ADVANCED STATISTICS


GENERAL DESCRIPTION OF THE COURSE

This course is a continuation of a freshmen course on basic statistics. The main topics of this course are various tests, whose aim is to either provide estimates of certain parameters of statistical variables, based on their random samples, or to possibly cast some doubt on the validity of certain hypothesis about them. Students must be able to work with arbitrary confidence levels and to present statistical results as tables of estimates, for example for confidence levels  0.90, 0.95, 0.99, 0.999 and 0.9999, which should enable users of statistics to make their own choices.

COURSE CONTENTS

The course will cover at least the following topics as well as their applications to practical problems in traffic engineering:

  • General idea of a statistical test, test function, test distribution, confidence levels, critical constants
  • Numerical integration and critical constants for standard Gauss distribution
  • Student distributions, chi-square distributions, Fisher distributions, their relation with standard Gauss distribution, their critical constants
  • Testing hypothesis for mean and standard deviation of a statistical variable
  • Estimating mean of a variable from its sample
  • Estimating standard deviation of a standard variable from its sample
  • Estimating probability of an event or a real percentage of general support or a poll answer
  • Testing hypothesis for distribution af a statistical variable
  • Testing if the mean of one variable is bigger than the mean of some other variable
  • Testing if the standard deviation of one variable is bigger than the standard variation of some other variable
  • Estimating the correlation coefficient between two statistical variables
  • Estimating both parameters of linear regression formula, in case of strongly correlated variables

 

STUDY MATERIALS:

  • Kreyszig, Advanced Engineering Mathematics, Wiley 2014
  • Langley, Practical Statistics simply explained, Dover Publications 1971
  • K. Kanji, 100 Statistical Tests, Sage Publications 2006
  • Montgomery, Runger, Hubele, Engineering Statistics, Wiley 2011
  • gapminder.org (Joys of Statistics)