# Scienze Ambientali | ELEMENTS OF STATISTICS

## Scienze Ambientali ELEMENTS OF STATISTICS

 0512500026 DEPARTMENT OF CHEMISTRY AND BIOLOGY "ADOLFO ZAMBELLI" EQF6 ENVIRONMENTAL MONITORING AND ASSESSEMENT 2016/2017

 YEAR OF COURSE 3 YEAR OF DIDACTIC SYSTEM 2010 SECONDO SEMESTRE
SSD CFU HOURS ACTIVITY TYPE OF ACTIVITY SECS-S/01 3 24 LESSONS COMPULSORY SUBJECTS, CHARACTERISTIC OF THE CLASS SECS-S/01 3 36 LAB COMPULSORY SUBJECTS, CHARACTERISTIC OF THE CLASS
 GIUSEPPINA ALBANO T
Objectives
THE AIM OF THE COURSE IS TO PROVIDE STATISTICAL METHODS FOR THE SOLUTION OF PROBLEMS IN REAL NATURE. SPECIFIC OBJECTIVE IS TO MAKE THE STUDENT ABLE TO APPLY IN VARIOUS CONTEXTS THE ACQUIRED SKILLS AND METHODS FOR A BETTER INTERPRETATION OF ENVIRONMENTAL DATA. ELEMENTS OF DESCRIPTIVE STATISTICS, PROBABILITY AND INFERENCE WILL BE PROVIDED.
Prerequisites
BASIC MATH SKILLS ARE REQUIRED.
Contents
WHAT IS STATISTICAL. INTRODUCTION TO STATISTICS. ORGANIZE DATA IN TABLES. DISTRIBUTIONS OF ABSOLUTE AND RELATIVE FREQUENCIES. PLOTS: BAR CHARTS, PIES, HISTOGRAMS, TIME SERIES GRAPHS. LOCATION INDEXES: ARITHMETIC MEAN, WEIGHTED ARITHMETIC MEAN, MEDIAN AND MODE. VARIABILITY AND ITS MEASUREMENT: RANGE, VARIANCE, STANDARD DEVIATION. DATA TRANSFORMATION. Z-SCORES. THE PROBLEM OF OUTLIERS. ROBUST CENTRAL TENDENCY: THE MEDIAN, QUARTILES AND OTHER PERCENTILES. ROBUST VARIABILITY INDICES. BOX PLOTS AND PARALLEL BOXPLOTS. OUTLINE OF THE SHAPE INDEXES. BASICS OF PROBABILITY THEORY. PROBABILITY DISTRIBUTIONS FOR DISCRETE VARIABLES. EXPECTED VALUE AND VARIANCE OF A DISCRETE RANDOM VARIABLE. MAIN MODELS OF DISCRETE RANDOM VARIABLES: UNIFORM, BINOMIAL, POISSON. CONTINUOUS RANDOM VARIABLES. THE UNIFORM CONTINUOUS RANDOM VARIABLE AND NORMAL RANDOM VARIABLE. THE STANDARD NORMAL RANDOM VARIABLE. THE RANDOM VARIABLE OF STUDENT'S T AND CHI-SQUARE. NORMAL RANDOM VARIABLES TRANSFORMATIONS. THE CENTRAL LIMIT THEOREM. THE INFERENTIAL LOGIC. PARAMETERS AND STATISTICS. THE SAMPLING DISTRIBUTION. EFFECT OF SAMPLE SIZE ON SAMPLING DISTRIBUTION. ESTIMATORS, CORRECT, EFFICIENT AND CONSISTENT. ESTIMATORS OF THE MEAN, VARIANCE AND PROPORTION. CONFIDENCE INTERVAL FOR A PROPORTION. CONFIDENCE INTERVAL FOR THE MEAN AND FOR THE VARIANCE. CHOICE OF SAMPLE SIZE. THE LOGIC OF HYPOTHESIS TESTING. HYPOTHESIS TESTING ON THE AVERAGE. THE LINK BETWEEN HYPOTHESIS TESTING AND CONFIDENCE INTERVALS. HYPOTHESIS TESTING ON A PROPORTION. HYPOTHESIS TESTING ON THE COMPARISON BETWEEN POPULATIONS. COMPARISON BETWEEN INDEPENDENT POPULATIONS. THE CASE OF DEPENDENT DATA. SCATTER DIAGRAMS. COVARIANCE. THE LINEAR CORRELATION COEFFICIENT. LINEAR REGRESSION. COEFFICIENT ESTIMATE. THE COEFFICIENT OF DETERMINATION. THE PROBLEM OF OUTLIERS IN THE REGRESSION. USING THE REGRESSION MODEL: ESTIMATION, PREDICTION AND INTERPOLATION.
Teaching Methods
THE COURSE CONSISTS OF LECTURES AND EXERCISES IN THE COMPUTER LAB. IT WILL USE THE SOFTWARE R.
Verification of learning
EACH STUDENT HAS TO DEVELOP A STATISTICAL REPORT ON DATA PROVIDED BY THE TEACHER. AN LATER ORAL EXAMINATION FOCUS ON THE DISCUSSION OF THE REPORT AND THEORETIC TOPICS.
Texts
INTRODUZIONE ALLA STATISTICA APPLICATA. CON ESEMPI IN R. FEDERICO STEFANINI.EDITORE: PEARSON
LABORATORIO DI STATISTICA CON R. ESERCIZIARIO. ANNA M. PAGANONI, FRANCESCA IEVA, VALERIA VITELLI. EDITORE: PEARSON