Monday, November 16, 2015

Confounding Compounding

Fact checking numbers (especially estimates and forecasts) is too often overlooked.  As promised, I wanted to "audit" my own statement/claim:

The good news is, that in just over two thousand and ten years, the Christian population increased from the power of one (Jesus) to over 2 billion. Pretty awesome! - but that still is only a compounded growth rate of only 1.08% - just about what a Certificate of Deposit can get you today.

Checking several sources of data discovered various estimates of 2010 Christians. I had used 2.184 Billion Christians from a 2011 Pew Research report.   However the most recent report:  "The Future of the Worlds Religions 2010 - 2050" has revised the 2010 figure down to 2,168,330,000.  The total world population 6.895,850 remained the same.  Either way saying "over 2 billion" was accurate. 

However - what about the 1.08%?  I used the following assumptions:  2.184 Christians in 2010; ONE Christian in 0000 so a total of 2010 years.  Then rounded to the nearest hundredth (actual compound growth was 1.0756%). 

So what is wrong with the data? 

(1) Well, you might say that the start year should have been when Jesus started his ministry (at 30 years old).   According to Luke 3:1, John the Baptist began his ministry in the 15th year of Tiberius Caesar’s reign. Tiberius was appointed as co-regent with Augustus in AD 11, and 15 years later would be AD 26. Jesus began His ministry shortly thereafter at approximately the age of thirty (Luke 3:23). This gives us a basis upon which we can approximate what year Jesus began His public ministry: around AD 26. However there are others that say 29AD (see "What year was Jesus born")

Choosing the lowest number (26AD) then the number of years would be 1984  (2010 minus 26).

(2) Use the new revised Pew Research number of Christians in 2010:  2,168,330,000

(3) Use four decimals for the compound growth rate for accuracy

The new answer:  1.0894%  which rounded would be 1.09%  Sounds close enough to my claim.

But even with adjusting for greater accuracy, one should test what does this really mean.  Is a compounded growth rate even an appropriate example to illustrate the growth of Christianity?

Do we really believe in 27AD there was 1.0894 Christians and only by 35AD did the world have 2 Christians (after all we lost one to crucifixion by that date).

NOT REALLY!   So what was the underlying assumption problem?

Population is not a function of compound growth -  it is a function of fertility and mortality.

Christian population is a function of:

(1) Converted Jews and Gentiles to Christianity
(2) Christians offspring that were raised and baptized as Christians (although that starts the argument of what defines a Christian)
(3) Longevity of Christians (i.e. longevity/mortality would increase the % of population over time)
(4) Any loss of Christians (i.e. Christians falling from the flock, wars, martyrdom etc. )

SO......   How do you model the future population of Christianity?

That will be the subject of a future blog.  In the meantime - for the statisticians read:

"The Future of World Religions: Population Growth Projections, 2010-2050"

P.S.  Some religion trivia -  Jesus ministry was only three and a half years.

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