Introduction

• Statistics:
  • is a strict mathematical discipline
    • based on probability theory
    • grounded on Kolmogorov axioms
  • is applied almost everywhere
  • is taught in many disciplines
  • has a very bad public reputation
• Popular quotes:
  • Mark Twain, attributing it to Disraeli:
    • "There are three kinds of lies: lies, damn lies, and statistics."
  • Churchill:
    • "Never trust any statistics that you didn’t forge yourself."
    • or as often quoted in German
    • "Traue keiner Statistik, die du nicht selbst gefälscht hast."
• Common problems:
  • biased or wrong data
  • wrong conclusions
    • e.g. correlation ↔ causality
  • wrong assumptions
    • normally distributed data
    • independent or even i.i.d. data
• Goal of this talk:
  • present another often overlooked problem
  • analyse its consequences using numerical experiments
    
    • to get and validate/invalidate ideas
    • to find relevant parameters
  • show how to cope with the problem