Changshan Pharmaceutical's "Statistical Fraud"

Two years ago, Changshan Pharmaceuticals caused a heated discussion by saying that "about 140 million Chinese men suffer from impotence, and the market for its products is vast." The company announced on December 28 that it had received the "Administrative Penalty Decision" from the China Securities Regulatory Commission, which determined that some of the information disclosure in Changshan Pharmaceuticals' Announcement No. 2018-28 was in violation of regulations, and the company was given a warning and fined 600,000 yuan. Changshan Pharmaceuticals once again became a hot topic.

There is no doubt that the so-called data source of about 140 million is definitely a generalization, because statistics can lie.

There seems to be a book named like this in the past, just like the figure below, which adjusts the coordinate system for the same data.

In fact, Changshan Pharmaceutical is similar.

We often see various data, such as how many billions of xx there are in China,

Changshan Pharmaceutical previously said that there are 127 million impotence patients in China, Guizhou Bailing previously said that there are more than 110 million diabetes patients in China, Tongce Medical said that there are more than 50 million infertile people, and Corning Hospital said that one in every five people suffers from mental illness.

However, in theory, apart from the national population census, no organization can conduct a nationwide census, and even the annual census is based on sampling.

So, how did Changshan Pharmaceutical come to this conclusion?

In fact, the method is to calculate the probability through sampling survey and then multiply it by the total population.

For example, we surveyed dozens or hundreds of people and found that the proportion of male impotence in the sample group was 20%. Finally, we multiplied it by the approximately 700 million men in the country, which is 140 million.

However, there is a problem here:

When conducting sampling surveys in statistics, there are strict requirements for sampling.

How is Changshan Pharmaceutical’s sample sampling conducted?

Is the place representative? Is it a national sample? Or is it represented by a certain city?

There are so many cities and counties across the country, and the local customs and people in different regions are different, and people's living habits are also different. Are they included?

What is the age distribution?

There are differences in personal sexual function at different age groups, especially for children and adolescents who are not yet sexually mature.

What is the occupational distribution?

There may be differences in different occupations

Even the method of investigation has a great impact: Internet? Phone? Door-to-door?

For example, will the Internet survey involve the issue of Internet users and non-Internet users? Currently, there are 900 million people in my country with Internet access, and there are still more than 500 million people without Internet access.

If these are not clear, then this sampling survey will not be convincing. Here is a typical example:

When the reporter went to the train to interview, he found that everyone had a ticket, so the reporter reported: the problem of difficulty in getting a ticket during the Spring Festival travel rush has been solved.

This is a typical problem of survey sample selection.

But often, we will encounter some problems, that is, is the other party deliberately making mistakes? Or is it that they are not capable enough and do not know that there are so many tricks in sampling surveys?