[Special Feature: Yukichi Fukuzawa and Statistics] Masao Yokoyama and Statistical Education / Masahiro Sato

2020/06/05

Image: Masao Yokoyama (Collection of the Keio University Fukuzawa Memorial Center for Modern Japanese Studies)

When observing things in general, one should note that:

Single molecules and aggregates may exhibit phenomena somewhat different from those of single molecules alone. Just as a handful of water has no color while the water of the great ocean is blue, and a small amount of atmosphere has no color while the sky appears azure when looking up, the affairs of society and the state can be clearly understood for what they are when reflected in the mirror of statistics.

In all things, there are constant causes and variable causes. Constant causes are ordinary causes, while variable causes are unusual causes.

So-called constant causes are lawful, while variable causes are unlawful.

When observations are few, variable causes are many and may exceed constant causes. Therefore, observations must be made on a large scale to overwhelm the variable causes.*1

This is a transcription by a district secretary of a lecture given by Masao Yokoyama at the 2nd Fukushima Prefecture Statistical Training Session held in 1909. Its content is an explanation of the "Law of Large Numbers," which remains one of the foundations of statistics today. While it is defined mathematically from the standpoint of mathematical statistics today,*2 Yokoyama's explanation uses very intuitive empirical rules as examples. I have cited this example here to give the reader an image of what the statistics Yokoyama relied upon was like.*3 Statistics at that time was based on simple probability theory, and its intended subjects were "society and the state." This was so-called social statistics. This lineage began with Koji Sugi, who is considered the founder of statistics in Japan,*4 and was passed down continuously through pre-war Japanese statistics.*5 From today's perspective, this statistics may seem undeveloped or even primitive at first glance. However, behind the many survey statistics (such as the Census, the Fact-finding Survey of Labor Statistics, and the Family Income and Expenditure Survey), administrative statistics (such as trade statistics and vital statistics), and processed statistics (such as national wealth statistics) created before the war, this kind of statistics existed as a theoretical backbone.

First, let me briefly mention Masao Yokoyama's connection with Keio University. Statistics courses began at Keio University in 1892, and following Paul Mayet and Kei Okamatsu, Ayatosi Kure taught from 1898. Yokoyama served as a substitute lecturer when Kure went to the United States in 1900 to inspect the state of statistics, and after Kure collapsed from a cerebral hemorrhage in 1916, Yokoyama took over the statistics courses as his successor. Subsequently, he was in charge of statistics lectures at the Keio University college and university for nearly 20 years.*6 In this article, I will focus on how he acquired his knowledge of statistics and how he subsequently conducted his activities. First, let us look at Yokoyama's encounter with statistics.

Masao Yokoyama received his statistical education at the Kyoritsu Statistical School, established in 1883 primarily by Koji Sugi, who is often called the founder of Japanese statistics. This school was originally planned as a public institution; in 1882, Koyata Torio, the head of the Statistics Board (Tokei-in), proposed that a statistical school should be established within the Board, but the proposal was rejected due to budget constraints. Following this, Sugi called upon his colleagues at the Statistics Board within the same year to open a statistical training center using private funds. Sugi recalled the school as follows:

Human life is short while great works are eternal; having already grown old*7 and with the sun setting on a long road ahead, I desired to establish a school to educate several hundred students. I consulted with Director Torio on this matter, and he gladly assisted. Various gentlemen within the Board also contributed funds according to their means, and with a grant from the Imperial Household Ministry, we leased land from the Army at the foot of Kudanzaka in the spring of 1883 and built the Kyoritsu Statistical School there. In collaboration with Jiro Takahashi, Yukichi Terada, Kei Okamatsu, and others, we selected over 200 items for the subject of statistics and made them the curriculum. When we recruited students, over 80 applied, and in three years, we produced 36 graduates and 27 recipients of certificates of study. Just as we were about to start the second recruitment, a major reform occurred in December 1885,*8 the Statistics Board was abolished, and I too was left without a post. Unable to support it alone, the school, which was a joint venture, was closed by the disposition of the Tokyo Statistical Association, and the matter ended.*9

Masao Yokoyama was one of these 36 graduates. While I will not describe the curriculum of the Kyoritsu Statistical School in detail here, it was an education that combined theory and practice, including Western statistics such as that of Haushofer, as well as practical training in statistical surveys.

The graduates of this school later entered various government offices and became the core of statistical operations, also serving as instructors at various statistical training sessions described later. They formed an organization called the "Ushibuchi Alumni Association" and continued mutual interaction and information exchange even after the school closed. Yokoyama's official position after graduation was as an Army Professor.

Setting aside modern mathematical statistics for a moment, social statistics at that time was not merely a scientific theory but had the practice of designing and conducting statistical surveys of social phenomena as an indispensable part. Generally, in statistical surveys targeting social phenomena, it is of course necessary for those designing the survey to have knowledge of statistics, but it is also necessary for those who come into direct contact with the subjects in the field to have a certain degree of knowledge regarding the work they are engaged in—namely, statistics. Furthermore, the general public who are the subjects of the survey are also required to have a minimum level of knowledge about what the statistical survey is asking of them—specifically, how to answer the survey. Where these two conditions are lacking, statistical surveys (at least self-administered ones*10) cannot be established. Because of these circumstances, statisticians of the time devoted themselves to the basic education of those in charge of statistical surveys in various regions and to enlightenment activities for the general public who were to be the subjects of the surveys. Let us look at three examples below. The first is the local statistical training sessions held in various prefectures during the Meiji period; the second is the training sessions for enumerators held in various locations for the 1920 Census; and the third is the writing activities for primary education textbooks. Yokoyama was highly active in all of these.

First, let me discuss the local statistical training sessions.

In 1899, the "Central Statistical Training Session" was held, centered on graduates of the Kyoritsu Statistical School and statisticians who had been disciples of Koji Sugi since before then. Initiated by members of the Tokyo Statistical Association and the Statistical Society, six training sessions were held between 1899 and 1906, producing 817 graduates. Many of them were statistics officials in central government offices or prefectural secretaries. In response to this, training sessions at the prefecture level (including colonies) began to be held. If we look at the number of participants in training sessions at the central level (the total of the Central Statistical Training Session and training sessions by central government offices) and the prefecture level, they are as shown in the table. There were 1,067 participants in central-level training sessions, which, considering retirement and turnover, suggests that approximately two to three people with knowledge of statistics were likely assigned to each central ministry and each prefecture.

Furthermore, the number of participants in prefecture-level training sessions exceeded 16,000 over these 13 years. Since participants in training sessions at this level were primarily district and city secretaries, it suggests that, simply put, someone with knowledge of statistics was likely assigned to every district and city across the country.

Masao Yokoyama served as an instructor at these local training sessions an overwhelmingly greater number of times compared to other statisticians. His movements were energetic. For example, tracing Yokoyama's actions from July 1911 onwards, he traveled across the country with almost no rest: Saga on July 11, Kagawa on the 19th, Tokushima on the 27th, Miyagi on August 1, Mie on the 14th, Kyoto on the 21st, Okinawa on September 4, Osaka on the 17th, Hokkaido on October 4, and Aichi on the 27th. Although it was an era when the main railway network was nearing completion, in a time without Shinkansen, airplanes, or common use of automobiles, managing such a dense schedule must have been a task requiring more physical and mental strength than we can imagine.

Now, how were the local-level statistical training sessions conducted? Below, I will introduce the training session held in Fukushima Prefecture in 1902.

The 1st Fukushima Prefecture Statistical Training Session was held for 20 days from August 17 to September 5, 1902, for 40 trainees, primarily district secretaries. The instructors and their subjects were Masao Yokoyama for "History of Statistics, Theory, Methods, and Institutions of Statistics, and Census Methods," Saburo Mizushina for "Political, Economic, and Social Statistics," and Sensaburo Wada for "Population and Ethical Statistics."*11

The administrative documents of Fukushima Prefecture include, in addition to ordinary administrative papers such as securing venues, appointing instructors, creating materials, and recruiting trainees, the completion exam questions set by the three instructors at the end of the session, the answer sheets submitted by the trainees, and a list of the grading results for those answers. Since I cannot cover all of them here, I will introduce Yokoyama's questions and the answers to them as an example.

Masao Yokoyama set the following three questions for the completion exam:

Question 1: Who is the founder of statistics in our country, and approximately how many years ago was it?

Question 2: In the nature of statistical observation, there are items that are impossible, impermissible, or disadvantageous; give examples of each.

Question 3: Here are two prefectures, A and B. A has a population of 1,102,853 and 8,523 elementary school students; B has a population of 1,600,829 and 10,500 elementary school students. Show the equation to obtain the proportion of elementary school students to the population.

The first question required the name of Koji Sugi, and for the "how many years ago" part, full marks were given even if the answers varied among students, such as "about 43 years ago," "almost 30 years ago," or "roughly 50 years ago from now." Since it would affect the dignity of the district and city secretaries, who were local notables, if they returned home without scoring points, Yokoyama likely set this question out of consideration to give them points.

In contrast, Yokoyama graded strictly on the second and third questions. The second question asked about basic concepts in survey design, such as not asking questions that intrude into people's thoughts or beliefs, or questions that are unusually detailed compared to the budget and lack utility. The third question was to find the ratio of the number of elementary school students to the total population of the prefecture, which belongs to elementary arithmetic today, but looking at the trainees' answers, they seem to have struggled considerably. Yokoyama's intention was likely that he wanted those who handle statistics in each district and city to understand how statistics are designed and how data is processed.

Another point I would like to draw attention to regarding the statistical training sessions in Fukushima Prefecture is their downward expansion. Upon returning to their posts, the district and city secretaries who participated in the training session held district-level training sessions as instructed by the prefecture, serving as instructors themselves to provide statistical training to town and village-level secretaries. This was possible because when Yokoyama and many other instructors gave lectures, they used a method of reading aloud a passage from their own lecture notes (in Yokoyama's case, the textbook "General Theory of Statistics"), having the trainees transcribe it, inserting notes on it, and then having them transcribe the main text again. There were still teachers who used such old-fashioned lecture methods when the author was a university student, but with this method, the trainees would have a complete copy of the textbook in their hands at the end of the training. They could then print it using methods such as the hectograph and distribute it to the participants of the district training sessions, who were primarily town and village-level secretaries. Incidentally, Masao Yokoyama's "General Theory of Statistics" went through over 40 editions from its publication in 1901 until the end of the Taisho era, and it is thought to have been the de facto standard textbook and reference tool for statistical personnel, especially practitioners, at the time.

The example given here is limited to Fukushima Prefecture, but the situation was likely similar in other prefectures. In any case, it can be seen that during this period, statistical training organized people in a branching manner like the legs of an octopus. Yokoyama played a major role in this.

Next, let me discuss the training sessions for Census enumerators.

When Japan's first Census was conducted in 1920, the statisticians in a position to implement it faced a difficult problem. It was the unprecedented scale of the Census. This survey required responses from all Japanese citizens, who numbered about 50 million at the time. The number of households, the unit of reporting, was also around 10 million, which was far greater than any previous statistics. Along with this, several thousand enumerators to distribute and collect survey forms had to be appointed in each prefecture. Many of them had never been involved in statistics before, and it was thought that how to enlighten them would determine the success or failure of the survey. Each prefecture gathered enumerators at the district and city level and held very simple training sessions on statistics. Yokoyama was active here as well, along with other graduates of the Kyoritsu Statistical School.

Let us take Kitatama District in Tokyo Prefecture as an example. On April 15 and 16, 1920, a training session was held at the district office in Fuchu, gathering Census enumerators from various towns and villages within the district. Peeking at part of the lecture notes of Magoshiro Koyanagi, who participated from Kokubunji Village, there is the following description:

The next day, the 16th, Instructor Yokoyama said: The Census is to survey matters related to the survival of the country, such as population and industrial production; in English, it is called 'Census.' However, in the Census to be conducted in our country this time, humans are the main foundation. If the investigation of this is complete, good governance can be achieved. And in investigating this, even in the case of population, there are the following distinctions:

1. Registered population: Based on the family register

2. Resident population: Those residing within a fixed period

3. Present population: The actual population at a single second in time

The Census to be conducted this time is the third of these (omitted below)

Looking at Koyanagi's "Business Diary," he proudly records having received a lecture from Masao Yokoyama, who was dispatched from the center: "April 16: Dr. Yokoyama, a Cabinet Statistician, came to the district office and gave a training session on the Census." It is unknown how much understanding was gained from just two sessions of a few hours each, but the fact that far more people than in the local statistical training sessions received such training likely became the foundation that led the first Census in Japan to success.

Finally, let me discuss primary education textbooks.

What I have described so far concerned people involved in statistics in prefectures, districts, cities, towns, and villages, as well as those involved in the survey as Census enumerators. However, Yokoyama's activities did not stop there. In 1910, "Lesson 30: Statistics*12" was added to the Ministry of Education's "Higher Elementary School Reader, Volume 3," for the first time as a primary education textbook. To give an example, the Law of Large Numbers is explained here as follows:

When looking at a single family, there are those with a significant difference in the number of males and females, or there are families with only females. However, when surveying a single village, the ratio of that difference is not as significant as in a single family. A district is less than a village, and a prefecture is less than a district; the ratio of the difference gradually decreases. Thus, reaching the total for the whole country, one sees that the ratio of the difference is extremely slight.

According to old materials from the Statistics Bureau, it was Masao Yokoyama who wrote this manuscript, and the number of pages written was several times the number actually published. The article in the Higher Elementary School Reader can be said to be the essence of what statisticians of the time told elementary school students when talking about what statistics is. Thus, from 1910 onwards, at least residents who graduated from higher elementary school would have studied the matter of "statistics" somewhere. Conversely, people before this would have had no opportunity to encounter the statistical way of looking at things unless they entered at least a secondary school. Yokoyama was also a pioneer of statistical education in primary education.

As we have seen, the role Masao Yokoyama played in the dissemination of statistics in Japan was extremely large. Starting from primary education, he trained statistical practitioners in prefectures, colonies, districts, cities, towns, and villages, and on those occasions, he wrote the de facto standard textbook "General Theory of Statistics."

By the way, it is known that this "General Theory of Statistics" was not only a common textbook in Japan but was also widely circulated in neighboring China. I would like to conclude by touching on this point.

The author had the opportunity to survey the provincial libraries of Shaanxi and Liaoning twice, in 1998 and 1999. At that time, in Shaanxi, I discovered a card for "General Theory of Statistics" (1913, 392 pages, Chinese version) published by the Shanghai Commercial Press, and in Liaoning, a card for the 1909 edition (6th edition, translated by Meng Sen) of the same book. In the 1910s during the Republic of China period, Yokoyama's "General Theory of Statistics" seems to have gone through multiple editions and circulated as a textbook for statistics. Later, in the 1920s and 30s, statistics textbooks by Chinese authors who were likely influenced by Yokoyama began to be published, and this group of authors continued their activities even after the founding of New China. However, the situation changed completely in the late 1950s. Looking at the cards in the Liaoning Provincial Library, a book titled "Purging the Poison of Bourgeois Statistical Academic Thought" was suddenly published in 1959, and from then on, the names of statisticians in Yokoyama's lineage disappeared. They were likely purged. What appeared in their place were direct translations of statistics textbooks from the Academy of Sciences of the USSR.

Viewed in this way, Yokoyama's influence extended not only to Japan but also to Taiwan and Korea, which were Japanese colonies, and even to the Republic of China and the early People's Republic of China, and can be seen as having had a major impact throughout East Asia at the time.