Coin Tossing and Spinning – Useful Classroom Experiments for Teaching Statistics

  • Helmut Küchenhoff

A dicer’s dispute in 1654 led to the creation of the theory of probability by Blaise Pascal and Pierre de Fermat. Later, 350 years after their famous correspondence, throwing a dice is still the standard way of teaching the basic ideas of probability. The second classical example for randomness is tossing of a coin. Famous experiments were run by Buffon (he observed 2048 heads in 4040 coin tosses), Karl Pearson (12012 heads in 24000 coin tosses), and by John Kerrich (5067 heads in 10000 coin tosses) while he was war interned at a camp in Jutland during the second world war. The coin tossing or rolling dice experiments are often performed in the classes to introduce the ideas and concepts of probability theory. In higher classes students sometimes do not find them attractive and get bored. An attempt is made here to illustrate how these experiments can be made interesting by simple extensions. Dunn (2005) proposed some nice variations rolling special types of dice. In this article we focus on repeated coin spinning experiment by several students. We show how planning experiments including the determination of sample size, multiple testing, random effects models, overdispersion, non standard testing and autocorrelation can be illustrated in the context of coin spinning.


Classroom Experiment Sample Size Determination Fair Coin Coin Toss Famous Experiment 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Boyes R, Baldwin T, Hawkes N (2002) Heads I win, tails you lose. The Times (London)Google Scholar
  2. Diaconis P, Holmes S, Montgomery R (2007) Dynamical bias in the coin toss. Society for Industrial and Applied Mathematics 49:211-235MATHMathSciNetGoogle Scholar
  3. Dunn PK (2005) We can still learn about probability by rolling dice and tossing coins. Teaching Statistics 27:37-41CrossRefGoogle Scholar
  4. Gelman A, Nolan D (2002) You can load a die, but you can’t bias a coin. The American Statistician 56:308-311CrossRefMathSciNetGoogle Scholar
  5. Greven S, Crainiceanu C, Küchenhoff H, Peters A (2008) Restricted likelihood ratio testing for zero variance components in linear mixed models. Journal of Graphical and Computational Statistics (Appear-ing)Google Scholar
  6. Shuster JJ (2006) Using a two-player coin game paradox in the classroom. The American Statistician 60:68-70CrossRefMathSciNetGoogle Scholar
  7. Moffatt HK (2000) Euler’s disk and its finite-time singularity. Nature 404:833-834CrossRefGoogle Scholar
  8. Molenberghs G, Verbeke G (2005) Models for Discrete Longitudinal Data. Springer, New YorkMATHGoogle Scholar
  9. Paulos JA (1995) A Mathematician Reads the Newspaper. Basic BooksGoogle Scholar
  10. Rao CR, Toutenburg H, Shalabh, Heumann C (2008) Linear Models and Generalizations - Least Squares and Alternatives (3rd edition). Springer Verlag, Berlin, Heidelberg, New YorkMATHGoogle Scholar
  11. Scheipl F, Greven S, Küchenhoff H (2008) Size and power of tests for a zero random effect variance or polynomial regression in additive and linear mixed models. Computational Statistics and Data Analysis (Appearing)Google Scholar
  12. Toutenburg H (2002) Statistical Analysis of Designed Experiments. Springer, New YorkMATHGoogle Scholar
  13. Toutenburg H (2005) Induktive Statistik. Eine Einführung mit SPSS für Windows. Springer, HeidelbergGoogle Scholar
  14. Tutz G (2000) Die Analyse kategorialer Daten. OldenbourgGoogle Scholar

Copyright information

© Physica-Verlag Heidelberg 2008

Authors and Affiliations

  • Helmut Küchenhoff
    • 1
  1. 1.Department of StatisticsUniversity of MunichMunichGermany

Personalised recommendations