twosample tests of the difference in mean, things get a little confusing, here,
More informationANOVA  Analysis of Variance
ANOVA  Analysis of Variance ANOVA  Analysis of Variance Extends independentsamples t test Compares the means of groups of independent observations Don t be fooled by the name. ANOVA does not compare
More informationChapter 14: Repeated Measures Analysis of Variance (ANOVA)
Chapter 14: Repeated Measures Analysis of Variance (ANOVA) First of all, you need to recognize the difference between a repeated measures (or dependent groups) design and the between groups (or independent
More information12: Analysis of Variance. Introduction
1: Analysis of Variance Introduction EDA Hypothesis Test Introduction In Chapter 8 and again in Chapter 11 we compared means from two independent groups. In this chapter we extend the procedure to consider
More informationSTATISTICS FOR PSYCHOLOGISTS
STATISTICS FOR PSYCHOLOGISTS SECTION: STATISTICAL METHODS CHAPTER: REPORTING STATISTICS Abstract: This chapter describes basic rules for presenting statistical results in APA style. All rules come from
More informationMultivariate Analysis of Variance. The general purpose of multivariate analysis of variance (MANOVA) is to determine
2  Manova 4.3.05 25 Multivariate Analysis of Variance What Multivariate Analysis of Variance is The general purpose of multivariate analysis of variance (MANOVA) is to determine whether multiple levels
More informationChapter 9. TwoSample Tests. Effect Sizes and Power Paired t Test Calculation
Chapter 9 TwoSample Tests Paired t Test (Correlated Groups t Test) Effect Sizes and Power Paired t Test Calculation Summary Independent t Test Chapter 9 Homework Power and TwoSample Tests: Paired Versus
More informationAnalysis of Variance. MINITAB User s Guide 2 31
3 Analysis of Variance Analysis of Variance Overview, 32 OneWay Analysis of Variance, 35 TwoWay Analysis of Variance, 311 Analysis of Means, 313 Overview of Balanced ANOVA and GLM, 318 Balanced
More informationSPSS Tests for Versions 9 to 13
SPSS Tests for Versions 9 to 13 Chapter 2 Descriptive Statistic (including median) Choose Analyze Descriptive statistics Frequencies... Click on variable(s) then press to move to into Variable(s): list
More informationJanuary 26, 2009 The Faculty Center for Teaching and Learning
THE BASICS OF DATA MANAGEMENT AND ANALYSIS A USER GUIDE January 26, 2009 The Faculty Center for Teaching and Learning THE BASICS OF DATA MANAGEMENT AND ANALYSIS Table of Contents Table of Contents... i
More informationKSTAT MINIMANUAL. Decision Sciences 434 Kellogg Graduate School of Management
KSTAT MINIMANUAL Decision Sciences 434 Kellogg Graduate School of Management Kstat is a set of macros added to Excel and it will enable you to do the statistics required for this course very easily. To
More informationAnalysis of numerical data S4
Basic medical statistics for clinical and experimental research Analysis of numerical data S4 Katarzyna Jóźwiak k.jozwiak@nki.nl 3rd November 2015 1/42 Hypothesis tests: numerical and ordinal data 1 group:
More informationt Tests in Excel The Excel Statistical Master By Mark Harmon Copyright 2011 Mark Harmon
ttests in Excel By Mark Harmon Copyright 2011 Mark Harmon No part of this publication may be reproduced or distributed without the express permission of the author. mark@excelmasterseries.com www.excelmasterseries.com
More informationPASS Sample Size Software
Chapter 250 Introduction The Chisquare test is often used to test whether sets of frequencies or proportions follow certain patterns. The two most common instances are tests of goodness of fit using multinomial
More informationMain Effects and Interactions
Main Effects & Interactions page 1 Main Effects and Interactions So far, we ve talked about studies in which there is just one independent variable, such as violence of television program. You might randomly
More informationTesting Group Differences using Ttests, ANOVA, and Nonparametric Measures
Testing Group Differences using Ttests, ANOVA, and Nonparametric Measures Jamie DeCoster Department of Psychology University of Alabama 348 Gordon Palmer Hall Box 870348 Tuscaloosa, AL 354870348 Phone:
More informationIBM SPSS Statistics 20 Part 4: ChiSquare and ANOVA
CALIFORNIA STATE UNIVERSITY, LOS ANGELES INFORMATION TECHNOLOGY SERVICES IBM SPSS Statistics 20 Part 4: ChiSquare and ANOVA Summer 2013, Version 2.0 Table of Contents Introduction...2 Downloading the
More information1 Overview. Fisher s Least Significant Difference (LSD) Test. Lynne J. Williams Hervé Abdi
In Neil Salkind (Ed.), Encyclopedia of Research Design. Thousand Oaks, CA: Sage. 2010 Fisher s Least Significant Difference (LSD) Test Lynne J. Williams Hervé Abdi 1 Overview When an analysis of variance
More informationStatistics Review PSY379
Statistics Review PSY379 Basic concepts Measurement scales Populations vs. samples Continuous vs. discrete variable Independent vs. dependent variable Descriptive vs. inferential stats Common analyses
More information1.5 Oneway Analysis of Variance
Statistics: Rosie Cornish. 200. 1.5 Oneway Analysis of Variance 1 Introduction Oneway analysis of variance (ANOVA) is used to compare several means. This method is often used in scientific or medical experiments
More informationChapter 6: t test for dependent samples
Chapter 6: t test for dependent samples ****This chapter corresponds to chapter 11 of your book ( t(ea) for Two (Again) ). What it is: The t test for dependent samples is used to determine whether the
More informationFactorial Analysis of Variance
Chapter 560 Factorial Analysis of Variance Introduction A common task in research is to compare the average response across levels of one or more factor variables. Examples of factor variables are income
More informationMultipleComparison Procedures
MultipleComparison Procedures References A good review of many methods for both parametric and nonparametric multiple comparisons, planned and unplanned, and with some discussion of the philosophical
More informationHow To Run Statistical Tests in Excel
How To Run Statistical Tests in Excel Microsoft Excel is your best tool for storing and manipulating data, calculating basic descriptive statistics such as means and standard deviations, and conducting
More informationMINITAB 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. OneWay
More informationModule 5 Hypotheses Tests: Comparing Two Groups
Module 5 Hypotheses Tests: Comparing Two Groups Objective: In medical research, we often compare the outcomes between two groups of patients, namely exposed and unexposed groups. At the completion of this
More informationGeneral Procedure for Hypothesis Test. Five types of statistical analysis. 1. Formulate H 1 and H 0. General Procedure for Hypothesis Test
Five types of statistical analysis General Procedure for Hypothesis Test Descriptive Inferential Differences Associative Predictive What are the characteristics of the respondents? What are the characteristics
More informationCHAPTER 13. Experimental Design and Analysis of Variance
CHAPTER 13 Experimental Design and Analysis of Variance CONTENTS STATISTICS IN PRACTICE: BURKE MARKETING SERVICES, INC. 13.1 AN INTRODUCTION TO EXPERIMENTAL DESIGN AND ANALYSIS OF VARIANCE Data Collection
More informationRegression stepbystep using Microsoft Excel
Step 1: Regression stepbystep using Microsoft Excel Notes prepared by Pamela Peterson Drake, James Madison University Type the data into the spreadsheet The example used throughout this How to is a regression
More informationIndependent t Test (Comparing Two Means)
Independent t Test (Comparing Two Means) The objectives of this lesson are to learn: the definition/purpose of independent ttest when to use the independent ttest the use of SPSS to complete an independent
More information" Y. Notation and Equations for Regression Lecture 11/4. Notation:
Notation: Notation and Equations for Regression Lecture 11/4 m: The number of predictor variables in a regression Xi: One of multiple predictor variables. The subscript i represents any number from 1 through
More informationSimple Tricks for Using SPSS for Windows
Simple Tricks for Using SPSS for Windows Chapter 14. Followup Tests for the TwoWay Factorial ANOVA The Interaction is Not Significant If you have performed a twoway ANOVA using the General Linear Model,
More informationNCSS Statistical Software Principal Components Regression. In ordinary least squares, the regression coefficients are estimated using the formula ( )
Chapter 340 Principal Components Regression Introduction is a technique for analyzing multiple regression data that suffer from multicollinearity. When multicollinearity occurs, least squares estimates
More informationindividualdifferences
1 Simple ANalysis Of Variance (ANOVA) Oftentimes we have more than two groups that we want to compare. The purpose of ANOVA is to allow us to compare group means from several independent samples. In general,
More informationTechnology StepbyStep Using StatCrunch
Technology StepbyStep Using StatCrunch Section 1.3 Simple Random Sampling 1. Select Data, highlight Simulate Data, then highlight Discrete Uniform. 2. Fill in the following window with the appropriate
More informationIntroduction to Statistics with GraphPad Prism (5.01) Version 1.1
Babraham Bioinformatics Introduction to Statistics with GraphPad Prism (5.01) Version 1.1 Introduction to Statistics with GraphPad Prism 2 Licence This manual is 201011, Anne SegondsPichon. This manual
More informationGeneral Regression Formulae ) (N2) (1  r 2 YX
General Regression Formulae Single Predictor Standardized Parameter Model: Z Yi = β Z Xi + ε i Single Predictor Standardized Statistical Model: Z Yi = β Z Xi Estimate of Beta (Betahat: β = r YX (1 Standard
More informationUnit 31 A Hypothesis Test about Correlation and Slope in a Simple Linear Regression
Unit 31 A Hypothesis Test about Correlation and Slope in a Simple Linear Regression Objectives: To perform a hypothesis test concerning the slope of a least squares line To recognize that testing for a
More informationABSORBENCY OF PAPER TOWELS
ABSORBENCY OF PAPER TOWELS 15. Brief Version of the Case Study 15.1 Problem Formulation 15.2 Selection of Factors 15.3 Obtaining Random Samples of Paper Towels 15.4 How will the Absorbency be measured?
More informationUsing Microsoft Excel to Analyze Data from the Disk Diffusion Assay
Using Microsoft Excel to Analyze Data from the Disk Diffusion Assay Entering and Formatting Data Open Excel. Set up the spreadsheet page (Sheet 1) so that anyone who reads it will understand the page (Figure
More informationUNDERSTANDING ANALYSIS OF COVARIANCE (ANCOVA)
UNDERSTANDING ANALYSIS OF COVARIANCE () In general, research is conducted for the purpose of explaining the effects of the independent variable on the dependent variable, and the purpose of research design
More informationProfile analysis is the multivariate equivalent of repeated measures or mixed ANOVA. Profile analysis is most commonly used in two cases:
Profile Analysis Introduction Profile analysis is the multivariate equivalent of repeated measures or mixed ANOVA. Profile analysis is most commonly used in two cases: ) Comparing the same dependent variables
More information8. Comparing Means Using One Way ANOVA
8. Comparing Means Using One Way ANOVA Objectives Calculate a oneway analysis of variance Run various multiple comparisons Calculate measures of effect size A One Way ANOVA is an analysis of variance
More informationMultivariate Analysis of Variance (MANOVA): I. Theory
Gregory Carey, 1998 MANOVA: I  1 Multivariate Analysis of Variance (MANOVA): I. Theory Introduction The purpose of a t test is to assess the likelihood that the means for two groups are sampled from the
More informationUNDERSTANDING THE DEPENDENTSAMPLES t TEST
UNDERSTANDING THE DEPENDENTSAMPLES t TEST A dependentsamples t test (a.k.a. matched or pairedsamples, matchedpairs, samples, or subjects, simple repeatedmeasures or withingroups, or correlated groups)
More informationInferential Statistics. Probability. From Samples to Populations. Katie RommelEsham Education 504
Inferential Statistics Katie RommelEsham Education 504 Probability Probability is the scientific way of stating the degree of confidence we have in predicting something Tossing coins and rolling dice
More informationMultiple Regression in SPSS This example shows you how to perform multiple regression. The basic command is regression : linear.
Multiple Regression in SPSS This example shows you how to perform multiple regression. The basic command is regression : linear. In the main dialog box, input the dependent variable and several predictors.
More informationPosthoc comparisons & twoway analysis of variance. Twoway ANOVA, II. Posthoc testing for main effects. Posthoc testing 9.
Twoway ANOVA, II Posthoc comparisons & twoway analysis of variance 9.7 4/9/4 Posthoc testing As before, you can perform posthoc tests whenever there s a significant F But don t bother if it s a main
More informationSPSS Explore procedure
SPSS Explore procedure One useful function in SPSS is the Explore procedure, which will produce histograms, boxplots, stemandleaf plots and extensive descriptive statistics. To run the Explore procedure,
More informationPart 2: Analysis of Relationship Between Two Variables
Part 2: Analysis of Relationship Between Two Variables Linear Regression Linear correlation Significance Tests Multiple regression Linear Regression Y = a X + b Dependent Variable Independent Variable
More informationTHE UNIVERSITY OF TEXAS AT TYLER COLLEGE OF NURSING COURSE SYLLABUS NURS 5317 STATISTICS FOR HEALTH PROVIDERS. Fall 2013
THE UNIVERSITY OF TEXAS AT TYLER COLLEGE OF NURSING 1 COURSE SYLLABUS NURS 5317 STATISTICS FOR HEALTH PROVIDERS Fall 2013 & Danice B. Greer, Ph.D., RN, BC dgreer@uttyler.edu Office BRB 1115 (903) 5655766
More informationPSYCHOLOGY 320L Problem Set #3: OneWay ANOVA and Analytical Comparisons
PSYCHOLOGY 30L Problem Set #3: OneWay ANOVA and Analytical Comparisons Name: Score:. You and Dr. Exercise have decided to conduct a study on exercise and its effects on mood ratings. Many studies (Babyak
More informationChapter 2 Probability Topics SPSS T tests
Chapter 2 Probability Topics SPSS T tests Data file used: gss.sav In the lecture about chapter 2, only the OneSample T test has been explained. In this handout, we also give the SPSS methods to perform
More informationUnit 31: OneWay ANOVA
Unit 31: OneWay ANOVA Summary of Video A vase filled with coins takes center stage as the video begins. Students will be taking part in an experiment organized by psychology professor John Kelly in which
More informationChapter 7. Comparing Means in SPSS (ttests) Compare Means analyses. Specifically, we demonstrate procedures for running DependentSample (or
1 Chapter 7 Comparing Means in SPSS (ttests) This section covers procedures for testing the differences between two means using the SPSS Compare Means analyses. Specifically, we demonstrate procedures
More informationSPSS on two independent samples. Two sample test with proportions. Paired ttest (with more SPSS)
SPSS on two independent samples. Two sample test with proportions. Paired ttest (with more SPSS) State of the course address: The Final exam is Aug 9, 3:30pm 6:30pm in B9201 in the Burnaby Campus. (One
More informationHypothesis Testing & Data Analysis. Statistics. Descriptive Statistics. What is the difference between descriptive and inferential statistics?
2 Hypothesis Testing & Data Analysis 5 What is the difference between descriptive and inferential statistics? Statistics 8 Tools to help us understand our data. Makes a complicated mess simple to understand.
More informationRegression Analysis: A Complete Example
Regression Analysis: A Complete Example This section works out an example that includes all the topics we have discussed so far in this chapter. A complete example of regression analysis. PhotoDisc, Inc./Getty
More informationPSYC 381 Statistics Arlo ClarkFoos, Ph.D.
OneWay Within Groups ANOVA PSYC 381 Statistics Arlo ClarkFoos, Ph.D. Comparing Designs Pros of Between No order or carryover effects BetweenGroups Design Pros of Within More costly Higher variability
More informationUnit 29 ChiSquare GoodnessofFit Test
Unit 29 ChiSquare GoodnessofFit Test Objectives: To perform the chisquare hypothesis test concerning proportions corresponding to more than two categories of a qualitative variable To perform the Bonferroni
More informationMultivariate analyses
14 Multivariate analyses Learning objectives By the end of this chapter you should be able to: Recognise when it is appropriate to use multivariate analyses (MANOVA) and which test to use (traditional
More informationUNDERSTANDING THE TWOWAY ANOVA
UNDERSTANDING THE e have seen how the oneway ANOVA can be used to compare two or more sample means in studies involving a single independent variable. This can be extended to two independent variables
More informationAn Introduction to Statistics Course (ECOE 1302) Spring Semester 2011 Chapter 10 TWOSAMPLE TESTS
The Islamic University of Gaza Faculty of Commerce Department of Economics and Political Sciences An Introduction to Statistics Course (ECOE 130) Spring Semester 011 Chapter 10 TWOSAMPLE TESTS Practice
More informationTwoSample TTests Assuming Equal Variance (Enter Means)
Chapter 4 TwoSample TTests Assuming Equal Variance (Enter Means) Introduction This procedure provides sample size and power calculations for one or twosided twosample ttests when the variances of
More informationChris Slaughter, DrPH. GI Research Conference June 19, 2008
Chris Slaughter, DrPH Assistant Professor, Department of Biostatistics Vanderbilt University School of Medicine GI Research Conference June 19, 2008 Outline 1 2 3 Factors that Impact Power 4 5 6 Conclusions
More informationCHAPTER 11 CHISQUARE: NONPARAMETRIC COMPARISONS OF FREQUENCY
CHAPTER 11 CHISQUARE: NONPARAMETRIC COMPARISONS OF FREQUENCY The hypothesis testing statistics detailed thus far in this text have all been designed to allow comparison of the means of two or more samples
More informationSPSS Guide: Regression Analysis
SPSS Guide: Regression Analysis I put this together to give you a stepbystep guide for replicating what we did in the computer lab. It should help you run the tests we covered. The best way to get familiar
More informationReporting Statistics in Psychology
This document contains general guidelines for the reporting of statistics in psychology research. The details of statistical reporting vary slightly among different areas of science and also among different
More informationLesson 1: Comparison of Population Means Part c: Comparison of Two Means
Lesson : Comparison of Population Means Part c: Comparison of Two Means Welcome to lesson c. This third lesson of lesson will discuss hypothesis testing for two independent means. Steps in Hypothesis
More informationAdditional sources Compilation of sources: http://lrs.ed.uiuc.edu/tseportal/datacollectionmethodologies/jintselink/tselink.htm
Mgt 540 Research Methods Data Analysis 1 Additional sources Compilation of sources: http://lrs.ed.uiuc.edu/tseportal/datacollectionmethodologies/jintselink/tselink.htm http://web.utk.edu/~dap/random/order/start.htm
More informationresearch/scientific includes the following: statistical hypotheses: you have a null and alternative you accept one and reject the other
1 Hypothesis Testing Richard S. Balkin, Ph.D., LPCS, NCC 2 Overview When we have questions about the effect of a treatment or intervention or wish to compare groups, we use hypothesis testing Parametric
More informationTwoSample TTests Allowing Unequal Variance (Enter Difference)
Chapter 45 TwoSample TTests Allowing Unequal Variance (Enter Difference) Introduction This procedure provides sample size and power calculations for one or twosided twosample ttests when no assumption
More information