Basic statistical concepts

• real world problem --> statistical analysis
• The complete set of the objects, which are subject of the analysis
  is called the population.
• we are not interested in the population itself, but more in
  the properties of the population measured by one or several
  quantities of interest X

Inferential Statistics

• Inference about the population (complete data set) on the basis of
  a sample
• Testing statistical hypothesis, building condence intervals,
  measuring reliability of the tests and procedures

absolute scale
quantity, number of students enrolled at a university

qualitative if it has a finite set of possible
realizations

quantitative attributes (for
example, age, income, price)

discrete, if the set of possible realizations is a
countable set.

continuous, if it is has
uncountably many possible realizations.

interval scale
temperature values in Celsius, year of birth

ordinal scale
can be naturally ordered
ranks,grades

Sample Variance

Empirical Covariance
sXY = sYX
|sXY|<= sXsY

Correlation measures for ordinal data
Idea of the ranks: assign to each observation of the sample x1; : : : ; xn
its position in the ordered sample x(1),. . . ,x(n),

Rank correlation coecient of Spearman

where R(hat) = (n + 1)/2.

Correlation measures for nominal variables

x^2 large, X and Y are dependent.

the contingency coecient of Pearson

corrected contingency coecient of Pearson

The smaller is CKorr, the weaker is dependency. CKorr = 0 only if X and Y are independent