Applied Statistics - Week 1

Overview:
  • The basics of statistics
  • Central limit theorem
  • Visualising data
    Program files can be found at: /scrx/hep/petersen/AS09/Week1/
    Copy by: cp -r /scrx/hep/petersen/AS09/Week1/ .

    Anscombes Quartet:

    We start with Anscombes Quartet, which illustrates the importance of "looking" at the data visually, and not just fitting it blindly. This ROOT macro is also an introcution to ROOT, which we'll be using in the future.

    In the directory AnscombesQuartet (cd AnscombesQuartet) you will find the relevant ROOT macro, which you run by starting ROOT (root) and then executing in the ROOT prompt (.x AnscombesQuartet.c).

    This should result in four plots in a new window, each fitted by the same line - however, the data varies a bit in the four cases.

    Central Limit Theorem:

    Next we take a look at the Central Limit Theorem. Contrary to Anscombes Quartet, this is a C++ program that uses ROOT. First it needs to be compiled (make) and then run (./CentralLimit).

    The result is a ROOT file (results.root), which contains histograms produced by the program. When having understood what they contain from the program, one can consider these results in ROOT (root results.root).

    An quick and easy way of considering ROOT histograms is with TBrowser (TBrowser a), which allows you to navigate between different files, histograms, and visual posibilities using the mouse.

    Box-Muller Method:

    This is also a C++ program, which uses ROOT inside (again for histograms). This routine simply shows how one can from uniformly distributed random numbers (available from most computers) produce Gaussianly distributed randam numbers (used very often) by the Box-Muller transformation.

    Table Measurements:

    A ROOT macro containing the result of the Auditorium A desk measurement by the students. There are two samples, namely one with a 30cm ruler, and one with a 2m folding ruler, both of which with measurements, where the person measuring has also given their estimated uncertainty.
    More to be added, if found necessary. Last updated 7th of September 2009.