Applied Statistics - Week 1
Monday the 16th - Friday the 20th of November 2020
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 on Zoom. I will start by giving a general
introduction to the course, and go through the different parts, so that you know what
to expect. Then I will lecture on Mean(s), Standard Deviation, Correlations, Significant
Digits, and the Central Limit Theorem (CLT). You almost surely know about all of these,
and this is simply to set the scene.
At 9:45 we will move to the exercises (in person on Frederiksberg!), where we'll work on
the below exercise on
Central Limit Theorem, which is the reason why the Gaussian
distribution plays such a central role in statistics.
Reading:
Barlow, chapter 1, 2 (most of which you should know), and 4.1 + 4.2.
Podcast:
Introduction to Mean, Standard Deviation (aka. RMSE), Correlations, and Central Limit Theorem.
Lecture(s):
Mean and Width.
Correlations.
Significant Digits.
Central Limit Theorem.
Why Statistics?.
Zoom: Link to lecture.
Recording of Lecture video (course information) and
Lecture audio (course information).
Recording of Lecture video,
Lecture audio, and
Lecture chat.
Computer Exercise(s):
Central Limit Theorem:
CentralLimit.ipynb (empty version)
Anscombe's Quartet:
AnscombesQuartet.ipynb (just for illustration!)
Simpson's Paradox:
Simpsons_Paradox.ipynb and Simpsons_paradox.csv (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.
Podcast:
Introduction to Error Propagation.
Lecture(s):
Error Propagation.
Zoom: Link to lecture.
Recording of Lecture video,
Lecture audio, and
Lecture chat.
Computer Exercise(s):
Error Propagation: ErrorPropagation.ipynb (empty version)
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.
Podcast:
Introduction to ChiSquare.
Lecture(s):
ChiSquare Test
Zoom: Link to lecture.
Recording of Lecture video (with information) and
Lecture audio (with information).
Recording of Lecture video,
Lecture audio, and
Lecture chat.
Computer Exercise(s):
ChiSquare Test: ChiSquareTest.ipynb (empty version)
ChiSquare Test - several examples:
ChiSquareTest_SeveralExamples.ipynb
Weighted Mean - and relation to ChiSquare:
WeightedMeanSigmaChi2.ipynb (small exercise for "anytime")
Notes:
Analytical Linear Fit note: StraightLineFit.pdf
Analytical Linear Fit implementation: AnalyticalLinearFit.ipynb
General notes, links, and comments:
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: 13th of November 2020.