Statistics
Statistics
S210016
Geneva School of Economics and Management
University of Geneva
Fall semester
Statistics - Fall semester
1/ 16
Statistics
Motivation and setting
Outline
Motivation and setting
Explanatory data analysis (EDA)
Type of variables
Statistics - Fall semester
2/ 16
Statistics
Motivation and setting
Practical informations
All practical informations available on the moodle page
https:
//moodle.unige.ch/course/view.php?id=19456.
Statistics - Fall semester
3/ 16
Statistics
Motivation and setting
Resources
Bibliography
▶ Christian Heumann, Michael Schomaker, Shalabh (2016)
Introduction to Statistics and Data Analysis With Exercises,
Solutions and Applications in R, Springer.
PDF available from the UNIGE library
▶ Moore D. S. & McCabe J. P. (1993). Introduction to the
Practice of Statistics, Freeman, New York.
▶ Rice J. A. (1995). Mathematical Statistics and Data
Analysis Duxbury Press, 2nd edition, Belmont, CA.
Statistics - Fall semester
4/ 16
Statistics
Motivation and setting
Resources
R software:
Free software available at www.r-project.org/
Statistics - Fall semester
5/ 16
Statistics
Motivation and setting
How to install R and RStudio
▶ Go on www.r-project.org/.
▶ In ”Getting Started” clic on ”CRAN mirror”.
▶ Select any mirror (preferably not one too far).
▶ Clic on your corresponding OS.
▶ MAC :
▶ Mac : Choose your version.
▶ Download !
▶ Windows :
▶ Choose ”base” subdirectory.
▶ Download !
▶ Go on https://www.studio.com (redirected to
https://posit.co)
▶ Navigate to ”download/rstudio-desktop” section
https://posit.co/download/rstudio-desktop.
▶ Choose the appropriate installer and install the free
version.
Statistics - Fall semester
6/ 16
Statistics
Motivation and setting
Why statistics?
Video at
https://www.youtube.com/watch?v=wV0Ks7aS7YI
Statistics - Fall semester
7/ 16
Statistics
Motivation and setting
Population vs Sample
POPULATION
*
*
* *
*
DRAW
SAMPLE
*
* * * * *
* * * *
*
*
* * *
*
*
*
* *
* **
*
*
*
* *
* *
*
° ° ° °°
° ° ° ° °
° ° ° ° °
INFERENCE
The population is a collection of objects or individuals with
common properties that we want to study/analyze. Statistics
allows to infer about the population based on what is observed
on the sample.
Statistics - Fall semester
8/ 16
Statistics
Motivation and setting
Examples
Examples of populations: the population of a country, the
University of Geneva students, all the watches produced by a
given company during one year, ...
Examples of problems:
▶ Election polls
▶ Survey: unemployment, consumption, health, environment,
income,....
▶ Quality control.
▶ Groups comparison.
▶ Treatments comparison.
▶ . . ..
Statistics - Fall semester
9/ 16
Statistics
Motivation and setting
Why use samples?
Sample are used to cope with:
▶ Budget restrictions (too costly).
▶ Rare observations.
▶ Destructive tests.
▶ Sampling can be more precise than full screening of a
population !
Similar individuals (from the same population) can have
different values ⇝ variability.
Statistics is the analysis of this variability. Being able to
quantifying the variability makes the incomplete information of
the sample useful.
Statistics - Fall semester
10/ 16
Statistics
Motivation and setting
Notation
Drawing a random sample of size n from a population is
equivalent to generate n observations from a random variable
X , whose distribution is determined by the population
characteristics.
We can represent this process
x1
↗
either by X ...
or by
↘
xn
X1
..
.
→ x1
..
.
independent
Xn
→ xn
Statistics - Fall semester
11/ 16
Statistics
Explanatory data analysis
Outline
Motivation and setting
Explanatory data analysis (EDA)
Type of variables
Statistics - Fall semester
12/ 16
Statistics
Explanatory data analysis
Type of variables
Table of Contents
Motivation and setting
Explanatory data analysis (EDA)
Type of variables
Statistics - Fall semester
13/ 16
Statistics
Explanatory data analysis
Type of variables
Type of variables - categorical
Categorical or qualitative variables take on values that are
names or labels. The (limited number of) possible values are
called categories (which allow to classify the population into
groups).
We distinguish between:
▶ nominal variables: no intrinsic order to the categories
Examples: sex, race, hair color, educational program,...
▶ ordinal variables: clear ordering of the variables
Examples: level of education, score or rating (e.g. low,
medium, high),...
Categorical variables are sometimes coded numerically (e.g.
0 = “male”, 1 = “female”), but they don’t become a quantitative
variable!
Statistics - Fall semester
14/ 16
Statistics
Explanatory data analysis
Type of variables
Type of variables - quantitative or numerical
Quantitative or numerical variables. They are measured on a
numerical scale.
We distinguish between:
▶ discrete variables: can only take particular values, but
there may potentially be an infinite number of those values.
The values can differ only by fixed amounts.
Examples: size of a population, number of “head” when
flipping a coin 100 times, ...
▶ continuous variables: can take any value over a continuous
range. Between any two continuous data values there may
be an infinite number of others. Values can differ by any
amount. These variables are often grouped in intervals.
Examples: temperature, response time, body-mass index
of a person, income, ...
Statistics - Fall semester
15/ 16
Statistics
Explanatory data analysis
Type of variables
Data from a population
For a variable X , we call P the set of possible values in the
population. For categorical and discrete variables, the elements
of P can be listed, for continuous variables the possible values
belongs to intervals.
Examples:
P = {“male”, “female” } or P = {1, 2, 3, 4, 5, 6} or
P = {[0, 20[ , [20, 50[ , [50, 100[ , [100, 200[ , [200, ∞[}.
From now on, we consider having observed a sample
S = {x1 , . . . , xn },
from a population of interest. The sample size is n and the
variable xi represents the measurement.
Statistics - Fall semester
16/ 16
0
