Most readers would have read of Darell Huff’s book on “How to Lie with Statistics” which is written back in 1954. Some materials may come from there. This is goes hand in hand with Tversky and Kahneman’s framing theory which was published back in 1981. Basically, how one would use statistics in such a way that it would frame the readers into thinking something that the authors wanted to.
Let’s start with the basic. Suppose that there is a fund management report that states an increased in the return by 50%. It is not a lie when the fund’s return for the previous period is 0.1% while the current period records 0.2% return. It is indeed a 50% increment from the previous period to the current period and this will entice investors to the fund. Kindly be aware that 50% increment represent a relative difference while the absolute difference of the fund’s performance would be 0.1%. Surely, combining both relative and absolute difference in the reporting of fund’s performance is crucial in helping investors understand the fund better.
Average is a common misunderstood statistics among public. Firstly, average is not a robust statistics which means that the average value is highly affected by outliers. Suppose a fund reports the following quarterly return: 4%, 5%, 6% and 19%. The average of first 3 quarters will give 5% whereas the last 3 quarters would give 10%. For those who studied statistics could explain that average or mean could be viewed as a location parameter. The remedy is to report the average figure together with the respective standard deviation.
Secondly, the term average is ambiguous. With the above example, the averaging of the first 3 quarters would produce 5% only if the arithmetic average is used. The geometric average and harmonic average are 4.9324% and 4.8649% respectively for the first 3 quarters. Note that the averaging of returns is best done using geometric average. There is a mathematical proof that the arithmetic average is always higher than geometric average. Therefore, use geometric average to report fund performance rather than the arithmetic average else the reported figure would be overestimated.
This article provided some simple example that statistics could be used to manipulate investors into certain actions. It is up to the investors to decipher where the reported statistics are being presented in the correct manner. Failure to do so would cause the investors to display framing bias which may not act in the best interest of the investor.