Comparing Numbers

[] This is first part of second lecture of Descriptive Statistics: An Islamic Approach DSIA 02A . The 15m video is followed by a 1000 word writeup

The simplest statistical operation is to compare two numbers and decide which is larger. If we look at the numbers only, then this is completely TRIVIAL. For example, here is World Bank data on GDP for Pakistan and Morocco in 2109:

Country GDP in Billions of Dollars 2019 GDP/capita in Dollars 2019
Morocco 119 3345
Pakistan 284 1388


Which country has higher GDP? Gross GDP of Pakistan is much higher than that of Morocco, but GDP per capita of Morocco is much higher than that of Pakistan. So what can we conclude from this comparison? Nothing, unless we go beyond the numbers to ask WHY we want to make this comparison.

Four Questions will guide our study of statistics. These questions are not part of conventional approach to statistics.

  1. Why are we comparing numbers?
  2. What do the numbers MEAN?
  3. How were these number computed?
  4. What will be done with the analysis?

Instead of thinking of statistics as the analysis of numbers in isolation from the real world, we will consider statistics as a branch of Rhetoric: how do we use numbers to make arguments, and to persuade?

When asked to compare GDP to decide “Which country is “Wealthier”?”, we need to go into the background.  WHY are we asking this question? Depending on the why, different analyses will be appropriate.  In case of WAR between the two countries, gross GDP matters – this indicates the economic resources available to the country – this was the original context of “Wealth of the Nations” by Adam Smith. If we want to compare living standards, GDP/capita matters. This shows how Statistical Analysis CANNOT be separated from real world context and purpose of analysis.

When we want to think about the arguments being made with numbers, we have to look at the historical context. Even though Adam Smith introduced the concept of the “Wealth of Nations” in 1776, measure of GDP were first introduced by Simon Kuznet’s in 1934. Why this long delay? To understand this, it is important to realize that History is the conquest song of the victors. The measure of development is defined by the powerful to make them look good. There is no entry for “democracy” in 1930 Encyclopedia Brittanica; the British were an aristocratic society. For more on how the concept of development, and corresponding measures, have changed over time, see: “What is Development?” –

When we think about the meanings of the GDP measure, several possibilities emerge:

  1. Measure of POWER?
  3. Measure of HAPPINESS?
  4. Measure of fulfillment of basic needs?

We have considered the possibility of measuring national power by GDP. But if this is the purpose, we should also consider military power, political power, and other factors which contribute to national power, in addition to the economic power which may be measured by GDP.  Similarly, for the other three possible meanings, in each case, GDP is seriously deficient.

The question of “How can we compute BETTER numbers?” is considered in depth by the Stiglitz-Sen-Fitoussi Report on GDP. We briefly summarize some of the key issues presented in this report.

They explain that we need to study deficiencies of the GDP measure because GDP/Capita is CENTRAL measure of National Wealth. This measure DRIVES economic policy across the globe. Flaws in this measure lead to flawed policies. They establish that there ARE very serious flaws in GDP. One way to see this is to note that measures of inflation, growth, prosperity from national income accounts, differ drastically from public perception of the same phenomena. There are many reasons for this. One of the important reasons is that the statistical AVERAGE does not reflect the experience of the masses. For example, high inflation in food prices will hurt the poor masses, and make them experience a very high inflation. However average inflation may be low if non-food commodities are not changing in price.

Another question which statistician do not ask is: “What will we do with this analysis?”. Stiglitz-Sen-Fitoussi consider the policy implications of changing the GDP measures. They say that the Global Financial Crisis occurred because we were NOT measuring the right numbers. Similarly, the Environmental Crisis, Looming Destruction of Human and Animal Habitat, is happening because the GDP numbers do not reflect these concerns. Better measures of human prosperity would lead to better policies. So it is vital to go beyond the narrow focus on numbers, and look at the four questions posed earlier.

The Stiglitz-Sen-Fitoussi report ends up with the following Recommendations

  1. Shift from Production to Well-Being
  2. Look at Income & Consumption, rather than production.
  3. Emphasize Household Perspective, breakdown by income categories.
  4. Broaden Wealth to non-market activities.
  5. Improved measures of health, education, environment.
  6. Improved measures of social networks, family, friends, community

All of these changes would radically affect the standard GDP measure. When we analyze GDP without taking into account what it means and how our analysis will affect the future, we become part of the chain of ignorance and neglect which leads to major disasters on economic and environmental fronts.

Concluding Remarks: We have seen that connecting Numbers to Real World Applications requires going far beyond standard scope of statistics. From the Islamic point of view, every small participant in an act gets credit or blame for the whole act. So, the statistician CANNOT escape responsibility for how statistical analysis is used. THEREFORE, we MUST broaden the scope of study to include questions discussed earlier, beginning with the WHY of analysis. We cannot say that I will just analyze numbers, let the others USE my analysis for whatever purpose they want to use it. This leads to End-To-End analysis – we start with a real world question, consider how to answer it, and use statistics for solution if it is required. Statistical analysis is a means to an end, and not the goal in itself.

LINKS to related materials

This lecture: DSIA02A: Comparing Numbers:

First Lecture in four parts:

  1. Descriptive Statistics: An Islamic Approach – []
  2. Purpose: Heart of An Islamic Approach: []
  3. Eastern and Western Knowledge: []
  4. Islamic Pedagogical Principles: []
This entry was posted in Uncategorized by Asad Zaman. Bookmark the permalink.

About Asad Zaman

BS Math MIT (1974), Ph.D. Econ Stanford (1978)] has taught at leading universities like Columbia, U. Penn., Johns Hopkins and Cal. Tech. Currently he is Vice Chancellor of Pakistan Institute of Development Economics. His textbook Statistical Foundations of Econometric Techniques (Academic Press, NY, 1996) is widely used in advanced graduate courses. His research on Islamic economics is widely cited, and has been highly influential in shaping the field. His publications in top ranked journals like Annals of Statistics, Journal of Econometrics, Econometric Theory, Journal of Labor Economics, etc. have more than a thousand citations as per Google Scholar.

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