# ANOVA IN THE EDUCATIONAL PROCESS

Save this PDF as:
Size: px
Start display at page:

## Transcription

1 U.P.B. Sci. Bull., Series C, Vol. 70, No. 3, 008 ISSN ANOVA IN THE EDUCATIONAL PROCESS Mihaela Florentina MATEI Analiza dispersiei, ANOVA, reprezintă una din metodele statistice, dintre cele mai puternice în ceea ce priveşte datele de observaţie. În următorul studiu de caz, ca şi element de noutate referitor la studiile ANOVA, se analizează omogenitatea grupelor de lucru, formate din studenţi, în ceea ce priveşte materiile de studiu diferite (este analizat aici procesul de învăţământ din punctul de vedere al cadrelor didactice sau din punctul de vedere al diferitelor materii de studiu şi totodată sunt analizate diferenţele care apar la diferitele materii: materii cu conţinut legat mai mult de inginerie- inginerie electrică, şi materii economice). Analysis Of Variance, ANOVA, represents one of the statistical procedure proceedings, the most powerful procedure for the observation dates. In the following case study, like an element of improving concerning the ANOVA studies, it is analyzed the homogeneity of the working groups of students referring at different disciplines (it is analyzed here the teaching process from teaching s or discipline s point of view and the differences who comes up at different disciplines like: electrical and economics). Keywords: ANOVA, homogeneity, teaching process, normal distribution, Fisher test, educational process.. Introduction Analysis of Variance, ANOVA, was put in practice by the mathematician Fisher. Pointedly the problem solved by Fisher was: the mean of a population to another mean of population, meaning testing the homogeneity of the means. The economic component of such an eperimental procedures is that, it allows to identify the significant effects with a minimal eperimental effort, meaning a low number of measurements. The methods established by Fisher and the generalizations are known as planning or eperiments programming or shorter ANOVA. [], [] Generally it is considered that the eperiment is a research method, in which the researcher has the power to change one or more eplicative variables (independent), and that, after the change is made, you can measure its effect on the resultant variables (flows). [3] In another definition, ANOVA is an assembly of methods for the eamination of the study dates, dates which depend on several factors with Assist., Dept. of Electrical Measurements, Electrical Apparatus and Static Converters; University POLITEHNICA of Bucharest, Romania

2 Mihaela Florentina Matei simultaneous action, in purpose of establishing the most important of them and to estimate their effects. [4] After the calculation in Mathematics, the ANOVA table will show, in the displayed result by Mathematics, the squares sum, which is split in four or five components. For each component, the table shows: the squares sum, degree freedom, the square media and ratio F. Each ratio F is the ratio of the square media s value for that variance source of the residual square media. If the null hypothesis is true, the ratio F is proimate. If it is not true, F is higher than. [5], [6]. Case study, the analysis of variance The specific analyzed eample concerns about the students from the Electrical Engineering Faculty, on three different working groups. The first group of students, group A Table Number of students at X at Y

3 ANOVA in the educational process 3 Table The second group of students, group B Number of students at X at Y Table 3 The third group of students, group C Number of students at X at Y The case study follows the results from these three different groups of students (we will speak about these groups like A group, B group, C group), from the two disciplines (we will speak about these two s like X and Y ). In the tables seen above, we have the grades from those 3 groups of students, at the X and Y. The maimum is 0, meaning the best possible and the lowest is. So, the scale is to 0. X The first- A group The second-b group The third- C group Number of students 5 7 Fig.. The grades for the students at X

4 4 Mihaela Florentina Matei Y Number of students 5 7 Fig.. The grades for the students at Y There are used the methods of the analysis of variance, and we withhold like an influence factor: the deployment of the teaching process. For this we will use like a work technique, the ANOVA analysis. Anova can be two-ways Anova and one-way Anova. Two-ways Anova answers simultaneous at three questions: The first factor affects the results? The second factors affect the results? Those two factors interconnect? One-way Anova, in our case, wants to show if the mean results of this two s are the same for those three groups of students. We will study the main effects, observed between the columns means. Anova will test if the possible main effects are statistically significant- that the errors are not only from the sample s error. Table 4 ANOVA table Groups of The samples Rows mean students X Y A group B group C group Columns mean The eperiments which depend on one factor only, are the simplest scheme of projection. The objective of this type of eperiment is the measurement of the effect of the one or more levels of the eperimental factor on two or more eperimental groups. If we analyze a certain process and we check the influence of a certain factor, we can then say that the factor is a controlled factor. The eperiment s

5 ANOVA in the educational process 5 diagram may have one or more controlled factors. The rest of factors are called uncontrolled factors. This ones determine a normal variation of the investigate characteristic. For reaching the target (testing the homogeneity), it is need to take into consideration the most important factors, from the point of view of their contribution to the new engineer s shaping. The simplest case is the one in which the variation of the characteristic is dependent on a single factor, A. Based on the eperiments, we have for k variants, n variants specific to the X characteristic. So, we have the following table: A X X a a The eperimental values.. a i i i.... Table 5 a k X X X.... n n It can be observed that the variation of the results represents a consequence of the all factors without the controlled factor, including the measurement errors. The statistic study of the plan of the eperiments values, shows: - Hypothesis : all the k results have a normal distribution, independent; - Hypothesis : the normal distributions have the same parameter. If the normality doesn t eist then, we will compare the mean values, using the F test. The hypothesis means that the controlled factor influences the mean, not the variance. in k k kn 3. The implementation in Mathematics For this case study, the dates are implemented in Mathematics 5., which is a soft used for calculation, including reliability case studies. The first step for analysis is to test if the two samples of dates have a normal distribution, using the Kolmogorov-Smirnov test. [4] Than it will be test the normality using mathematics and it will be calculate the maimum difference between the theoretical and empirical functions: D = , respective: D = na nb

6 6 Mihaela Florentina Matei The problem is to test the equality between the variances for those two samples. For this are analyzed the results from calculation and from the tables (on s A one hand it is calculate an indicator: F c = and on the other hand, for a certain sb significance level, it is etracted a value from the Fisher table). [7], [8], [9] From the Fisher table it is etracted the value F (,4) =. 74 for α = 0., and, s A are the numbers of the freedom degrees. But F c = =.5 sb so,.5 <.74, this means that the means of the two samples aren t significant different, and the influence of the controlled factor (professors in this case) isn t significant. The ANOVA table splits the total variability between measurements (showed like a sum of squares) in four components: - interaction between rows and columns; - variability lengthways of columns; - variability leng - thways of rows; - residual error. With many measurements, Anova has another component: - variability between s. The ANOVA table shows the squares sum which is split in four components (or five components). For each component, the table shows: sum of squares, degree freedom, mean square and ratio F. Each ratio is the ratio of the value of the mean square for that source of variation of the residual mean square. If the null hypothesis is true, the ratio F is almost. If it is not true, F is higher than. 4. Conclusions Using the Anova steps, in this case study few elements are analyzed. First of all it is tested if the two samples have a normal distribution. For this it is calculate the means, the variances, the theoretical functions of repartition, and the values of the theoretical functions of repartition, the values of the empirical functions of repartition, the calculation of the difference modules, the maimum of the difference between the theoretical and empirical functions. For a trust level of 5% for those two samples, the values from the Kolmogorov - Smirnov table are lower that the calculate values. So, this means that none of the two distributions are normal. The net step is Fisher test which tests the hypothesis concerning the equality of the means of the two samples. α

7 ANOVA in the educational process 7 s A This test reveals that the calculated value ( F c = =. 5 ) is lower that sb DA the value from the Fisher table ( < F α, Fα (,4) =. 74 ). So, that means that DR the means of those two samples aren t significant different, this also means that the influence of the controlled factor (in our case, the professors) it is not significant. Those two samples represent: A = the grades for X, for those three working groups; B= the grades for Y, for those three working groups. Total amount for each sample is 6 dates. The means for the two samples are: for A is 6.40 and for B is So the means are significant different and this means that those two working groups are homogene from the point of view of the didactical process. The homogeneity is the same although we have different s like content (electrical and economic), also different teachers with different didactical methods, and different specializations. So it is tested one way ANOVA, especially we tested the mean results at two s of study, on three working groups of students. The independent variables were those two s of study and the dependent variables were the grades measured on a scale from to 0. After the factors took into consideration, the eperiments can be: - with one factor (simple); - with multiple factors, where we study not only the action of each factor but also the dependence between them. From this point of view, the analysed case study reffers to a one way eperiment (simple eperiment). After the variables type, so after factors, the eperiments can be: - eperiments concerning the quantitative factors, who can be easy measured (like temperature, time, speed, and so on); - eperiments made on attributive factors (profession, area, and so on). From this point of view, the eperiment involved in this case study concerns the quantitative factors, easy to measure: grades. After the purpose, the eperiments can be: - preliminary eperiments, where we want to test a lots of factors for an idea concerning the future researches; - critical eperiments, where it is compared the results of different treatments, for an identification and a test for the ones with a significant influence;

8 8 Mihaela Florentina Matei - demonstrative eperiments, where it can be tested few treatments with a determined standard. From this point of view, the case study deals with a critical eperiment. Are compared the results of the different didactical methods applied on different working groups, to be able to identify (where are significant differences) and test the ones significant like influence. [0], [] The personal contribution of the author on this paper is, on one hand, a comple study on the statistical method Anova and on the other hand, a case study concerning the student groups homegeneity taking into consideration different disciplines. This case study is a new domain which hasn t been approached very often until now. R E F E R E N C E S [] V. Panaite., M.O. Popescu, Calitatea produselor si fiablitate, v. Metoda Fisher, Matrirom, Bucharest 003 [] V. Panaite., M.O. Popescu, Ghid pentru caliatea si fiabilitatea produselor, U.P.B., Bucharest 003 [3] V. Panaite., Statistica si fiablitate in domeniul tehnic, U.P.B., Bucharest, 978 [4] M. Craiu., L. Panzar, Probabilitati si statistica, Printech, 005 [5] M. Craiu., Statistica matematica, Printech, 003 [6] [7] [8] [9] V. Panaite., M.O. Popescu, Calitatea produselor si fiablitate indrumar de laborator si seminar, Ed. Printech, Bucharest 007 [0] Mildred L. Patten, Understanding research methods: An Overview of the essentials (3rd ed.), Los Angeles: Pyrczak Publishing, 00 [] Daniel Yates, David Moore, George McCabe, The Practice of statistics: TI-83 graphing calculator enhanced, New York: W.H. Freeman and Company, 999

### SOME APPLICATIONS OF THE HILBERT TRANSFORM

U.P.B. Sci. Bull. Series A, Vol. 71, Iss. 3, 2009 ISSN 1223-7027 SOME APPLICATIONS OF THE HILBERT TRANSFORM Ştefania Constantinescu 1 În acest articol, se dau unele proprietăţi ale transformării Hilbert,

### Analysis of Variance and Co-variance. By Manza Ramesh

Analysis of Variance and Co-variance By Manza Ramesh Contents Analysis of Variance (ANOVA) What is ANOVA? The Basic Principle of ANOVA ANOVA Technique Setting up Analysis of Variance Table Short-cut Method

### AN APPROACH TO THE NONLINEAR LOCAL PROBLEMS IN MECHANICAL STRUCTURES

U.P.B. Sci. Bull., Series D, Vol. 74, Iss. 3, 2012 ISSN 1454-2358 AN APPROACH TO THE NONLINEAR LOCAL PROBLEMS IN MECHANICAL STRUCTURES Marius-Alexandru GROZEA 1, Anton HADĂR 2 Acest articol prezintă o

### LOSS FUNCTIONS USED IN THE QUALITY THEORY

U.P.B. Sci. Bull. Series A, Vol. 73, Iss. 1, 2011 ISSN 1223-7027 LOSS FUNCTIONS USED IN THE QUALITY THEORY Constantin TÂRCOLEA 1, Adrian Stere PARIS 2 Filosofia Taguchi reprezintă un nou punct de vedere

### AN ECONOMETRICAL MODEL FOR CALCULATING THE ROMANIAN GROSS DOMESTIC PRODUCT

An Econometrical Model For Calculating The Romanian Gross Domestic Product AN ECONOMETRICAL MODEL FOR CALCULATING THE ROMANIAN GROSS DOMESTIC PRODUCT Abstract Ana Maria Mihaela Iordache 1 Ionela Catalina

### U.P.B. Sci. Bull., Series A, Vol. 74, Iss. 3, 2012 ISSN SCALAR OPERATORS. Mariana ZAMFIR 1, Ioan BACALU 2

U.P.B. ci. Bull., eries A, Vol. 74, Iss. 3, 212 IN 1223-727 A CALAR OPERATOR Mariana ZAMFIR 1, Ioan BACALU 2 În această lucrare studiem o clasă nouă de operatori numiţi -scalari. Aceştia apar în mod natural,

### DISCRIMINANT ANALYSIS IN THE STUDY OF ROMANIAN REGIONAL ECONOMIC DEVELOPMENT

ANALELE ŞTIINŢIFICE ALE UNIVERSITĂŢII ALEXANDRU IOAN CUZA DIN IAŞI Tomul LIV Ştiinţe Economice 007 DISCRIMINANT ANALYSIS IN THE STUDY OF ROMANIAN REGIONAL ECONOMIC DEVELOPMENT ELISABETA JABA * DĂNUŢ VASILE

### ECONOMETRIC ANALYSIS OF THE COMPANY ON STOCK EXCHANGE

ECONOMETRIC ANALYSIS OF THE COMPANY ON STOCK EXCHANGE Macovei Anamaria Geanina Ştefan cel Mare of University Suceava,Faculty of Economics and Public Administration street Universității, no. 3, city Suceava,

### SYLLABUS 1. Study using a manual, course materials, bibliography and lecture notes 25

SYLLABUS 1 1. Information about the program 1.1 Higher education institution University Politehnica Timisoara 1. Faculty / Department 3 Faculty of Industrial Chemistry and Environmental Engineering / CAICAM

### MULTI-VARIABLE PREDICTION OF PHYSICAL DATA

U.P.B. Sci. Bull., Series A, Vol. 72, Iss., 200 ISSN 223-7027 MULTI-VARIABLE PREDICTION OF PHYSICAL DATA Dan ŞTEFĂNOIU, Janetta CULITĂ 2 Lucrarea prezintă un studiu comparativ între diferite abordari adoptate

### One-way ANOVA. Experimental Design. One-way ANOVA

Method to compare more than two samples simultaneously without inflating Type I Error rate (α) Simplicity Few assumptions Adequate for highly complex hypothesis testing 09/30/12 1 Outline of this class

### ASSISTED RESEARCH OF THE FOURIER SPECTRUM OF THE ROBOTS WITH MAGNETORHEOLOGICAL DAMPER

U.P.B. Sci. Bull., Series D, Vol. 72, Iss. 3, 2010 ISSN 1454-2358 ASSISTED RESEARCH OF THE FOURIER SPECTRUM OF THE ROBOTS WITH MAGNETORHEOLOGICAL DAMPER Şerban OLARU 1, Aurel OPREAN 2, Adrian OLARU 3 În

### IMPROVING ELECTRIC ARC FURNACE (EAF) OPERATION THROUGH MATHEMATICAL MODELLING

U.P.B. Sci. Bull., Series B, Vol. 78, Iss. 3, 2016 ISSN 1454-2331 IMPROVING ELECTRIC ARC FURNACE (EAF) OPERATION THROUGH MATHEMATICAL MODELLING Adrian IOANA 1, Anda PREDA 2, Liviu BEŞEA 3, Petru MOLDOVAN

### Chapter 4. Probability-The Study of Randomness

Chapter 4. Probability-The Study of Randomness 4.1.Randomness Random: A phenomenon- individual outcomes are uncertain but there is nonetheless a regular distribution of outcomes in a large number of repetitions.

### IDENTIFICATION AND OPTIMAL CONTROL OF BLOWING SYSTEM

U.P.B. Sci. Bull., Series C, Vol. 70, Iss. 4, 2008 ISSN 1454-234x IDENTIFICATION AND OPTIMAL CONTROL OF BLOWING SYSTEM Messaouda AZZOUZI 1 Obiectivul important al lucrării de constă în dezvoltarea unor

### FAULT DIAGNOSIS IN ANALOG CIRCUITS BASED ON PARAMETRIC DEVIATION OF COMPONENTS COMPUTATION

UPB Sci Bull, Series C, Vol 7, No 2, 28 ISSN 454-234 FAUL DIAGNOSIS IN ANALOG CIRCUIS BASED ON PARAMERIC DEVIAION OF COMPONENS COMPUAION Dragos NICULAE Lucrarea prezintă o metodă de diagnosticare a defectelor

### TWO BOUNDARY ELEMENT APPROACHES FOR THE COMPRESSIBLE FLUID FLOW AROUND A NON-LIFTING BODY

U.P.B. Sci. Bull., Series A, Vol. 7, Iss., 9 ISSN 3-77 TWO BOUNDARY ELEMENT APPROACHES FOR THE COMPRESSIBLE FLUID FLOW AROUND A NON-LIFTING BODY Luminiţa GRECU, Gabriela DEMIAN, Mihai DEMIAN 3 În lucrare

### Analysis of Variance: Part 1

Analysis of Variance: Part 1 Oneway ANOVA When there are more than two means Each time two means are compared the probability (Type I error) =α. When there are more than two means Each time two means are

### Department of Economics. Business Statistics. Chapter 12 Chi-square test of independence & Analysis of Variance ECON 509. Dr.

Department of Economics Business Statistics Chapter 1 Chi-square test of independence & Analysis of Variance ECON 509 Dr. Mohammad Zainal Chapter Goals After completing this chapter, you should be able

### IJESMR International Journal OF Engineering Sciences & Management Research

METHOD OF IMPLEMENTING ANALYSIS OF VARIANCE (ANOVA) IN RESEARCH STUDIES Asha Singh * & Balkeshwar Singh *Department of Business Management, Mewar University, Chittorghar, Rajasthan, India Mechanical Engineering

### COMPARATIVE DISCUSSION ABOUT THE DETERMINING METHODS OF THE STRESSES IN PLANE SLABS

74 COMPARATIVE DISCUSSION ABOUT THE DETERMINING METHODS OF THE STRESSES IN PLANE SLABS Codrin PRECUPANU 3, Dan PRECUPANU,, Ștefan OPREA Correspondent Member of Technical Sciences Academy Gh. Asachi Technical

### M A N O V A. Multivariate ANOVA. Data

M A N O V A Multivariate ANOVA V. Čekanavičius, G. Murauskas 1 Data k groups; Each respondent has m measurements; Observations are from the multivariate normal distribution. No outliers. Covariance matrices

### ELECTRONIC TECHNIQUES IN TIMING MEASUREMENTS FOR NUCLEAR STRUCTURE

U.P.B. Sci. Bull., Series A, Vol. 70, Iss. 4, 2008 ISSN 1223-7027 ELECTRONIC TECHNIQUES IN TIMING MEASUREMENTS FOR NUCLEAR STRUCTURE Dan Gabriel GHIŢĂ 1 Prezenta lucrare descrie în detaliu două metode

### APPLYING TAGUCHI METHOD FOR CONTROL PARAMETERS OF AN INDUCTION MOTOR

U.P.B. Sci. Bull., Series C, Vol. 78, Iss., 06 ISSN 86-3540 APPLYING TAGUCHI METHOD FOR CONTROL PARAMETERS OF AN INDUCTION MOTOR Catalin Silviu NUTU, Mihai Octavian POPESCU This paper is intended to provide

### INFLUENCE OF THE CARRIER (DIBENZO-18 CROWN-6) ON LIQUID MEMBRANE IODIDE SEPARATION

U.P.B. Sci. Bull., Series B, Vol. 73, Iss. 2, 2011 ISSN 1454-2331 INFLUENCE OF THE CARRIER (DIBENZO-18 CROWN-6) ON LIQUID MEMBRANE IODIDE SEPARATION Niculina-Nina BADEA 1, Mihaela Emanuela CRĂCIUN 2, Ovidiu

### SOME ASPECTS ABOUT WEAVING PROCESS OPTIMIZATION

SOME ASPECTS ABOUT WEAVING PROCESS OPTIMIZATION A. Bucevschi, "Aurel Vlaicu" University from Arad, Arad, ROMANIA I. Barbu, "Aurel Vlaicu" University from Arad, Arad, ROMANIA M. Pustianu, "Aurel Vlaicu"

### Nonparametric statistic methods. Waraphon Phimpraphai DVM, PhD Department of Veterinary Public Health

Nonparametric statistic methods Waraphon Phimpraphai DVM, PhD Department of Veterinary Public Health Measurement What are the 4 levels of measurement discussed? 1. Nominal or Classificatory Scale Gender,

### A3. Statistical Inference

Appendi / A3. Statistical Inference / Mean, One Sample-1 A3. Statistical Inference Population Mean μ of a Random Variable with known standard deviation σ, and random sample of size n 1 Before selecting

### Ordinary Least Squares Regression Explained: Vartanian

Ordinary Least Squares Regression Eplained: Vartanian When to Use Ordinary Least Squares Regression Analysis A. Variable types. When you have an interval/ratio scale dependent variable.. When your independent

### A GENERALIZATION OF A CLASSICAL MONTE CARLO ALGORITHM TO ESTIMATE π

U.P.B. Sci. Bull., Series A, Vol. 68, No., 6 A GENERALIZATION OF A CLASSICAL MONTE CARLO ALGORITHM TO ESTIMATE π S.C. ŞTEFĂNESCU Algoritmul Monte Carlo clasic A1 estimeazează valoarea numărului π bazându-se

### CONCERNS REGARDING TEMPERATURE DISTRIBUTION OBTAINED BY EXPERIMENTS AND FINITE ELEMENT ANALYSES FOR TWO TYPES OF BRAKE DISCS

U.P.B. Sci. Bull., Series D, Vol. 74, Iss. 3, 2012 ISSN 1454-2358 CONCERNS REGARDING TEMPERATURE DISTRIBUTION OBTAINED BY EXPERIMENTS AND FINITE ELEMENT ANALYSES FOR TWO TYPES OF BRAKE DISCS Ştefan VOLOACĂ

### The goodness-of-fit test Having discussed how to make comparisons between two proportions, we now consider comparisons of multiple proportions.

The goodness-of-fit test Having discussed how to make comparisons between two proportions, we now consider comparisons of multiple proportions. A common problem of this type is concerned with determining

### Area1 Scaled Score (NAPLEX) .535 ** **.000 N. Sig. (2-tailed)

Institutional Assessment Report Texas Southern University College of Pharmacy and Health Sciences "An Analysis of 2013 NAPLEX, P4-Comp. Exams and P3 courses The following analysis illustrates relationships

### How to Plan Experiments

How to Plan Eperiments Formulate a hypothesis Choose independent variable values Eperimental planning Scientific method Statistical design of eperiments Setting specifications Formulating a Hypothesis

### Mixed- Model Analysis of Variance. Sohad Murrar & Markus Brauer. University of Wisconsin- Madison. Target Word Count: Actual Word Count: 2755

Mixed- Model Analysis of Variance Sohad Murrar & Markus Brauer University of Wisconsin- Madison The SAGE Encyclopedia of Educational Research, Measurement and Evaluation Target Word Count: 3000 - Actual

### Nonlinear Vibrations of Elastic Beams

Acta Technica Napocensis: Civil Engineering & Architecture Vol. 56, No. 1, (2013) Journal homepage: http://constructii.utcluj.ro/actacivileng Nonlinear Vibrations of Elastic Beams Iacob Borş 1, Tudor Milchiş

### CHAPTER 17 CHI-SQUARE AND OTHER NONPARAMETRIC TESTS FROM: PAGANO, R. R. (2007)

FROM: PAGANO, R. R. (007) I. INTRODUCTION: DISTINCTION BETWEEN PARAMETRIC AND NON-PARAMETRIC TESTS Statistical inference tests are often classified as to whether they are parametric or nonparametric Parameter

### Introduction to Business Statistics QM 220 Chapter 12

Department of Quantitative Methods & Information Systems Introduction to Business Statistics QM 220 Chapter 12 Dr. Mohammad Zainal 12.1 The F distribution We already covered this topic in Ch. 10 QM-220,

### FINDING THE TRACES OF A GIVEN PLANE: ANALYTICALLY AND THROUGH GRAPHICAL CONSTRUCTIONS

BULETINUL INSTITUTULUI POLITEHNI DIN IŞI Publicat de Universitatea Tehnică Gheorghe sachi din Iaşi Tomul LVII (LXI), Fasc. 3, 20 Secţia ONSTRUŢII DE MŞINI FINDING THE TRES OF GIVEN PLNE: NLYTILLY ND THROUGH

### ATTENUATION OF THE ACOUSTIC SCREENS IN CLOSED SPACES

U.P.B. Sci. Bull., Series D, Vol. 69, No. 3, 007 ISSN 15-358 ATTENUATION OF THE ACOUSTIC SCREENS IN CLOSED SPACES Ioan MAGHEŢI 1, Mariana SAVU Lucrarea prezintă calculul atenuării acustice a unui ecran

### THE USE OF TIN SOFTWARE IN STATISTICAL HYPOTHESIS TESTING. CASE STUDY

THE USE OF TIN SOFTWARE IN STATISTICAL HYPOTHESIS TESTING. CASE STUDY R. Drienovsky 1, M. Drienovsky 2, M. Boldea 3 1 Student of Banat University of Agricultural Sciences and Veterinary Medicine Regele

### PSYC 331 STATISTICS FOR PSYCHOLOGISTS

PSYC 331 STATISTICS FOR PSYCHOLOGISTS Session 4 A PARAMETRIC STATISTICAL TEST FOR MORE THAN TWO POPULATIONS Lecturer: Dr. Paul Narh Doku, Dept of Psychology, UG Contact Information: pndoku@ug.edu.gh College

### A = Chapter 6. Linear Programming: The Simplex Method. + 21x 3 x x 2. C = 16x 1. + x x x 1. + x 3. 16,x 2.

Chapter 6 Linear rogramming: The Simple Method Section The Dual roblem: Minimization with roblem Constraints of the Form Learning Objectives for Section 6. Dual roblem: Minimization with roblem Constraints

### Presented at the 2008 SCEA-ISPA Joint Annual Conference and Training Workshop - Myung-Yul Lee 1 C-17 Program, The Boeing Company

Myung-Yul Lee 1 Using C-17 Program's Data to Build a Parametric Model for the Engineering Organization Introduction The Boeing Company, C-17 program, located in Long Beach, California has produced more

### Unit 4 Relations and Functions. 4.1 An Overview of Relations and Functions. January 26, Smart Board Notes Unit 4.notebook

Unit 4 Relations and Functions 4.1 An Overview of Relations and Functions Jan 26 5:56 PM Jan 26 6:25 PM A Relation associates the elements of one set of objects with the elements of another set. Relations

### One-Way ANOVA. Some examples of when ANOVA would be appropriate include:

One-Way ANOVA 1. Purpose Analysis of variance (ANOVA) is used when one wishes to determine whether two or more groups (e.g., classes A, B, and C) differ on some outcome of interest (e.g., an achievement

### UNDERWATER LIBS INVESTIGATIONS SETUP FOR METALS IDENTIFICATION

U.P.B. Sci. Bull., Series A, Vol. 72, Iss. 4, 2010 ISSN 1223-7027 UNDERWATER LIBS INVESTIGATIONS SETUP FOR METALS IDENTIFICATION Monica SIMILEANU 1, Roxana RADVAN 2, Niculae PUSCAS 3 LIBS este o tehnică

### OPTIMAL OBSERVABILITY OF PMU'S USING ANALYTIC HIERARCHY PROCESS (AHP) METHOD

U.P.B. Sci. Bull., Series C, Vol. 73, Iss. 4, 2011 ISSN 1454-234x OPTIMAL OBSERVABILITY OF PMU'S USING ANALYTIC HIERARCHY PROCESS (AHP) METHOD Sebastian ANGHELESCU 1, Gianfranco CHICCO 2 Lucrarea propune

### Acta Technica Napocensis: Civil Engineering & Architecture Vol. 54 No.1 (2011)

1 Technical University of Cluj-Napoca, Faculty of Civil Engineering. 15 C Daicoviciu Str., 400020, Cluj-Napoca, Romania Received 25 July 2011; Accepted 1 September 2011 The Generalised Beam Theory (GBT)

### Syllabus for MATHEMATICS FOR INTERNATIONAL RELATIONS

Syllabus for MATHEMATICS FOR INTERNATIONAL RELATIONS Lecturers: Kirill Bukin, Nadezhda Shilova Class teachers: Pavel Zhukov, Nadezhda Shilova Course description Mathematics for international relations

### ECON 497 Midterm Spring

ECON 497 Midterm Spring 2009 1 ECON 497: Economic Research and Forecasting Name: Spring 2009 Bellas Midterm You have three hours and twenty minutes to complete this exam. Answer all questions and explain

### AP Statistics Cumulative AP Exam Study Guide

AP Statistics Cumulative AP Eam Study Guide Chapters & 3 - Graphs Statistics the science of collecting, analyzing, and drawing conclusions from data. Descriptive methods of organizing and summarizing statistics

### THE ROYAL STATISTICAL SOCIETY HIGHER CERTIFICATE

THE ROYAL STATISTICAL SOCIETY 004 EXAMINATIONS SOLUTIONS HIGHER CERTIFICATE PAPER II STATISTICAL METHODS The Society provides these solutions to assist candidates preparing for the examinations in future

### Chapter 9 Regression. 9.1 Simple linear regression Linear models Least squares Predictions and residuals.

9.1 Simple linear regression 9.1.1 Linear models Response and eplanatory variables Chapter 9 Regression With bivariate data, it is often useful to predict the value of one variable (the response variable,

### Chapter 8 Student Lecture Notes 8-1. Department of Economics. Business Statistics. Chapter 12 Chi-square test of independence & Analysis of Variance

Chapter 8 Student Lecture Notes 8-1 Department of Economics Business Statistics Chapter 1 Chi-square test of independence & Analysis of Variance ECON 509 Dr. Mohammad Zainal Chapter Goals After completing

U.P.B. Sci. Bull., Series D, Vol. 70, Iss. 4, 2008 ISSN 1454-2358 ON THE LOAD OF AXIAL TURBOMACHINES BLADE Eugen DOBÂNDĂ 1 Principala problemă în folosirea metodelor numerice, în special în hidrodinamica

### Multiple Comparisons

Multiple Comparisons Error Rates, A Priori Tests, and Post-Hoc Tests Multiple Comparisons: A Rationale Multiple comparison tests function to tease apart differences between the groups within our IV when

### NUMERICAL STABILITY OF ADAPTIVE CONTROL ALGORITHMS

U.P.B. Sci. Bull., Series C, Vol. 72, Iss. 3, 2 ISSN 454-234x NUMERICAL STABILITY OF ADAPTIVE CONTROL ALGORITHMS Ciprian LUPU, Andreea UDREA 2, Dumitru POPESCU 3, Cătălin PETRESCU 4, Această lucrare analizează

### Polynomial Functions of Higher Degree

SAMPLE CHAPTER. NOT FOR DISTRIBUTION. 4 Polynomial Functions of Higher Degree Polynomial functions of degree greater than 2 can be used to model data such as the annual temperature fluctuations in Daytona

### Multiple Linear Regression

Multiple Linear Regression Simple linear regression tries to fit a simple line between two variables Y and X. If X is linearly related to Y this explains some of the variability in Y. In most cases, there

### Module 8: Linear Regression. The Applied Research Center

Module 8: Linear Regression The Applied Research Center Module 8 Overview } Purpose of Linear Regression } Scatter Diagrams } Regression Equation } Regression Results } Example Purpose } To predict scores

### THE ROYAL STATISTICAL SOCIETY 2015 EXAMINATIONS SOLUTIONS HIGHER CERTIFICATE MODULE 3

THE ROYAL STATISTICAL SOCIETY 015 EXAMINATIONS SOLUTIONS HIGHER CERTIFICATE MODULE 3 The Society is providing these solutions to assist candidates preparing for the examinations in 017. The solutions are

### Kumaun University Nainital

Kumaun University Nainital Department of Statistics B. Sc. Semester system course structure: 1. The course work shall be divided into six semesters with three papers in each semester. 2. Each paper in

### 14.30 Introduction to Statistical Methods in Economics Spring 2009

MIT OpenCourseWare http://ocw.mit.edu 4.0 Introduction to Statistical Methods in Economics Spring 009 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.

### Workshop Research Methods and Statistical Analysis

Workshop Research Methods and Statistical Analysis Session 2 Data Analysis Sandra Poeschl 08.04.2013 Page 1 Research process Research Question State of Research / Theoretical Background Design Data Collection

### Multiple Regression. Dan Frey Associate Professor of Mechanical Engineering and Engineering Systems

ultiple Regression Dan Frey Associate Professor of echanical Engineering and Engineering Systems Plan for Today ultiple Regression Estimation of the parameters Hypothesis testing Regression diagnostics

### Regression Analysis with Categorical Variables

International Journal of Statistics and Systems ISSN 973-2675 Volume, Number 2 (26), pp. 35-43 Research India Publications http://www.ripublication.com Regression Analysis with Categorical Variables M.

### THERMAL CONDUCTIVITY MEASUREMENT OF CONSTRUCTION MATERIALS USING THE THERMAL PROBE METHOD

BULETINUL INSTITUTULUI POLITEHNIC DIN IAŞI Publicat de Universitatea Tehnică Gheorghe Asachi din Iaşi Tomul LVIII (LXII), Fasc. 2, 2012 Secţia CONSTRUCŢII. ARHITECTURĂ THERMAL CONDUCTIVITY MEASUREMENT

### Multiple Regression. Inference for Multiple Regression and A Case Study. IPS Chapters 11.1 and W.H. Freeman and Company

Multiple Regression Inference for Multiple Regression and A Case Study IPS Chapters 11.1 and 11.2 2009 W.H. Freeman and Company Objectives (IPS Chapters 11.1 and 11.2) Multiple regression Data for multiple

### Overview. INFOWO Statistics lecture S1: Descriptive statistics. Detailed Overview of the Statistics track. Definition

Overview INFOWO Statistics lecture S1: Descriptive statistics Peter de Waal Introduction to statistics Descriptive statistics Department of Information and Computing Sciences Faculty of Science, Universiteit

### Do not copy, post, or distribute

14 CORRELATION ANALYSIS AND LINEAR REGRESSION Assessing the Covariability of Two Quantitative Properties 14.0 LEARNING OBJECTIVES In this chapter, we discuss two related techniques for assessing a possible

These materials may not be reproduced for any purpose. The reproduction of any part for an entire school or school system is strictly prohibited. No part of this publication may be transmitted, stored,

### Lecture 06. DSUR CH 05 Exploring Assumptions of parametric statistics Hypothesis Testing Power

Lecture 06 DSUR CH 05 Exploring Assumptions of parametric statistics Hypothesis Testing Power Introduction Assumptions When broken then we are not able to make inference or accurate descriptions about

### INTRODUCTION TO DESIGN AND ANALYSIS OF EXPERIMENTS

GEORGE W. COBB Mount Holyoke College INTRODUCTION TO DESIGN AND ANALYSIS OF EXPERIMENTS Springer CONTENTS To the Instructor Sample Exam Questions To the Student Acknowledgments xv xxi xxvii xxix 1. INTRODUCTION

### EVALUATION OF THE DEBYE LENGTH FOR A NEMATIC LIQUID CRYSTAL ALIGNED WITH CONDUCTIVE POLYMERS

U.P.B. Sci. Bull., Series A, Vol. 71, Iss. 4, 2009 ISSN 1223-7027 EVALUATION OF THE DEBYE LENGTH FOR A NEMATIC LIQUID CRYSTAL ALIGNED WITH CONDUCTIVE POLYMERS Constanta DASCALU 1, Ruxandra ATASIEI 2, Matei

### ASPECTS REGARDING NUMERICAL MODELING OF INDUCTIVE HEATING PROCESS FOR LOW VOLTAGE ELECTRICAL CABLES

U.P.B. Sci. Bull., Series C, Vol. 72, Iss. 3, 2010 ISSN 1454-234x ASPECTS REGARDING NUMERICAL MODELING OF INDUCTIVE HEATING PROCESS FOR LOW VOLTAGE ELECTRICAL CABLES Costel PĂUN 1 În această lucrare se

### One-Way Analysis of Variance (ANOVA) Paul K. Strode, Ph.D.

One-Way Analysis of Variance (ANOVA) Paul K. Strode, Ph.D. Purpose While the T-test is useful to compare the means of two samples, many biology experiments involve the parallel measurement of three or

11 pter11 Chap Analysis of Variance Overview of ANOVA Multiple Comparisons Tests for Homogeneity of Variances Two-Factor ANOVA Without Replication General Linear Model Experimental Design: An Overview

### Statistiek II. John Nerbonne using reworkings by Hartmut Fitz and Wilbert Heeringa. February 13, Dept of Information Science

Statistiek II John Nerbonne using reworkings by Hartmut Fitz and Wilbert Heeringa Dept of Information Science j.nerbonne@rug.nl February 13, 2014 Course outline 1 One-way ANOVA. 2 Factorial ANOVA. 3 Repeated

### Chapter 26: Comparing Counts (Chi Square)

Chapter 6: Comparing Counts (Chi Square) We ve seen that you can turn a qualitative variable into a quantitative one (by counting the number of successes and failures), but that s a compromise it forces

### ScienceDirect. Who s afraid of the effect size?

Available online at www.sciencedirect.com ScienceDirect Procedia Economics and Finance 0 ( 015 ) 665 669 7th International Conference on Globalization of Higher Education in Economics and Business Administration,

### Using SPSS for One Way Analysis of Variance

Using SPSS for One Way Analysis of Variance This tutorial will show you how to use SPSS version 12 to perform a one-way, between- subjects analysis of variance and related post-hoc tests. This tutorial

### HYDRODYNAMIC AND THERMODYNAMIC ASPECTS OF DIFFUSION COEFFICIENTS IN THE TERNARY SYSTEM WATER-CHLOROFORM-ACETIC ACID AT 25 C

U.P.B. Sci. Bull., Series A, Vol. 69, No. 3, 27 ISSN 223-727 HYDRODYNAMIC AND THERMODYNAMIC ASPECTS OF DIFFUSION COEFFICIENTS IN THE TERNARY SYSTEM WATER-CHLOROFORM-ACETIC ACID AT 25 C Daniela BUZATU,

### 1 Descriptive statistics. 2 Scores and probability distributions. 3 Hypothesis testing and one-sample t-test. 4 More on t-tests

Overall Overview INFOWO Statistics lecture S3: Hypothesis testing Peter de Waal Department of Information and Computing Sciences Faculty of Science, Universiteit Utrecht 1 Descriptive statistics 2 Scores

### Dynamical Systems. 1.0 Ordinary Differential Equations. 2.0 Dynamical Systems

. Ordinary Differential Equations. An ordinary differential equation (ODE, for short) is an equation involves a dependent variable and its derivatives with respect to an independent variable. When we speak

### An Analysis of College Algebra Exam Scores December 14, James D Jones Math Section 01

An Analysis of College Algebra Exam s December, 000 James D Jones Math - Section 0 An Analysis of College Algebra Exam s Introduction Students often complain about a test being too difficult. Are there

### PACKET Unit 4 Honors ICM Functions and Limits 1

PACKET Unit 4 Honors ICM Functions and Limits 1 Day 1 Homework For each of the rational functions find: a. domain b. -intercept(s) c. y-intercept Graph #8 and #10 with at least 5 EXACT points. 1. f 6.

### Taguchi Method and Robust Design: Tutorial and Guideline

Taguchi Method and Robust Design: Tutorial and Guideline CONTENT 1. Introduction 2. Microsoft Excel: graphing 3. Microsoft Excel: Regression 4. Microsoft Excel: Variance analysis 5. Robust Design: An Example

### CALITATEA VIEŢII ÎN ORAŞELE ROMÂNEŞTI ÎN CONTEXTUL REFORMEI STATULUI

QUALITY OF LIFE IN ROMANIAN CITIES IN THE CONTEXT OF STATE REFORM CALITATEA VIEŢII ÎN ORAŞELE ROMÂNEŞTI ÎN CONTEXTUL REFORMEI STATULUI Cristina ALPOPI Associate Professor Ph.D., Administration and Public

### Comparing Several Means: ANOVA

Comparing Several Means: ANOVA Understand the basic principles of ANOVA Why it is done? What it tells us? Theory of one way independent ANOVA Following up an ANOVA: Planned contrasts/comparisons Choosing

### A Marginal Maximum Likelihood Procedure for an IRT Model with Single-Peaked Response Functions

A Marginal Maximum Likelihood Procedure for an IRT Model with Single-Peaked Response Functions Cees A.W. Glas Oksana B. Korobko University of Twente, the Netherlands OMD Progress Report 07-01. Cees A.W.

### A Generalised Fuzzy Soft Set Based Student Ranking System

Int J Advance Soft Comput Appl, Vol, No, November 0 ISSN 0-; Copyright ICSRS Publication, 0 wwwi-csrsorg A Generalised Fuzzy Soft Set Based Student Ranking System Pinaki Majumdar, SK samanta Department

### Chapter 16. Simple Linear Regression and Correlation

Chapter 16 Simple Linear Regression and Correlation 16.1 Regression Analysis Our problem objective is to analyze the relationship between interval variables; regression analysis is the first tool we will

### Dynamic Response of Beams on Elastic Foundation with Axial Load

Acta Technica Napocensis: Civil Engineering & Architecture Vol. 56, No. 1, (2013) Journal homepage: http://constructii.utcluj.ro/actacivileng Dynamic Response of Beams on Elastic Foundation with Axial

### OPENPH - NUMERICAL PHYSICS LIBRARY

U.P.B. Sci. Bull., Series A, Vol. 68, No. 1, 2006 OPENPH - NUMERICAL PHYSICS LIBRARY G. MILESCU, G. NOAJE, Fl. POP * Fizica numerică a căpătat o importanţă deosebită în ultimele decenii, eficienţa sa fiind

### Ron Heck, Fall Week 3: Notes Building a Two-Level Model

Ron Heck, Fall 2011 1 EDEP 768E: Seminar on Multilevel Modeling rev. 9/6/2011@11:27pm Week 3: Notes Building a Two-Level Model We will build a model to explain student math achievement using student-level

### Do we have any graphs that behave in this manner that we have already studied?

Boise State, 4 Eponential functions: week 3 Elementary Education As we have seen, eponential functions describe events that grow (or decline) at a constant percent rate, such as placing capitol in a savings

### Hypothesis testing. 1 Principle of hypothesis testing 2

Hypothesis testing Contents 1 Principle of hypothesis testing One sample tests 3.1 Tests on Mean of a Normal distribution..................... 3. Tests on Variance of a Normal distribution....................