CityReads | On the Ubiquity of Statistics

楼市 2024-09-27 21:43 上海

517

On the Ubiquity of Statistics

The enduring wisdom encapsulated within statistical principles

Rao, C. R. (1997). Statistics and truth: Putting chance to work (2nd ed). Singapore: World Scientific.

Sources:https://www.worldscientific.com/worldscibooks/10.1142/3454#t=aboutBook

https://www.nature.com/articles/d41586-023-03200-5

https://www.deccanchronicle.com/lifestyle/a-comprehensive-exploration-of-statistical-wisdom-unraveling-statistics-and-truth-putting-chance-to-work-by-cr-rao-882770?infinitescroll=1

I encountered a quote by C. R. Rao the other day:

“All knowledge is, in final analysis, history.

All sciences are, in the abstract, mathematics.

All judgements are, in their rationale, statistics.”

This passage is from the 1997 book Statistics and Truth: Putting Chance to Work by C. R. Rao, which I recently picked up to read. I discovered that many examples I’ve encountered in other statistics-related books were already covered in C. R. Rao’s work. For instance, one longstanding mystery in American history—who authored the 12 disputed essays in The Federalist Papers? This question was finally resolved in 1963 by two statisticians, Frederick Mosteller and David Wallace, through a comparative analysis of word frequency (for more details, refer to "City Reads | When Words Meet Numbers: What It Reveals about Writing"). Only now do I realize my limited knowledge and the importance of this classic work in statistics.

C. R. Rao’s full name is Calyampudi Radhakrishna Rao. In Indian names, "Rao" is a suffix that indicates social status and lineage, much like the prefix "Sir" in British names, signifying that he was born into a noble family. Despite having no material concerns, he didn’t rely on his family’s wealth but worked hard. As a child, his mother would wake him at 4 a.m. to study by the light of an oil lamp in the quiet early hours of the morning. After earning his master’s degrees in mathematics and statistics in India, C. R. Rao worked at the Indian Statistical Institute. He was later sent to Cambridge University’s Museum of Archaeology and Anthropology in the UK, where he analyzed measurements of ancient skulls unearthed from burial sites in Sudan, classifying them by tribe and age. During this time, he studied under Ronald Fisher, the father of modern statistics, conducting research on the relationship between chromosomes and genes by breeding and dissecting mice. In 1948, he received his Ph.D. in statistics. After graduation, C. R. Rao returned to the Indian Statistical Institute, eventually becoming its director. Following his retirement, he moved to the U.S., teaching at Pennsylvania State University and the University at Buffalo. C. R. Rao’s work has had a profound impact not only on statistics but also on economics, genetics, anthropology, geology, national planning, demography, biostatistics, and medicine.

In 1987, C. R. Rao was invited to deliver three lectures at the inaugural Ramanujan Centenary Lecture in Delhi, organized by India’s Council of Scientific & Industrial Research in honor of Ramanujan, the brilliant mathematician who "appeared like a meteor in the mathematical firmament." In 1989, based on these three lectures on the history and development of statistics, C. R. Rao wrote and published Statistics and Truth: Putting Chance to Work. The second edition was released in 1997, with the lecture material reorganized and expanded into five chapters, and a newly added sixth chapter discussing the public’s understanding of statistics. Rao also wrote a biography of Ramanujan, which is included in the appendix.

This book serves as both a popular science introduction to statistical principles and a philosophical exploration of the field. It also functions as a practical guide, offering insights for both laypeople and seasoned statisticians alike.

Chapter 1 discusses the concepts of uncertainty, randomness, chaos, and chance, emphasizing their importance in investigating and explaining natural phenomena. Chapter 2 introduces common methods for generating new knowledge—induction, deduction, and abduction—and explains how to measure uncertainty to make optimal decisions. Chapters 3 and 4 cover the historical development of statistics. Chapters 5 and 6 present numerous examples illustrating the widespread applications of statistics in scientific research, government policymaking, and everyday life. These examples show how statistical thinking and methods uncover truths across various fields and convincingly argue why statistical reasoning should be considered the fourth fundamental skill everyone must develop, in addition to reading, writing, and arithmetic.

The book also discusses the ubiquity of uncertainty in both nature and human society, as well as the difficulties it creates. It explains how the role of statistics in addressing uncertainty gradually emerged. In the past, societies relied on magic and astrology to cope with uncertainty, but it wasn’t until the 20th century that we discovered statistics as a better tool, though it hasn’t completely replaced the former two. Statistics is a method for extracting useful information from observed data, as well as the logic behind decision-making under uncertainty. It is the science of quantifying uncertainty and a tool that helps us in our pursuit of knowledge that approaches truth.

C. R. Rao pointed out that the uniqueness of statistics lies in the fact that it has no inherent subject matter of its own; it exists and thrives by solving problems in other fields. He quoted L. J. Savage, who said:“Statistics is basically parasitic: it lives on the work of others. This is not a slight on the subject for it is now recognized that many hosts die but for the parasites they entertain. Some animals could not digest their food. So it is with many fields of human endeavors, they may not die but they would certainly be a lot weaker without statistics.

Rao elaborated on the ubiquity of statistics, showcasing numerous examples from ancient and modern times and across different cultures, to illustrate how statistical tools have been widely applied in fields as diverse as industrial production, public policy, scientific research, business, medicine, literature, archaeology, and the courtroom. Rao said: “there has rarely been a technological invention like statistical quality control, which is so wide in its application yet so simple in theory, which is so effective in its results yet so easy to adopt, and which yields so high a return yet needs so small an investment."

Rao shared a statistical story about salt from India. In 1947, shortly after India gained independence, riots erupted in Delhi, and some refugees took shelter in a place called the Red Fort, where the government provided them with food. The government didn’t know the exact number of refugees but was faced with hefty bills. Suspecting that contractors were inflating the costs, they asked a statistician to estimate the number of refugees inside the Red Fort. The challenge was that the statistician had no prior information and couldn’t safely enter the fort to conduct a survey. The only available data was the contractor’s records, which listed the quantities of food supplies provided to the refugees, including rice, beans, and salt. The statistician calculated the quantities of these supplies and found that rice, being the most expensive, had likely been overestimated, while salt, which was very inexpensive, was unlikely to have been exaggerated. Using the quantity of salt as the most reliable figure, the statistician estimated the number of refugees in the fort and then calculated how much rice should have been provided.

The understanding, study, and practical application of statistics have now expanded across natural sciences, social sciences, engineering, management, economics, the arts, and literature. Even ordinary people use statistical knowledge (gleaned from media and other sources) to make various decisions in their daily lives based on the data and analysis available to them.

Rao argued that, in addition to the three basic skills of reading, writing, and arithmetic (3R), everyone should develop a fourth fundamental skill: statistical reasoning (4R). Only by doing so can we understand the uncertainties present in nature and human behavior, and minimize risk when making decisions based on our own or others' experiences. He incisively noted: “He who accepts statistics indiscriminately will often be duped unnecessarily. But he who distrusts statistics indiscriminately will often be ignorant unnecessarily.”

The core theme of Statistics and Truth is that we see truth only with some uncertainty, which we need to understand to make responsible use of the glimpse of truth we have had. C. R. Rao summarized this with the following equation:

Uncertain knowledge + knowledge of the amount of uncertainty in it

= usable knowledge.

Statistics provides the second term on the left and thus is essential in obtaining "usable knowledge."

This equation represents a new way of thinking, freeing humanity from reliance on oracles and fortune-tellers and helping to reduce risks and make informed decisions.

“* If we have to take a decision under uncertainty, mistakes cannot be avoided.

* If mistakes cannot be avoided, we better know how often we make mistakes (knowledge of amount of uncertainty) by following a particular rule of decision making (creation of new but uncertain knowledge).

* Such a knowledge could be put to use in finding a rule of decision making which does not betray us too often or which minimizes the frequency of wrong decisions, or which minimizes the loss due to wrong decisions.“

Rao gives a common example from daily life in his book: Suppose the weather forecast predicts a 60% chance of rain tomorrow. How do you decide whether to carry an umbrella? It depends on which situation results in less loss: bringing or not bringing an umbrella. Suppose the inconvenience caused by bringing an umbrella on any given day can be measured in monetary terms, denoted as mdollars, and the loss caused by getting wet due to not bringing an umbrella is rdollars. Then, when there is a 60% chance of rain, the expected loss in dollars for both decisions can be calculated as follows:

Decision	Expected Loss
Carry an umbrella	m
Don’t carry an umbrella	0.6 × r + 0.4 × 0 = 0.6r

Thus, when m ≤ 0.6r, you should decide to carry the umbrella; when m > 0.6r, not carryinging the umbrella will minimize your loss.

When analyzing superstition and psychological effects using statistics, Rao mentioned a phenomenon where people seem to have the ability to delay death until they experience a significant or auspicious moment. A study on the mortality rates of Chinese-American women before and after the Mid-Autumn Festival found that the death rate in the week leading up to the festival was 35.1% lower than usual, while in the week following the festival, the death rate was 34.6% higher than normal. Another related study analyzed the months of death for famous individuals, finding that fewer people died just before their birth month compared to those who died in or after their birth month. It seems that people often attempt to delay death until after their birth month. C. R. Rao was born on September 10, 1920, and passed away on August 22, 2023, just short of his 103rd birthday. Unlike the patterns observed in most famous individuals, Rao passed away just before his birth month.

CityQuotes

1.“To understand God’s thoughts we must study statistics, for these are the measures his purpose.”-Francis Nightingale, see Karl Pearson, The Life, Letters and Labours for Francis Galton, 1924

2.“The quiet statisticians have changed our world一not by discovering new facts or technical developments, but by changing the ways we reason, experiment, and form our opinions about it."-Ian Hacking, Trial by number, Science,1984

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