Round The World

New Delhi, 15 December 2023

Statistical Literacy

WHY IS IT IMPORTANT?

By Rajiv Gupta 

Suppose you take your temperature on two successive days. On the first day it is 98.2 degrees, on the second day it is 98.8 degrees. What would you infer from these readings? More importantly, what course of action would be warranted as a result? A lot of people take notice and act on information not very different from the example cited above. We often read items in newspapers with statistics to make a point. The numbers could be about the economy, the number of accidents, or the crime rate, etc. We read the numbers but not everyone reflects on what the numbers mean. Numbers convey meaning and it is up to the reader to discern the meaning. Let us take an example. 

A leading English national daily had a news item titled: “Fatal Accidents Down, Traffic Cops Cite Proactive Measures” on November 14, 2023, which gave statistics of road accidents in Delhi from 2019 to 2023 (up to October 31). There were 1433 fatal accidents in Delhi in 2019, 1163 in 2020, 1206 in 2021, 1428 in 2022, and 1141 up to October 31 in 2023. The Delhi Traffic Police cited these numbers to convey that there was a 4.7 per cent reduction in fatal accidents between 2022 and 2023 and that was due to proactive measures taken by the police. Is this a correct claim? Does it mean that in 2024 we should expect a further reduction in fatal road accidents? 

Statistics can either convey relevant information which can lead to sound decisions, or they could be misinterpreted leading to action when none is warranted. In the temperature example at the beginning of the article, it should be clear that no action needs to be taken. Why? Because typical human temperatures fluctuate in a range, the range depending on the individual circumstances. If any medication is taken because the body temperature reaches 98.8, it can lead to undesirable side-effects. Similarly, we need to examine the data in the newspaper article. The observations will be valid not just for the article but for a host of numbers seen in newspapers, television, and other media. 

The reason we should not start medicating ourselves when the body temperature reaches 98.8 is because body temperature has a natural range of variation. This variation is due to various factors such as the ambient temperature, our clothing, what we may have eaten, whether we have just exercised, etc. Dr. W.E. Deming, noted statistician and management guru who helped the Japanese industry become world leaders, called this natural variation caused by “common causes.” If the statistic (in this case the body temperature) is within some defined limits, no action is required. But if it goes outside these limits, then Deming said that we need to investigate and possibly take action. So once the body temperature crosses, say 100 degrees, it may be a sign that one needs to see a doctor. 

Returning to the accident data, If we plot the data points, something interesting emerges.  

What does the graph tell us? Should we conclude that some specific action resulted in a decrease in accidents? Or does it look like random variations in data which do not reveal any specific pattern or trend? Even without defining any limits which would indicate any unusual pattern of behaviour, it is easy to see that the number of accidents over the five-year period reported in the article is relatively stable. Not many people would interpret the reduction from the fourth to the fifth year as remarkable. 

A natural question which a reader can ask is “So what?” What is the harm in misreading natural variation and taking action to compensate for any effect that we feel necessary? Is it necessary for the problem to get big before we act on it? Should we not ward of problems by taking preventive measures? 

Deming wrote that if the data only shows natural or random variation, any action in response to a change from one period to the next would make the system unstable with the potential to increase the variation in the data. In the case of the body temperature example given in the beginning of this article, most healthcare professionals agree that unnecessary medication to counter random changes in the body temperature can lead to problems. We should take steps to improve one’s health such as eating well and exercise. But action should not be taken to counter a slight blip in the body temperature. 

Similarly, in the case of accidents, the authorities ought to take systemic actions to reduce the overall incidence of accidents. Actions such as better patrolling, better lighting, better road maintenance, etc. should result in a reduction in accidents. But these actions should not be taken as a knee-jerk reaction to a slight change in one year’s accident data. 

According to Deming, any unnecessary intervention based on short term changes in data would make the system unstable, with higher highs and lower lows. However, when the change is significant, i.e., the data crosses the limits beyond the natural variation, investigation into the cause of that occurrence is warranted and action needs to be taken. In the body temperature analogy, if the temperature were to cross 100 degrees, it often signals an infection for which some treatment becomes necessary. 

Examples of misguided overreaction to data are seen in several walks of life. Perhaps one of the more glaring examples is when a company announces a drop in the sales or profit number compared to the previous quarter or year. The immediate reaction of the stock market is to selling of the stock which often leads to a drop in its price. Sales and profits of organizations do not always go up in a straight line. Any panic selling of a company’s stock in response to a poor quarter or year is unwarranted as long as the company remains healthy. 

This article was written to emphasise the need to develop literacy in reading statistical data. Data is important for managing organisations, communities, and nations. However, collecting data involves time and cost. Therefore, we need to make sure that the data is put to proper use. In addition to the cost of collecting data, incorrect reaction to random fluctuations in the data can lead to worsening the system. The message should be clear. We need a better understanding of how to interpret statistical data.---INFA 

(Copyright, India News & Feature Alliance)