Questionable CAI/FCAR 2020 facts

My analysis of the data presented in the 2020-2021 Statistical Review and CAI Factbook for 2020 by the CAI affiliate, Foundation for Community Association Research, brings me to suspect the data.  I painstakingly extracted the raw data as presented and subjected it to my own analysis using an EXCEL spreadsheet.  Almost immediately a very disturbing result appeared that should have been obvious to a statistician as highly unlikely.  Of the 27 top states by number of  HOA organizations, my analysis revealed a fixed 3.3% of Volunteers to HOA residents for the state. Restated, each state showed 3.3% of all HOA residents as CAI volunteers.research

From a point of view of statistics, events and activities generally follow the normal probability curve, more or less, but when there is no variation then the conclusion is that some other factors are at play that produced the result.  The normal distribution is the most important probability distribution in statistics because many continuous data in nature and psychology displays this bell-shaped curve when compiled and graphed.  For example, if we randomly sampled 100 individuals we would expect to see a normal distribution frequency curve for many continuous variables, such as IQ, height, weight and blood pressure.

Consequently, this result should have been caught if it were some error, or if not an error then an explanation as to what caused this highly unusual result.  There was no explanation. Therefore the validity and integrity of the Statistical Review is suspect. The data used to generate the results cannot be accepted as a factual free choice representation of the underlying reality.  To repeat, the “error” is too obvious not to  have stood out and been corrected. As such, the entire factsheet is suspect, and probably earlier factsheets as well.

Looking for some rational explanation, I then looked into the possibility that the Top 27 states were somehow different from all the states so I examined a random 5 states, one from each corner and one from central US.  They, too, showed this suspect 3.3% ratio.

My research also revealed  the percent of HOA residents to the total US population as 21.1% and 22.4% (a variation ascribed to intermediate rounding of numbers and not significant). CAI has touted the number as 25% – 27%,  also in 2019, but in 2016 the number was in line with the 22% figure.  I cannot explain how this CAI number was obtained.

Hopefully, CAI and FCAR have an explanation.

For the mathematically inclined, the EXCEL spreadsheet (PDF) can be viewed. data analysis.pdf

In case you were wondering about my background in statistics, I have taken courses in statistical analysis in psychological research, product marketing  (MS Management), participated in a queuing theory analysis of computer messaging throughput for international wall street firm, set up the methodology for the calculation of business sales for business brokerage industry, and analyzed the TV show, Deal or No Deal, probabilities of winning the million dollar prize (see website).