Chapter 79 <Sophistry in Statistical Law>

Counting the quantity of things belongs to quantitative analysis.If the statistical method is scientific, and the statistical figures are real and accurate, it will have strong argumentation and persuasion.But the facts tell us that there is a lot to be done in terms of statistical methods, units and standards used in statistics.It is for this reason that sophists are interested in statistics, and employ all sorts of tricks in their application to achieve their desired ends. The most common statistical sophistry techniques are: one.Deliberately using biased samples in statistical inference Statistical inference is the inference that the sample has (or does not have) a certain attribute and the population also has (or does not have) this attribute.

Statistics should refer to all the objects under investigation as the population (or matrix); call each of the objects an individual; This number is called the sample size. There are many statistical methods, and here we only introduce the stratified sampling method to illustrate the nature of statistical reasoning. To give a very simple example: when an agricultural production unit estimates the average yield of 400 mu of wheat per mu, it divides the land into three levels or grades according to the soil fertility, among which the fertile land is 200 mu, and the medium land is 100 mu. One hundred and fifty acres of barren land and fifty acres of barren land; then two percent of the land was randomly selected from these three levels, that is, four acres, three acres, and one acres, a total of eight acres, to form a sample.Knowing that the average yield per mu of the eight-acre sample is 800 catties, the average yield per mu of 400 mu of wheat is also 800 catties.

From the above example, we can see that statistical reasoning is reasoning from part to whole, the scope of the conclusion is beyond the premise, and the conclusion is probable.Therefore, statistical reasoning belongs to incomplete inductive reasoning.In order to improve the reliability of statistical reasoning conclusions. Statistics requires: First, the sample should be representative.To this end, it is necessary to take into account the different levels or different stages of development of each individual in the population, and pay attention to extract sample individuals from objects at different levels and different stages of development to ensure that the sample is widely representative;

Second, the sample size should be large enough.Because if the number of individuals included in the sample is too small, it is difficult to reflect the overall situation. Sophists deliberately violate the above two requirements when applying statistical reasoning. They only select a small number of individuals that are currently needed to form a sample, and then draw conclusions that are beneficial to them.This error is called the sophistry of using a biased sample. Please see examples: (1) Every year in a certain country, after the admission of freshmen to colleges is over, a weekly magazine will launch an album on the experience of students who failed the rankings, and specially invite some famous experts and scholars who have failed in the college entrance examination in the past and have made achievements in certain fields to talk about their opinions on The perception of failure in the college entrance examination.What these famous people say is the same, but I also had the frustration of failing the exam, but in the long run, it is beneficial to my life.

In a sense, such experience talks may have a certain comfort and encouragement effect on those candidates who are troubled by failing the exam.But judging from the magazine's approach, it is playing with biased samples.Because not all the students who fail the rankings are sure to become famous and get married. In fact, the experts and scholars specially selected by the magazine are only a very small number of all the students who fail the rankings.The real purpose of the magazine is to use the psychology and emotions of the students who failed to sell the magazine. (2) An advertisement promoting a certain medicine stated that the cure rate of 98.3% is 98.3% when the medicine is used to treat XX disease.Seeing such an advertisement, people can't help but wonder: How did the figure of 98.3% come about?How many patients with XX disease were counted?

It is likely to be the highest rate picked from multiple counts.Since everyone has their own jobs, no one takes the time to investigate whether this number is true.In addition, there is another advantage of this statement. When someone uses this drug and it doesn't work, he will think: I probably belong to one of the 1.7 percent. (3) A famous politician in a foreign country said something like this: I trust food counters more than statistics.On this issue, I think the mood of the average housewife is a better indicator of the state of our economy than the Bureau of Statistics.Our statisticians sometimes deliberately distort the truth.The numbers they put in the newspapers to whitewash the economy are not available in the shops.

The above examples are all sophistry playing with biased samples in statistical reasoning. two.Sophistry on Statistical Units (1) In Western countries, whenever a plane crashes, people from the airlines often hear that it is safer to take a plane than to take a train.The reason is that the death rate of a plane flying 100,000 kilometers is one person, while a train travels 50,000 kilometers and one person dies. These words, at first glance, seem to have some truth.But careful consideration reveals that this method of comparison is problematic. Not to mention whether the statistics mentioned are reliable, even if they are assumed to be true, it is impossible to draw the conclusion that flying is safer than taking trains.Because it is very unscientific to compare the safety of two vehicles with very different speeds by using the running distance as a unit.

According to people's specific feelings, in terms of measuring the degree of safety, instead of using running distance as a unit, it is more realistic to use running time as a unit for comparison.Assuming that the average speed of the train is 40 kilometers per hour, and the average speed of the plane is 500 kilometers per hour, and calculated according to the unit of running time, the statistical result becomes that the death rate of the plane is one person for every 200 hours of flying, while the average speed of the train is 500 kilometers per hour. One person died after driving for 1250 hours.

This leads to the exact opposite conclusion of what the airlines are saying: traveling by train is safer than flying. (2) There is a shop that sells rabbit meatballs cheaply. Someone asked the shopkeeper: Why sell such a cheap price? The owner replied: To be honest, there is horse meat in it, which is half of rabbit meat and half of horse meat.I could have sworn it was half rabbit and half horse. Even half horsemeat is cheap because rabbit is more expensive than horsemeat. Yeah, so to add half of the horse meat, we use one horse meat and one rabbit meat, and we will never use more horse meat.

A horse and a rabbit are equal to each other. This is the shop owner's statistical method: the unit of calculation is not the weight of the horse and rabbit, but the number of individuals.What a clever sophistry. (3) When using statistical methods to express a country's natural resources and economic development level, only calculating the total amount and not the per capita amount is also a sophistry in statistics. Because the total amount of natural resources and material production of a country may be among the best in the world, but in terms of per capita quantity, it may still be at the middle or lower level.Therefore, when measuring the degree of prosperity of a country, it is necessary to examine the overall national strength through the statistics of various aspects, and not just look at the situation in one aspect.In this way, more realistic conclusions can be drawn.

three.Arbitrarily fabricate statistics according to subjective needs This is statistics at its worst, and it takes many forms.For example, in order to obtain the title of advanced, a small number of cadres tried to exaggerate the figures when counting the work performance of their units. The exaggerated style of my country's Great Leap Forward in 1958 is a typical example.At that time, almost all walks of life were putting satellites on the digital, and the situation in agriculture was particularly prominent.Inspired by the slogan "how bold people are and how much land is productive", many people are comparing each other. Since you can produce 10,000 catties per mu, I can produce 100,000 catties per mu. There is also the opposite situation, that is, instead of reporting the output truthfully, they try to lower the number and conceal the output.For another example, in order to show their victories, the two warring parties often use exaggerated statistics to display brilliant results, while saying as little as possible or even not talking about their losses in terms of personnel and materials.But sometimes for certain needs (such as asking the other party to compensate for losses, or to win sympathy and assistance from others), they will exaggerate their own losses in number. In short, the sophistry is capable of inventing statistics to his advantage at any time, according to different circumstances.