Chapter 2: ANOVA and regression. Caroline Verhoeven
|
|
|
- Jonathan Carson
- 5 years ago
- Views:
Transcription
1 Chapter 2: ANOVA and regression Caroline Verhoeven
2 Table of contents 1 ANOVA One-way ANOVA Repeated measures ANOVA Two-way ANOVA 2 Regression Simple linear regression Multiple regression 3 Conclusion Caroline Verhoeven BMOL-G / 29
3 1. ANOVA 1. One-way ANOVA One-way ANOVA We want to compare more than two groups Example : We want to compare the effect of treatment 1, treatment 2 and a placebo H 0 : µ 1 = µ 2 = = µ k H a : at least one of the means is different Caroline Verhoeven BMOL-G / 29
4 1. ANOVA 1. One-way ANOVA One-way ANOVA We want to compare more than two groups Example : We want to compare the effect of treatment 1, treatment 2 and a placebo H 0 : µ 1 = µ 2 = = µ k H a : at least one of the means is different Principle : Compare the variation of the means between the groups to the variation inside the groups. In SPSS : Analyse Comparer les moyennes ANOVA à 1 facteur (Analyze Compare Means One-Way ANOVA) Caroline Verhoeven BMOL-G / 29
5 Conditions 1. ANOVA 1. One-way ANOVA We must have simple random samples The samples must be independent σ1 2 = σ2 2 = = σ2 k We can use the Levene test (in SPSS) The variables must be normally distributed Caroline Verhoeven BMOL-G / 29
6 Conditions 1. ANOVA 1. One-way ANOVA We must have simple random samples The samples must be independent σ1 2 = σ2 2 = = σ2 k We can use the Levene test (in SPSS) The variables must be normally distributed If not : Kruskal-Wallis test Done in the same way as the Mann-Whitney test Caroline Verhoeven BMOL-G / 29
7 Preliminary test : Levene test 1. ANOVA 1. One-way ANOVA Are the variances the same for all the groups? Caroline Verhoeven BMOL-G / 29
8 Preliminary test : Levene test 1. ANOVA 1. One-way ANOVA Are the variances the same for all the groups? Do the Levene test : H 0 : σ 2 1 = σ2 2 = = σ2 k H a : At least 1 of the variances is different Caroline Verhoeven BMOL-G / 29
9 Preliminary test : Levene test 1. ANOVA 1. One-way ANOVA Are the variances the same for all the groups? Do the Levene test : H 0 : σ 2 1 = σ2 2 = = σ2 k H a : At least 1 of the variances is different p > 0, 05 : NRH 0 p < 0, 05 : RH 0 Caroline Verhoeven BMOL-G / 29
10 Preliminary test : Levene test 1. ANOVA 1. One-way ANOVA Are the variances the same for all the groups? Do the Levene test : H 0 : σ 2 1 = σ2 2 = = σ2 k H a : At least 1 of the variances is different p > 0, 05 : NRH 0 p < 0, 05 : RH 0 SPSS : ANOVA Options test d homogénéité des variances (ANOVA Options Homogeneity of variance test) Caroline Verhoeven BMOL-G / 29
11 1. ANOVA 1. One-way ANOVA what with a RH 0 for the Levene test? What do we do if we have a RH 0 for the Levene test? Caroline Verhoeven BMOL-G / 29
12 1. ANOVA 1. One-way ANOVA what with a RH 0 for the Levene test? What do we do if we have a RH 0 for the Levene test? A solution : the Welch test Caroline Verhoeven BMOL-G / 29
13 1. ANOVA 1. One-way ANOVA what with a RH 0 for the Levene test? What do we do if we have a RH 0 for the Levene test? A solution : the Welch test SPSS : ANOVA Options Welch Caroline Verhoeven BMOL-G / 29
14 After ANOVA 1. ANOVA 1. One-way ANOVA What to do when we have a RH 0 for the ANOVA? How can we know which means are different? Caroline Verhoeven BMOL-G / 29
15 After ANOVA 1. ANOVA 1. One-way ANOVA What to do when we have a RH 0 for the ANOVA? How can we know which means are different? If we have a NRH 0 : stop If we have a RH 0 : there are different multiple comparison tests Caroline Verhoeven BMOL-G / 29
16 After ANOVA 1. ANOVA 1. One-way ANOVA What to do when we have a RH 0 for the ANOVA? How can we know which means are different? If we have a NRH 0 : stop If we have a RH 0 : there are different multiple comparison tests Bonferroni Sidak Tukey Dunnett... Caroline Verhoeven BMOL-G / 29
17 1. ANOVA 1. One-way ANOVA After ANOVA What to do when we have a RH 0 for the ANOVA? How can we know which means are different? If we have a NRH 0 : stop If we have a RH 0 : there are different multiple comparison tests Bonferroni Sidak Tukey Dunnett... SPSS : ANOVA Post Hoc Caroline Verhoeven BMOL-G / 29
18 Principle 1. ANOVA 2. Repeated measures ANOVA A measurement is taken in k different situations, on the same subjects Caroline Verhoeven BMOL-G / 29
19 1. ANOVA 2. Repeated measures ANOVA Principle A measurement is taken in k different situations, on the same subjects Generalization of the t-test for 2 paired samples Caroline Verhoeven BMOL-G / 29
20 1. ANOVA 2. Repeated measures ANOVA Principle A measurement is taken in k different situations, on the same subjects Generalization of the t-test for 2 paired samples SPSS : Analyse Modèle Linéaire Général Mesures Répétées (Analyze General Linear Model Repeated Measures) Caroline Verhoeven BMOL-G / 29
21 1. ANOVA 2. Repeated measures ANOVA Conditions We must have a simple random sample the variances of the differences between two groups must be equal we can use the Mauchly test The variables must be normally distributed Caroline Verhoeven BMOL-G / 29
22 1. ANOVA 2. Repeated measures ANOVA Conditions We must have a simple random sample the variances of the differences between two groups must be equal we can use the Mauchly test The variables must be normally distributed If not : Friedman test Done in the same way as the signed rank Wilcoxon test Caroline Verhoeven BMOL-G / 29
23 Preliminary test : Mauchly test 1. ANOVA 2. Repeated measures ANOVA Are the variances of the differences between two groups equal? Caroline Verhoeven BMOL-G / 29
24 Preliminary test : Mauchly test 1. ANOVA 2. Repeated measures ANOVA Are the variances of the differences between two groups equal? Perform the Mauchly test H 0 : The variances of the differences are equal H a : At least 1 variance is different Caroline Verhoeven BMOL-G / 29
25 Preliminary test : Mauchly test 1. ANOVA 2. Repeated measures ANOVA Are the variances of the differences between two groups equal? Perform the Mauchly test H 0 : The variances of the differences are equal H a : At least 1 variance is different p > 0, 05 : NRH 0 p < 0, 05 : RH 0 Caroline Verhoeven BMOL-G / 29
26 1. ANOVA 2. Repeated measures ANOVA Preliminary test : Mauchly test Are the variances of the differences between two groups equal? Perform the Mauchly test H 0 : The variances of the differences are equal H a : At least 1 variance is different p > 0, 05 : NRH 0 p < 0, 05 : RH 0 If RH 0 : Greenhouse-Geisser correction (stronger correction) Huynh-Feldt correction Caroline Verhoeven BMOL-G / 29
27 1. ANOVA 2. Repeated measures ANOVA Preliminary test : Mauchly test Are the variances of the differences between two groups equal? Perform the Mauchly test H 0 : The variances of the differences are equal H a : At least 1 variance is different p > 0, 05 : NRH 0 p < 0, 05 : RH 0 If RH 0 : Greenhouse-Geisser correction (stronger correction) Huynh-Feldt correction To choose : look at the Greenhouse-Geisser epsilon Caroline Verhoeven BMOL-G / 29
28 Two-Way ANOVA 1. ANOVA 3. Two-way ANOVA We want to evaluate the effects of 2 factors Example : We want to study the white blood cells level for persons with and without leukemia and for children and adults Caroline Verhoeven BMOL-G / 29
29 Two-Way ANOVA 1. ANOVA 3. Two-way ANOVA We want to evaluate the effects of 2 factors Example : We want to study the white blood cells level for persons with and without leukemia and for children and adults 2 factors possibility of interaction Caroline Verhoeven BMOL-G / 29
30 1. ANOVA 3. Two-way ANOVA Two-Way ANOVA We want to evaluate the effects of 2 factors Example : We want to study the white blood cells level for persons with and without leukemia and for children and adults Formulation of the null hypotheses : 2 factors possibility of interaction H 0 : having leukemia or not makes no difference wrt the white blood cells levels H 0 : being a child or an adult makes no difference wrt the white blood cells levels H 0 : The effect of the illness on the white blood cells levels does not depend on being a child or an adult Caroline Verhoeven BMOL-G / 29
31 1. ANOVA 3. Two-way ANOVA Two-Way ANOVA We want to evaluate the effects of 2 factors Example : We want to study the white blood cells level for persons with and without leukemia and for children and adults Formulation of the null hypotheses : 2 factors possibility of interaction H 0 : having leukemia or not makes no difference wrt the white blood cells levels H 0 : being a child or an adult makes no difference wrt the white blood cells levels H 0 : The effect of the illness on the white blood cells levels does not depend on being a child or an adult SPSS :Analyse Modèle Linéaire Général Univarié (Analyze General Linear Model Univariate) Caroline Verhoeven BMOL-G / 29
32 2. Regression 1. Simple linear regression Linear regression x i : quantitative data, predictor y i : quantitative data, response Caroline Verhoeven BMOL-G / 29
33 2. Regression 1. Simple linear regression Linear regression x i : quantitative data, predictor y i : quantitative data, response Linear relationship between X and Y Caroline Verhoeven BMOL-G / 29
34 2. Regression 1. Simple linear regression Linear regression x i : quantitative data, predictor y i : quantitative data, response Linear relationship between X and Y Question : How do we determine the regression line y = b 0 + b 1 x, b 0? b 1? Caroline Verhoeven BMOL-G / 29
35 Linear regression : conditions 2. Regression 1. Simple linear regression Due to the measurement error and biological variability, we have : y i = b 0 + b 1 x i + ε i ε i : residue, condition : ε i N (0, σ 2 ) Caroline Verhoeven BMOL-G / 29
36 Linear regression : conditions 2. Regression 1. Simple linear regression Due to the measurement error and biological variability, we have : y i = b 0 + b 1 x i + ε i ε i : residue, condition : ε i N (0, σ 2 ) σ : independent of x Homocedasticity Age FCM Heterocedasticity Age Caroline Verhoeven BMOL-G / 29
37 Multiple regression : utility 2. Regression 2. Multiple regression A variable can depend simultaneously of several factors. Caroline Verhoeven BMOL-G / 29
38 2. Regression 2. Multiple regression Multiple regression : utility A variable can depend simultaneously of several factors. Exemple 1 Prediction of the height of a person from the height of his mother, his father and his gender Caroline Verhoeven BMOL-G / 29
39 2. Regression 2. Multiple regression Multiple regression : utility A variable can depend simultaneously of several factors. Exemple 1 Prediction of the height of a person from the height of his mother, his father and his gender Goal : Predict the values of Y from several variables X 1, X 2,..., X k Caroline Verhoeven BMOL-G / 29
40 2. Regression 2. Multiple regression Multiple regression : utility A variable can depend simultaneously of several factors. Exemple 1 Prediction of the height of a person from the height of his mother, his father and his gender Goal : Predict the values of Y from several variables X 1, X 2,..., X k X 1, X 2,...X k are generally quantitative or ordinal, a few can be nominal Caroline Verhoeven BMOL-G / 29
41 2. Regression 2. Multiple regression Multiple regression : utility A variable can depend simultaneously of several factors. Exemple 1 Prediction of the height of a person from the height of his mother, his father and his gender Goal : Predict the values of Y from several variables X 1, X 2,..., X k X 1, X 2,...X k are generally quantitative or ordinal, a few can be nominal Exemple 1 Gender is a nominal variable : 0=femme 1=homme Caroline Verhoeven BMOL-G / 29
42 2. Regression 2. Multiple regression Multiple regression : principle Study of the linear relationship between Y and variables X 1, X 2,..., X k : y = b 0 + b 1 x 1 + b 2 x b k x k. Caroline Verhoeven BMOL-G / 29
43 2. Regression 2. Multiple regression Multiple regression : principle Study of the linear relationship between Y and variables X 1, X 2,..., X k : y = b 0 + b 1 x 1 + b 2 x b k x k. looking for : b 0, b 1, b 2,..., b k SPSS : Analyse Régression Linéaire (Analyze Regression Linear) Caroline Verhoeven BMOL-G / 29
44 2. Regression 2. Multiple regression Methods for the regression I Enter Method : Method who introduces all the independent variables simultaneously Use it if you want to keep all the independent variabls int he regression equation. Caroline Verhoeven BMOL-G / 29
45 2. Regression 2. Multiple regression Methods for the regression I Enter Method : Method who introduces all the independent variables simultaneously Use it if you want to keep all the independent variabls int he regression equation. The other methods are hierarchal methods. Only use it if you think that some variables are more important than others Caroline Verhoeven BMOL-G / 29
46 Methods for the regression II 2. Regression 2. Multiple regression Forward method : Introduction of an independent variable at the time Order : decreasing order of correlation coefficient between dependent and independent variable If it doesn t enhance the model significantly, it is eliminated We stop at the first eliminated variable Caroline Verhoeven BMOL-G / 29
47 Methods for the regression II 2. Regression 2. Multiple regression Forward method : Introduction of an independent variable at the time Order : decreasing order of correlation coefficient between dependent and independent variable If it doesn t enhance the model significantly, it is eliminated We stop at the first eliminated variable Backward method All the independent variables are introduced The weakest variable is removed If the model is significantly worse, it is reintroduced We stop at the first reintroduced variable Caroline Verhoeven BMOL-G / 29
48 Methods for the regression II 2. Regression 2. Multiple regression Forward method : Introduction of an independent variable at the time Order : decreasing order of correlation coefficient between dependent and independent variable If it doesn t enhance the model significantly, it is eliminated We stop at the first eliminated variable Backward method All the independent variables are introduced The weakest variable is removed If the model is significantly worse, it is reintroduced We stop at the first reintroduced variable Stepwize method Introduction of an independent variable at the time Testing if the new variables, and the previous, are significant Non significant variables are eliminated Caroline Verhoeven BMOL-G / 29
49 2. Regression 2. Multiple regression Multiple regression : conditions 1 The same conditions as for a simple regression 2 There exists a linear relationship between Y and the X i 3 No multi-collinearity : X i variables must not be highly correlated 4 You need a lot of subjects. Minimum : 5k, k : number of factors Caroline Verhoeven BMOL-G / 29
50 3. Conclusion Use of ANOVA and regression Model Response Predictor One-way ANOVA 1 quantitative 1 qualitative Two-way ANOVA 1 quantitative 2 qualitative Simple regression 1 quantitative 1 quantitative Multiple regression 1 quantitative 2 or more quantitative Caroline Verhoeven BMOL-G / 29
51 4. Exercises Exercise 1 Open the file film.xls. Determine the regression equation of the income of a movie based on a book : Production costs Publicity costs Income of the book 10 movies are considered. Caroline Verhoeven BMOL-G / 29
52 Exercise 2 4. Exercises Open the file melatonin.sav in SPSS. Traveling to another timezone induces a jet lag. We re adapting gradually because our circadian rhythm is synchronized with the day-night cycle. This rhythm change is called a shift En 2002, Wright et Czeisler studied this phenomenon. The time of melatonin production for 22 subjects. Those subjects were randomly divided in 3 groups. Alle the groups were waken 3 hours during their sleep. The first group with light in the eyes, the second with lights behind the knee, while there was no light at all for the third group. Their meltatonin cycle was measure before the treatment and after 2 days. Caroline Verhoeven BMOL-G / 29
53 4. Exercises Exercise 2 Open the file melatonin.sav in SPSS. Traveling to another timezone induces a jet lag. We re adapting gradually because our circadian rhythm is synchronized with the day-night cycle. This rhythm change is called a shift En 2002, Wright et Czeisler studied this phenomenon. The time of melatonin production for 22 subjects. Those subjects were randomly divided in 3 groups. Alle the groups were waken 3 hours during their sleep. The first group with light in the eyes, the second with lights behind the knee, while there was no light at all for the third group. Their meltatonin cycle was measure before the treatment and after 2 days. The shift (in hours) is given in the file. A negative shifts corresponds to a delay. Determine if the type of lightning has an effect on the circadian cycle. Caroline Verhoeven BMOL-G / 29
54 Exercise 3 4. Exercises In 2005, Walker et al. studied stress among penguins. Some of those penguins reproduce in quite regions, while others reproduce in touristic regions. Caroline Verhoeven BMOL-G / 29
55 Exercise 3 4. Exercises In 2005, Walker et al. studied stress among penguins. Some of those penguins reproduce in quite regions, while others reproduce in touristic regions. We want to know how stress of young penguins is impacted by their age and by the type of region in which they re growing. Caroline Verhoeven BMOL-G / 29
56 4. Exercises Exercise 3 In 2005, Walker et al. studied stress among penguins. Some of those penguins reproduce in quite regions, while others reproduce in touristic regions. We want to know how stress of young penguins is impacted by their age and by the type of region in which they re growing. To answer this question, young penguins were captured and their corticosterone level was measured. This was done in both regions, with penguins which just hatched, which were 40 to 50 days old and with young adults. Caroline Verhoeven BMOL-G / 29
57 4. Exercises Exercise 3 In 2005, Walker et al. studied stress among penguins. Some of those penguins reproduce in quite regions, while others reproduce in touristic regions. We want to know how stress of young penguins is impacted by their age and by the type of region in which they re growing. To answer this question, young penguins were captured and their corticosterone level was measured. This was done in both regions, with penguins which just hatched, which were 40 to 50 days old and with young adults. Open the file penguin.xls. Determine if the age and the region have an impact on the stress level of the penguins. Caroline Verhoeven BMOL-G / 29
58 Exercise 4 4. Exercises Open the file intima media.xls in SPSS. 1 Do age and BMI influence significantly the thickness of the intima-media. 2 Is there a significant difference for the thickness of the intima-media depending on the consumption of tobacco and alcohol? Caroline Verhoeven BMOL-G / 29
59 Exercise 5 4. Exercises In the reality-show I m a celebrity, get me out of here, celebrities have to survive in the jungle and have to undergo humiliating tests. One of those tests is to swallow unappetizing food. 8 of those celebrities have to swallow 4 items each. The time between the moment they put the food item in the mouth, and which they feel sick is measured in seconds. The results can be found in the file celeb.xls. 1 Do we have different times for the different food items? Caroline Verhoeven BMOL-G / 29
60 Exercise 6 4. Exercises Mammals have mechanisms to reduce the brain temperature with respect to the body temperature when exposed to a long period of extreme heat. In 2003 Fuller et al did an experience on ostriches to see if they can do the same things. The results can be found in the file ostrich.xls. Do the brain and body temperature differ for ostriches? Caroline Verhoeven BMOL-G / 29
61 Exercise 7 4. Exercises We are testing the influence of various diets on lab rats. The weight gain of the rats can be found in the variable Weight expressed in grams. The value for the variable Calorie is 1 if the rats had a normal diet. The value is 2 if they had an hypercaloric diet. The value of the variable Vitamin is 1 if the rats didn t receive a vitamin supplement. The value is 2 if they received such a supplement. Is the wight gain of the rats influenced by the diet and the vitamin supplement? The data are in the file rats.xls. Caroline Verhoeven BMOL-G / 29
62 Exercise 8 4. Exercises The alarm call of a chickadee for a not flying predator sounds like dee-dee-dee. In 2005, Templeton et al. wanted to know if the number of dee is correlated with the weight of te predator. They perched 13 predators of different sizes before a flock of chicakdees. The average number of dee was measured for each predator. The data can be found in the file chickadee.xls. Can the weight of the predator be predicted from the average number of dee? Caroline Verhoeven BMOL-G / 29
63 4. Exercises Exercises on children with the down syndrome I In 2013, de Graaf et al. studied the importance of the choice of education system (specialized education or traditional education) for children with down syndrome. They asked parents with children with the down syndrome to fill a survey. The questions were about the performances of the children in reading, writing and maths. They also for the age and the IQ of the cild and the study level of the parents. The data can be found in the file down.xls Caroline Verhoeven BMOL-G / 29
64 4. Exercises Exercises on children with the down syndrome II Exercise 9 Is there a difference in performances in reading, writing and maths between children in the traditional and the specialized education system. Exercise 10 Is the IQ different for children in the traditional and specialized education system? Exercise 11 What is the effect of the study level of the parents on the performances of the child in writing. Exercise 12 What is the effect of the IQ and of the age of the child and the study level of the mother with respect to the performance of the child in maths. Exercice 13 What is the impact of the study level of the parents on the choice of the education system. Caroline Verhoeven BMOL-G / 29
Analysis of Variance. Copyright 2014 Pearson Education, Inc.
Analysis of Variance 12-1 Learning Outcomes Outcome 1. Understand the basic logic of analysis of variance. Outcome 2. Perform a hypothesis test for a single-factor design using analysis of variance manually
Name May 3, 2007 Math Probability and Statistics
Name May 3, 2007 Math 341 - Probability and Statistics Long Exam IV Instructions: Please include all relevant work to get full credit. Encircle your final answers. 1. An article in Professional Geographer
One-factor ANOVA by example
ANOVA One-factor ANOVA by example 2 One-factor ANOVA by visual inspection 3 4 One-factor ANOVA H 0 H 0 : µ 1 = µ 2 = µ 3 = H A : not all means are equal 5 One-factor ANOVA but why not t-tests t-tests?
ANOVA - Implementation.
ANOVA - Implementation http://www.pelagicos.net/classes_biometry_fa17.htm Doing an ANOVA With RCmdr Categorical Variable One-Way ANOVA Testing a single Factor dose with 3 treatments (low, mid, high) Doing
Introduction to Analysis of Variance (ANOVA) The Structural Model, The Summary Table, and the One- Way ANOVA
Introduction to Analysis of Variance (ANOVA) The Structural Model, The Summary Table, and the One- Way ANOVA Limitations of the t-test Although the t-test is commonly used, it has limitations Can only
1. Answer this student s question: Is a random sample of 5% of the students at my school large enough, or should I use 10%?
Econ 57 Gary Smith Fall 2011 Final Examination (150 minutes) No calculators allowed. Just set up your answers, for example, P = 49/52. BE SURE TO EXPLAIN YOUR REASONING. If you want extra time, you can
Legendre et al Appendices and Supplements, p. 1
Legendre et al. 2010 Appendices and Supplements, p. 1 Appendices and Supplement to: Legendre, P., M. De Cáceres, and D. Borcard. 2010. Community surveys through space and time: testing the space-time interaction
Chapter 13. Factorial ANOVA. Patrick Mair 2015 Psych Factorial ANOVA 0 / 19
Chapter 13 Factorial ANOVA Patrick Mair 2015 Psych 1950 13 Factorial ANOVA 0 / 19 Today s Menu Now we extend our one-way ANOVA approach to two (or more) factors. Factorial ANOVA: two-way ANOVA, SS decomposition,
Class 23: Chapter 14 & Nested ANOVA NOTES: NOTES: NOTES:
Slide 1 Chapter 13: ANOVA for 2-way classifications (2 of 2) Fixed and Random factors, Model I, Model II, and Model III (mixed model) ANOVA Chapter 14: Unreplicated Factorial & Nested Designs Slide 2 HW
INFLUENCE OF ENVIRONMENTAL PARAMETERS ON FISHERY
Chapter 5 INFLUENCE OF ENVIRONMENTAL PARAMETERS ON FISHERY 5. Introduction Environmental factors contribute to the population dynamics and abundance of marine fishery. The relationships between weather,
A few things to remember about ANOVA
A few things to remember about ANOVA 1) The F-test that is performed is always 1-tailed. This is because your alternative hypothesis is always that the between group variation is greater than the within
Navigate to the golf data folder and make it your working directory. Load the data by typing
Golf Analysis 1.1 Introduction In a round, golfers have a number of choices to make. For a particular shot, is it better to use the longest club available to try to reach the green, or would it be better
27Quantify Predictability U10L9. April 13, 2015
1 QUANTIFYING PREDICTABILITY Exercise #1: Make sure that your calculator has its r value on. 2 Exercise #2: In the following exercises four data sets with equal x values are given to illustrate different
Is lung capacity affected by smoking, sport, height or gender. Table of contents
Sample project This Maths Studies project has been graded by a moderator. As you read through it, you will see comments from the moderator in boxes like this: At the end of the sample project is a summary
Real-Time Electricity Pricing
Real-Time Electricity Pricing Xi Chen, Jonathan Hosking and Soumyadip Ghosh IBM Watson Research Center / Northwestern University Yorktown Heights, NY, USA X. Chen, J. Hosking & S. Ghosh (IBM) Real-Time
Design of Experiments Example: A Two-Way Split-Plot Experiment
Design of Experiments Example: A Two-Way Split-Plot Experiment A two-way split-plot (also known as strip-plot or split-block) design consists of two split-plot components. In industry, these designs arise
Chapter 12 Practice Test
Chapter 12 Practice Test 1. Which of the following is not one of the conditions that must be satisfied in order to perform inference about the slope of a least-squares regression line? (a) For each value
Running head: DATA ANALYSIS AND INTERPRETATION 1
Running head: DATA ANALYSIS AND INTERPRETATION 1 Data Analysis and Interpretation Final Project Vernon Tilly Jr. University of Central Oklahoma DATA ANALYSIS AND INTERPRETATION 2 Owners of the various
PLANNED ORTHOGONAL CONTRASTS
PLANNED ORTHOGONAL CONTRASTS Please note: This handout is useful background for the workshop, not what s covered in it. Basic principles for contrasts are the same in repeated measures. Planned orthogonal
y ) s x x )(y i (x i r = 1 n 1 s y Statistics Lecture 7 Exploring Data , y 2 ,y n (x 1 ),,(x n ),(x 2 ,y 1 How two variables vary together
Statistics 111 - Lecture 7 Exploring Data Numerical Summaries for Relationships between Variables Administrative Notes Homework 1 due in recitation: Friday, Feb. 5 Homework 2 now posted on course website:
Keywords: multiple linear regression; pedestrian crossing delay; right-turn car flow; the number of pedestrians;
Available online at www.sciencedirect.com ScienceDirect Procedia - Social and Behavioral Scien ce s 96 ( 2013 ) 1997 2003 13th COTA International Conference of Transportation Professionals (CICTP 2013)
Driv e accu racy. Green s in regul ation
LEARNING ACTIVITIES FOR PART II COMPILED Statistical and Measurement Concepts We are providing a database from selected characteristics of golfers on the PGA Tour. Data are for 3 of the players, based
Longitudinal analysis of young Danes travel pattern.
Aalborg trafikdage 24.08.2010 Longitudinal analysis of young Danes travel pattern. Sigrun Birna Sigurdardottir PhD student, DTU Transport. Background Limited literature regarding models or factors influencing
Announcements. % College graduate vs. % Hispanic in LA. % College educated vs. % Hispanic in LA. Problem Set 10 Due Wednesday.
Announcements Announcements UNIT 7: MULTIPLE LINEAR REGRESSION LECTURE 1: INTRODUCTION TO MLR STATISTICS 101 Problem Set 10 Due Wednesday Nicole Dalzell June 15, 2015 Statistics 101 (Nicole Dalzell) U7
APPROACH RUN VELOCITIES OF FEMALE POLE VAULTERS
APPROACH RUN VELOCITIES OF FEMALE POLE VAULTERS Peter M. McGinnis, Physical Education Department, SUNY College at Cortland, Cortland, New York INTRODUCTION Running speed is an important determinant of
Journal of Human Sport and Exercise E-ISSN: Universidad de Alicante España
Journal of Human Sport and Exercise E-ISSN: 1988-5202 jhse@ua.es Universidad de Alicante España SOÓS, ISTVÁN; FLORES MARTÍNEZ, JOSÉ CARLOS; SZABO, ATTILA Before the Rio Games: A retrospective evaluation
Quantitative Methods for Economics Tutorial 6. Katherine Eyal
Quantitative Methods for Economics Tutorial 6 Katherine Eyal TUTORIAL 6 13 September 2010 ECO3021S Part A: Problems 1. (a) In 1857, the German statistician Ernst Engel formulated his famous law: Households
One Way ANOVA (Analysis of Variance)
One Wa ANOVA (Analsis of Variance) The one-wa analsis of variance (ANOVA) is used to determine whether there are an significant differences between the means of two or more independent (unrelated) groups
Analysis of performance and age of the fastest 100- mile ultra-marathoners worldwide
CLINICAL SCIENCE Analysis of performance and age of the fastest 100- mile ultra-marathoners worldwide Christoph Alexander Rüst, I Beat Knechtle, I,II Thomas Rosemann, I Romuald Lepers III I University
Chapter 7. Comparing Two Population Means. Comparing two population means. T-tests: Independent samples and paired variables.
Chapter 7 Comparing Two Population Means Comparing two population means T-tests: Independent samples and paired variables. Usually subjects are assigned to treatment or control groups and one or more variables
HSIS. Association of Selected Intersection Factors With Red-Light-Running Crashes. State Databases Used SUMMARY REPORT
HSIS HIGHWAY SAFETY INFORMATION SYSTEM The Highway Safety Information Systems (HSIS) is a multi-state safety data base that contains accident, roadway inventory, and traffic volume data for a select group
Novel empirical correlations for estimation of bubble point pressure, saturated viscosity and gas solubility of crude oils
86 Pet.Sci.(29)6:86-9 DOI 1.17/s12182-9-16-x Novel empirical correlations for estimation of bubble point pressure, saturated viscosity and gas solubility of crude oils Ehsan Khamehchi 1, Fariborz Rashidi
PSY201: Chapter 5: The Normal Curve and Standard Scores
PSY201: Chapter 5: The Normal Curve and Standard Scores Introduction: Normal curve + a very important distribution in behavior sciences + three principal reasons why... - 1. many of the variables measured
Reported walking time and measured distances to water sources: Implications for measuring Basic Service
Reported walking time and measured distances to water sources: Implications for measuring Basic Service Anna Murray1, Maeve Kennard1, Daniele Lantagne2 1, 2Tufts University UNC Water and Health 2018 Background
DEVELOPMENT OF A SET OF TRIP GENERATION MODELS FOR TRAVEL DEMAND ESTIMATION IN THE COLOMBO METROPOLITAN REGION
DEVELOPMENT OF A SET OF TRIP GENERATION MODELS FOR TRAVEL DEMAND ESTIMATION IN THE COLOMBO METROPOLITAN REGION Ravindra Wijesundera and Amal S. Kumarage Dept. of Civil Engineering, University of Moratuwa
a) List and define all assumptions for multiple OLS regression. These are all listed in section 6.5
Prof. C. M. Dalton ECN 209A Spring 2015 Practice Problems (After HW1, HW2, before HW3) CORRECTED VERSION Question 1. Draw and describe a relationship with heteroskedastic errors. Support your claim with
Unit 4: Inference for numerical variables Lecture 3: ANOVA
Unit 4: Inference for numerical variables Lecture 3: ANOVA Statistics 101 Thomas Leininger June 10, 2013 Announcements Announcements Proposals due tomorrow. Will be returned to you by Wednesday. You MUST
JEPonline Journal of Exercise Physiologyonline
Walking Technique and Estimated VO 2 max Values 21 JEPonline Journal of Exercise Physiologyonline Official Journal of The American Society of Exercise Physiologists (ASEP) ISSN 1097-9751 An International
The Impact of Wolf Reintroduction on the Foraging Efficency of Elk and Bison
University of Wyoming National Park Service Research Center Annual Report Volume 22 22nd Annual Report, 1998 Article 1 1-1-1998 The Impact of Wolf Reintroduction on the Foraging Efficency of Elk and Bison
Algebra 1 Agenda 4.1. Monday. Tuesday. Thursday Lesson: Friday. No School! Linear Regression. Correlation Coefficient. Association & Causation
Name: Class Period: Algebra 1 Agenda 4.1 Grade Monday 1/4/2016 Homework: No School! Hope you enjoyed your break :) Tuesday 1/5/2016 Linear Regression Homework: HW 1 Wednesday 1/6/2016 Correlation Coefficient
Women and Marathons: A Low Participation. Recreation Research Proposal. PRM 447 Research and Evaluation in PRM. Jaimie Coastman.
Running WOMEN head: AND WOMEN MARATHONS: AND MARATHONS: A LOW PARTICIPATION A LOW 1 PARTICIPATION Women and Marathons: A Low Participation Recreation Research Proposal PRM 447 Research and Evaluation in
Business and housing market cycles in the euro area: a multivariate unobserved component approach
Business and housing market cycles in the euro area: a multivariate unobserved component approach Laurent Ferrara (a) and Siem Jan Koopman (b) http://staff.feweb.vu.nl/koopman (a) Banque de France (b)
Setting up group models Part 1 NITP, 2011
Setting up group models Part 1 NITP, 2011 What is coming up Crash course in setting up models 1-sample and 2-sample t-tests Paired t-tests ANOVA! Mean centering covariates Identifying rank deficient matrices
Prediction model of cyclist s accident probability in the City of Malang
MATEC Web of Conferences 8, 04003 (208) ISTSDC 207 https://doi.org/0.05/matecconf/208804003 Prediction model of cyclist s accident probability in the City of Malang Imma Widyawati Agustin,*, Muhammad Zainul
8th Grade. Data.
1 8th Grade Data 2015 11 20 www.njctl.org 2 Table of Contents click on the topic to go to that section Two Variable Data Line of Best Fit Determining the Prediction Equation Two Way Table Glossary Teacher
Unit4: Inferencefornumericaldata 4. ANOVA. Sta Spring Duke University, Department of Statistical Science
Unit4: Inferencefornumericaldata 4. ANOVA Sta 101 - Spring 2016 Duke University, Department of Statistical Science Dr. Çetinkaya-Rundel Slides posted at http://bit.ly/sta101_s16 Outline 1. Housekeeping
A Case Study of Leadership in Women s Intercollegiate Softball. By: DIANE L. GILL and JEAN L. PERRY
A Case Study of Leadership in Women s Intercollegiate Softball By: DIANE L. GILL and JEAN L. PERRY Gill, D.L. & Perry, J.L. (1979). A case study of leadership in women's intercollegiate softball. International
MGB 203B Homework # LSD = 1 1
MGB 0B Homework # 4.4 a α =.05: t = =.05 LSD = α /,n k t.05, 7 t α /,n k MSE + =.05 700 + = 4.8 n i n j 0 0 i =, j = 8.7 0.4 7. i =, j = 8.7.7 5.0 i =, j = 0.4.7. Conclusion: µ differs from µ and µ. b
Math 121 Test Questions Spring 2010 Chapters 13 and 14
Math 121 Test Questions Spring 2010 Chapters 13 and 14 1. (10 pts) The first-semester enrollment at HSC was 1120 students. If all entering freshmen classes were the same size and there were no attrition,
An Empirical Comparison of Regression Analysis Strategies with Discrete Ordinal Variables
Kromrey & Rendina-Gobioff An Empirical Comparison of Regression Analysis Strategies with Discrete Ordinal Variables Jeffrey D. Kromrey Gianna Rendina-Gobioff University of South Florida The Type I error
ESP 178 Applied Research Methods. 2/26/16 Class Exercise: Quantitative Analysis
ESP 178 Applied Research Methods 2/26/16 Class Exercise: Quantitative Analysis Introduction: In summer 2006, my student Ted Buehler and I conducted a survey of residents in Davis and five other cities.
BODY FORM INFLUENCES ON THE DRAG EXPERIENCED BY JUNIOR SWIMMERS. Australia, Perth, Australia
1 BODY FORM INFLUENCES ON THE DRAG EXPERIENCED BY JUNIOR SWIMMERS Andrew Lyttle 1, Nat Benjanuvatra 2, Brian A Blanksby 2, Bruce C Elliott 2 1 Western Australian Institute of Sport, Perth, Australia 2
COMPLETING THE RESULTS OF THE 2013 BOSTON MARATHON
COMPLETING THE RESULTS OF THE 2013 BOSTON MARATHON Dorit Hammerling 1, Matthew Cefalu 2, Jessi Cisewski 3, Francesca Dominici 2, Giovanni Parmigiani 2,4, Charles Paulson 5, Richard Smith 1,6 1 Statistical
5.1 Introduction. Learning Objectives
Learning Objectives 5.1 Introduction Statistical Process Control (SPC): SPC is a powerful collection of problem-solving tools useful in achieving process stability and improving capability through the
Factorial ANOVA Problems
Factorial ANOVA Problems Q.1. In a 2-Factor ANOVA, measuring the effects of 2 factors (A and B) on a response (y), there are 3 levels each for factors A and B, and 4 replications per treatment combination.
Section I: Multiple Choice Select the best answer for each problem.
Inference for Linear Regression Review Section I: Multiple Choice Select the best answer for each problem. 1. Which of the following is NOT one of the conditions that must be satisfied in order to perform
BIOL 101L: Principles of Biology Laboratory
BIOL 101L: Principles of Biology Laboratory Sampling populations To understand how the world works, scientists collect, record, and analyze data. In this lab, you will learn concepts that pertain to these
Predator-Prey Interactions: Bean Simulation. Materials
Predator-Prey Interactions: Bean Simulation Introduction Interactions between predators and their prey are important in 1) determining the populations of both predators and prey, and 2) determining and
Select Boxplot -> Multiple Y's (simple) and select all variable names.
One Factor ANOVA in Minitab As an example, we will use the data below. A study looked at the days spent in the hospital for different regions of the United States. Can the company reject the claim the
Announcements. Lecture 19: Inference for SLR & Transformations. Online quiz 7 - commonly missed questions
Announcements Announcements Lecture 19: Inference for SLR & Statistics 101 Mine Çetinkaya-Rundel April 3, 2012 HW 7 due Thursday. Correlation guessing game - ends on April 12 at noon. Winner will be announced
GENETICS OF RACING PERFORMANCE IN THE AMERICAN QUARTER HORSE: II. ADJUSTMENT FACTORS AND CONTEMPORARY GROUPS 1'2
GENETICS OF RACING PERFORMANCE IN THE AMERICAN QUARTER HORSE: II. ADJUSTMENT FACTORS AND CONTEMPORARY GROUPS 1'2 S. T. Buttram 3, R. L. Willham 4 and D. E. Wilson 4 Iowa State University, Ames 50011 ABSTRACT
Pearson Edexcel Level 3 GCE Psychology Advanced Subsidiary Paper 2: Biological Psychology and Learning Theories
Write your name here Surname Other names Centre Number Candidate Number Pearson Edexcel Level 3 GCE Psychology Advanced Subsidiary Paper 2: Biological Psychology and Learning Theories Monday 23 May 2016
Initial Mortality of Black Bass in B.A.S.S. Fishing Tournaments
North American Journal of Fisheries Management 22:950 954, 2002 Copyright by the American Fisheries Society 2002 Initial Mortality of Black Bass in B.A.S.S. Fishing Tournaments GENE R. WILDE,* CALUB E.
Determination of the Design Load for Structural Safety Assessment against Gas Explosion in Offshore Topside
Determination of the Design Load for Structural Safety Assessment against Gas Explosion in Offshore Topside Migyeong Kim a, Gyusung Kim a, *, Jongjin Jung a and Wooseung Sim a a Advanced Technology Institute,
Validation of a Step Test in Children Ages 7-11
Validation of a Step Test in Children Ages 7-11 Emilene Clark Aurora Fry Colleen Smith Tonya Thomas Primary Advisor: Jim Farris, PT, PhD April 20, 2011 Background Exercise Testing Maximal Testing Sub-maximal
Relationship of Road Lane Width to Safety for Urban and Suburban Arterials
Relationship of Road Lane Width to Safety for Urban and Suburban Arterials Phd. Alma AFEZOLLI Polytechnic University of Tirana Construction and Infrastructure Department of Civil Engineering Faculty Tirana,
Lecture 22: Multiple Regression (Ordinary Least Squares -- OLS)
Statistics 22_multiple_regression.pdf Michael Hallstone, Ph.D. hallston@hawaii.edu Lecture 22: Multiple Regression (Ordinary Least Squares -- OLS) Some Common Sense Assumptions for Multiple Regression
A Description of Variability of Pacing in Marathon Distance Running
Original Research A Description of Variability of Pacing in Marathon Distance Running THOMAS A. HANEY JR. and JOHN A. MERCER Department of Kinesiology and Nutrition Sciences, University of Nevada, Las
One-way ANOVA: round, narrow, wide
5/4/2009 9:19:18 AM Retrieving project from file: 'C:\DOCUMENTS AND SETTINGS\BOB S\DESKTOP\RJS\COURSES\MTAB\FIRSTBASE.MPJ' ========================================================================== This
Analysis of Shear Lag in Steel Angle Connectors
University of New Hampshire University of New Hampshire Scholars' Repository Honors Theses and Capstones Student Scholarship Spring 2013 Analysis of Shear Lag in Steel Angle Connectors Benjamin Sawyer
WHAT CAN WE LEARN FROM COMPETITION ANALYSIS AT THE 1999 PAN PACIFIC SWIMMING CHAMPIONSHIPS?
WHAT CAN WE LEARN FROM COMPETITION ANALYSIS AT THE 1999 PAN PACIFIC SWIMMING CHAMPIONSHIPS? Bruce Mason and Jodi Cossor Biomechanics Department, Australian Institute of Sport, Canberra, Australia An analysis
EXPLORING MOTIVATION AND TOURIST TYPOLOGY: THE CASE OF KOREAN GOLF TOURISTS TRAVELLING IN THE ASIA PACIFIC. Jae Hak Kim
EXPLORING MOTIVATION AND TOURIST TYPOLOGY: THE CASE OF KOREAN GOLF TOURISTS TRAVELLING IN THE ASIA PACIFIC Jae Hak Kim Thesis submitted for the degree of Doctor of Philosophy at the University of Canberra
CPUE standardization of black marlin (Makaira indica) caught by Taiwanese large scale longline fishery in the Indian Ocean
CPUE standardization of black marlin (Makaira indica) caught by Taiwanese large scale longline fishery in the Indian Ocean Sheng-Ping Wang Department of Environmental Biology and Fisheries Science, National
Experimental Design and Data Analysis Part 2
Experimental Design and Data Analysis Part 2 Assump@ons for Parametric Tests t- test and ANOVA Independence Variance Normality t-test Yes Yes Yes ANOVA Yes Yes Yes Lecture 7 AEC 460 Assume homogeneity
NBA TEAM SYNERGY RESEARCH REPORT 1
NBA TEAM SYNERGY RESEARCH REPORT 1 NBA Team Synergy and Style of Play Analysis Karrie Lopshire, Michael Avendano, Amy Lee Wang University of California Los Angeles June 3, 2016 NBA TEAM SYNERGY RESEARCH
Juvenile Fish Travel Time and Survival a common currency for evaluating fish passage operations
FISH PASSAGE CENTER 1827 NE 44 th Ave., Suite 240, Portland, OR 97213 Phone: (503) 230-4099 Fax: (503) 230-7559 http://www.fpc.org/ e-mail us at fpcstaff@fpc.org MEMORANDUM TO: Ed Bowles, ODFW FROM: Michele
Algebra I: A Fresh Approach. By Christy Walters
Algebra I: A Fresh Approach By Christy Walters 2016 A+ Education Services All rights reserved. No part of this publication may be reproduced, distributed, stored in a retrieval system, or transmitted,
Conditioned Alarm Behavior in Fathead Minnows (Pimephales promelas) and Test Their Ability
Conditioned alarm behavior in fathead minnows 1 Meera Alshamsi Prof, Wisenden June 27 th,11 Conditioned Alarm Behavior in Fathead Minnows (Pimephales promelas) and Test Their Ability of Differentiate Between
Preparation for Salinity Control ME 121
Preparation for Salinity Control ME 121 This document describes a set of measurements and analyses that will help you to write an Arduino program to control the salinity of water in your fish tank. The
Prokopios Chatzakis, National and Kapodistrian University of Athens, Faculty of Physical Education and Sport Science 1
Differences between geographic areas (continents) in the distribution of medals at the Beijing Olympic Games 2008 and at the London Olympic Games. Prokopios Chatzakis, National and Kapodistrian University
The probability of winning a high school football game.
Columbus State University CSU epress Faculty Bibliography 2008 The probability of winning a high school football game. Jennifer Brown Follow this and additional works at: http://csuepress.columbusstate.edu/bibliography_faculty
Stat 139 Homework 3 Solutions, Spring 2015
Stat 39 Homework 3 Solutions, Spring 05 Problem. Let i Nµ, σ ) for i,..., n, and j Nµ, σ ) for j,..., n. Also, assume that all observations are independent from each other. In Unit 4, we learned that the
An Analysis of the Travel Conditions on the U. S. 52 Bypass. Bypass in Lafayette, Indiana.
An Analysis of the Travel Conditions on the U. S. 52 Bypass in Lafayette, Indiana T. B. T readway Research Assistant J. C. O ppenlander Research Engineer Joint Highway Research Project Purdue University
MRI-2: Integrated Simulation and Safety
MRI-2: Integrated Simulation and Safety Year 3 2 nd Quarterly Report Submitted by: Dr. Essam Radwan, P.E. (PI), Ahmed.Radwan@ucf.edu Dr. Hatem Abou-Senna, P.E., habousenna@ucf.edu Dr. Mohamed Abdel-Aty,
Abstract. Introduction Fiber neps generation in cotton processing
1864 Fiber neps generation in cotton processing Jaime Cantu, Mourad Krifa, and Mario Beruvides Texas Tech University Abstract Neps, formed by tight and dense entanglements of fibers, are among the most
Hare Today, Gone Tomorrow
Science Objectives Students will develop a method of graphing a population cycling model. Students will demonstrate an understanding of population dynamics. Students will describe several factors affecting
The Reliability of Intrinsic Batted Ball Statistics Appendix
The Reliability of ntrinsic Batted Ball Statistics Appendix Glenn Healey, EECS Department University of California, rvine, CA 92617 Given information about batted balls for a set of players, we review
Growth of Bristol Bay & Yukon River, Alaska Chum Salmon in Response to Climatic Factors & Inter-specific Competition
Growth of Bristol Bay & Yukon River, Alaska Chum Salmon in Response to Climatic Factors & Inter-specific Competition Bev Agler Alaska Department of Fish and Game Greg Ruggerone Natural Resources Consultants,
Distancei = BrandAi + 2 BrandBi + 3 BrandCi + i
. Suppose that the United States Golf Associate (USGA) wants to compare the mean distances traveled by four brands of golf balls when struck by a driver. A completely randomized design is employed with
Foal and Mare Behavior Changes during Repeated Human-Animal Interactions in the First Two Weeks after Foaling
Inquiry in ACES: An Undergraduate Research Journal College of Agricultural, Consumer and Environmental Sciences University of Illinois at Urbana-Champaign Foal and Mare Behavior Changes during Repeated
Puffy Head, Bird Legs
DESCRIPTION Science Concepts Puffy Head, Bird Legs Collect, organize, analyze, evaluate, make inferences, and predict trends from data. Investigate and identify how organisms, including humans respond
save percentages? (Name) (University)
1 IB Maths Essay: What is the correlation between the height of football players and their save percentages? (Name) (University) Table of Contents Raw Data for Analysis...3 Table 1: Raw Data...3 Rationale
Mediating effect of social support in relation between stress of golfers and exhaustion of exercise
, pp.156-161 http://dx.doi.org/10.14257/astl.2015.113.32 Mediating effect of social support in relation between stress of golfers and exhaustion of exercise Min-Jun Kim 1, Jung-In Yoo 2, Yong-Taek Rhim
Competitive Performance of Elite Olympic-Distance Triathletes: Reliability and Smallest Worthwhile Enhancement
SPORTSCIENCE sportsci.org Original Research / Performance Competitive Performance of Elite Olympic-Distance Triathletes: Reliability and Smallest Worthwhile Enhancement Carl D Paton, Will G Hopkins Sportscience
A Combined Recruitment Index for Demersal Juvenile Cod in NAFO Divisions 3K and 3L
NAFO Sci. Coun. Studies, 29: 23 29 A Combined Recruitment Index for Demersal Juvenile Cod in NAFO Divisions 3K and 3L David C. Schneider Ocean Sciences Centre, Memorial University St. John's, Newfoundland,
Hardware Triaxial and Consolidation Testing Systems Pressure Measurement and Control
25 GDS Helpsheet Hardware Triaxial and Consolidation Testing Systems Pressure Measurement and Control World Leaders in Computer Controlled Testing Systems for Geotechnical Engineers and Geologists 1. Digital
Exploring the relationship between Heart Rate (HR) and Ventilation Rate (R) in humans.
Exploring the relationship between Heart Rate (HR) and Ventilation Rate (R) in humans. The Research Question In this investigation I will be considering the following general research question: Does increased
Determination of the wind pressure distribution on the facade of the triangularly shaped high-rise building structure
Determination of the wind pressure distribution on the facade of the triangularly shaped high-rise building structure Norbert Jendzelovsky 1,*, Roland Antal 1 and Lenka Konecna 1 1 STU in Bratislava, Faculty
FLOW CONSIDERATIONS IN INDUSTRIAL SILENCER DESIGN
FLOW CONSIDERATIONS IN INDUSTRIAL SILENCER DESIGN George Feng, Kinetics Noise Control, Inc., 3570 Nashua Drive, Mississauga, Ontario Vadim Akishin, Kinetics Noise Control, Inc., 3570 Nashua Drive, Mississauga,
Analysis of Signalized Intersection Crashes Nasima Bhuiyan, EmelindaM. Parentela and Venkata S. Inapuri
Analysis of Signalized Intersection Crashes Nasima Bhuiyan, EmelindaM. arentela and Venkata S. Inapuri Abstract The goals of providing high levels of mobility and intersection efficiency while simultaneously