Applied Statistics - Week 1
Monday the 18th - Friday the 22nd of November 2019
The following is a description of what we will go through during this
week of the course. The chapter references and computer exercises are
considered read, understood, and solved by the beginning of the
following class, where I'll shortly go through the exercise
solution.
Monday:
The first day of class will start
8.15 in Auditorium A, where
I will give an introduction to the course, we will take photos (mug
shots) of all of you, and you will measure the length of the front
table.
Due to the large number of students in class, I have also booked
Aud. B. Following the initial course introduction (8:15-9:00)
and lecture on Central Limit Theorem (CLT), those with setup problems
can go to Aud. B to sort these and/or starting the exercise on CLT.
At 10:00 we will move to HCO, where we'll work on the below
exercise on
Central Limit Theorem, which is the reason why the
Gaussian (also called "Normal") distribution plays such a central role
in statistics.
Reading:
Barlow, chapter 1, 2 (most of which you should know), and 4.1 + 4.2.
Lecture(s):
Mean and Width.
Correlations.
Significant Digits.
Central Limit Theorem.
Computer Exercise(s):
Central Limit Theorem:
CentralLimit.ipynb
Anscombe's Quartet:
AnscombesQuartet.ipynb (just for illustration!)
Tuesday:
The main theme will be the Error propagation, which most of you
should know the basics of already. While error propagation is
craftsmanship, there are nevertheless smart ways of doing it
numerically.
You should also (when done with the exercise) do the analytical error
propagation for the two formulae for the gravitational acceleration, g,
from a pendulum and ball-on-incline experiments. You will need these in
the project and its preparation (estimating largest source of error).
Reading:
Barlow, chapter 4.3.
Lecture(s):
Error Propagation
Computer Exercise(s):
Error Propagation: ErrorPropagation.ipynb
Friday:
We will focus on the ChiSquare Method, which is basic method
behind performing a fit to data. As it turns out, this method has
the great advantage of providing a goodness-of-fit measure, which
can be used to test, if the fit really resembles data.
Reading:
Barlow, chapter 6.
Lecture(s):
ChiSquare Test
Computer Exercise(s):
ChiSquare Test: ChiSquareTest.ipynb
ChiSquare Test - several examples:
ChiSquareTest_SeveralExamples.ipynb
Notes:
Analytical Linear Fit note: StraightLineFit.pdf
Analytical Linear Fit implementation: AnalyticalLinearFit.ipynb
General notes, links, and comments:
Why Statistics:
Monday morning, I tried to answer the question "Why Statistics?",
and this presentation can be found here.
More Python intro:
A good Python exercise is to consider the below program, which
calculates and plots the distribution of prime numbers. As you
surely know the math behind, you can see if you can also follow
how it is programmed in Python: CalcAndPlotPrimeNumbers.ipynb.
Last updated: 15th of November 2019.