• John
  • Felde
  • University of Maryland
  • USA

Latest Posts

  • USA

  • James
  • Doherty
  • Open University
  • United Kingdom

Latest Posts

  • Andrea
  • Signori
  • Nikhef
  • Netherlands

Latest Posts

  • CERN
  • Geneva
  • Switzerland

Latest Posts

  • Aidan
  • Randle-Conde
  • Université Libre de Bruxelles
  • Belgium

Latest Posts

  • Vancouver, BC
  • Canada

Latest Posts

  • Laura
  • Gladstone
  • MIT
  • USA

Latest Posts

  • Steven
  • Goldfarb
  • University of Michigan

Latest Posts

  • Fermilab
  • Batavia, IL
  • USA

Latest Posts

  • Seth
  • Zenz
  • Imperial College London
  • UK

Latest Posts

  • Nhan
  • Tran
  • Fermilab
  • USA

Latest Posts

  • Alex
  • Millar
  • University of Melbourne
  • Australia

Latest Posts

  • Ken
  • Bloom
  • USA

Latest Posts

Warning: file_put_contents(/srv/bindings/215f6720ac674a2d94a96e55caf4a892/code/wp-content/uploads/cache.dat): failed to open stream: No such file or directory in /home/customer/www/quantumdiaries.org/releases/3/web/wp-content/plugins/quantum_diaries_user_pics_header/quantum_diaries_user_pics_header.php on line 170

Junpei Fujimoto | KEK | Japan

View Blog | Read Bio

TV viewer rate

There are more than 15,000,000 families in Tokyo area. TV viewer survey is performed with 600 families as samples in this region. One wonders whether 600 families are enough as representative of Tokyo area

Statistics tells us the TV viewer survey should be understood with an error bar. The error bar can be calculated with the following equation;

error bar = ±1.96×( p×(1p)/n)^(0.5) with 95% confidence level(CL),


error bar = ±2.58×( p×(1p)/n)^(0.5) with 99% CL,

where n is a number of effective samples and p is the rate. If we put n=600 and p=0.2, then the rate should be understood (20±3.2)% with 95%CL, which means that the rate is located between 16.8% and 23.2% in the probability of 95%. It is interesting that the case of 50% rate has the largest error of ±4.0%.

Now one can understand that why 600 families are picked up. If one likes to have 10 times better accurate rate, number of sampled families should be increased 100 times, then 60,000 families have to be surveyed. It costs much.

Sampling of 600 families seems to be so tiny, but the result from 600 families has enough meaning with an error bar of 3% or 4%. Conversely, it is stupid to assign great value to the difference of the rate in a few-percent level.

TV viewer rate has another good example of the error bar has important role to read the data. One needs to pay attention to the error bar more. It even has an essential role for physicists to see the results from experiments.



誤差の大きさ= ±1.96×( p×(1-p)/n)^(0.5)  (ただし、95%の信頼度で) ,


誤差の大きさ= ±2.58×( p×(1-p)/n)^(0.5)  (ただし、99%の信頼度で),

ここで、nが有効回答数、あるいは視聴率の場合は調査対象となった世帯数に対応し、p はその調査の結果得られた視聴率を表します。もし視聴率が20%でしたという報告があったとき、上の式にしたがって計算すると、95%の信頼度で、視聴率は(20±3.2)%と誤差棒つきで考えることとなります。その意味するところは、600世帯のセットを変えて、100回の調査を実行したら、そのうちの95回の結果は16.8%から23.2%の間に入ってくるでしょう、という予測をしているということです。この式で面白い点は、視聴率が50%のときが4%と一番誤差棒が大きくなるということです。