How to find out the cheeks dice in statistics

In famous Japaniese manga kaiji, there is a scene where the group leader will continue to win with gaming using Ikasama (fraud, Japanese word) dice. Since there are only 4, 5 and 6 faces in this dice, it can intentionally put out 4, 5 or 6 eyes. As dice are three in terms of one direction it is not possible to do so (1 eye is red, so I usually think that it will happen if you roll the dice). Kaiji finds this corruption. Because there are only 4, 5 and 6 eyes, if you examine the dice in detail, Ikasama’s proof is over. But, “How about a cheesecake dice with only a misaligned center of gravity?” Since every surface is the same as an ordinary dice, it is impossible to judge in appearance. The P value is used in such a situation.

In order to investigate the saw dice, first shake the dice and take the data. Let’s say that you swung six times and the data looks like the following.

【Result 1】

  • 1 pips: 0
  • 2 pips: 1
  • 3 pips: 1
  • 4 pips: 1
  • 5 pips: 1
  • 6 pips: 2

Looking at this result, there are a lot of six pips. Therefore, it seems to be a cassava dice. Here many people will think “it is a coincidence”. It is true that the results are likely to come out even with ordinary dice. I will do my best and try 1000 times.

【Result 2】

  • 1 pips: 100
  • 2 pips: 100
  • 3 pips: 100
  • 4 pips: 100
  • 5 pips: 100
  • 6 pips: 500

Looking at this result, it is obvious that the 6 pips are easy to get out. From the above, it turns out that “the difference becomes clear when collecting a lot of data”.

Indicator of difference “P value”

You can not deny the possibility of accident by seeing the result of shaking the dice 1000 times. However, Result 2 strongly indicates that the die is better than Result 1. Therefore, it is the P value to calculate how much probability it is a squid dice.

P value means “the probability that there is no difference”. For example, suppose that the P value is calculated for the difference between the probability that 1 to 5 and the probability that 6 pips appear, and 0.02 is calculated. This means that the probability that there is no difference between the probability that 1 to 5 pips appear and the probability that 6 pips will appear is 2%. Therefore, it is a translation to judge that there will be a difference first.

It is a measure of P value to be determined to be different, but 5% is customarily used. For that reason we calculate the P value for the difference between the probability that 1 to 5 pips will appear on a dice saw and the probability that the pips will come out, and if it is 5% or less, it can be shown that the dice is an ikasma. As an aside, I often hear it in graphs. If ✳︎ is attached, the P value is 5% or less, indicating that there is a difference in the data of the graph. If you want to claim difference from the graph, be sure to put the P value. Otherwise scientists do not believe there is a difference. (Although it is caution, even if the P value is 0.05, it is not a cheap 5% probability, that is, it is impossible to prove the complete squid model, but scientists have a difference if the P value is 5% or less So I certify that Ikasama dice with a P value of 0.05 or less is acceptable in the world.)

If there are differences in samples, increasing the number of data will result in P values ​​getting smaller and smaller. Therefore, if the difference is obvious, you can use a small number of data, but if the difference is subtle, the P value will not go down if the number of data is not large. There is a merit that it can distinguish small differences in the number of data.

From the above, it is said that if it is said that it is possible to prove the cheesecake dice again, it will be the following answer. “Although it is impossible to prove a full-sized dice, it is possible to obtain the consent of many people by collecting the data and showing that the P value is less than 0.05.” In manga, it is obvious that it is a crisp dice not apparent Because I can not prove it, you mean that I used a familiar rugged figure. Since calculating the P value in cartoons, the tempo is bad.