Consider the following statements:
Statement A: No swan is black, because I looked at four thousand swans and found none.
Statement B: Not all swans are white.
Statement A is an example of how statistics can be applied to a problem. A statistician would take a sample of the population and from the sample she would make conclusions about the population as a whole. This is useful because we often do not have the time or capacity to observe or collect data on an entire population.
Imagine trying to survey everyone in the UK about which party they will vote for in the next election. It’s hard enough getting people to vote in the real thing! The time and money spent would be extraordinary.
Unless every swan alive is checked, then you cannot for certain say that all swans are white. The statistician is simply making a good guess based on her sample. However, statement B only needs one counter example to be validated, compared to a whole population for statement A. Statement B was actually validated to Europeans in 1697 when Willem de Vlamingh’s expedition explored Western Australia and found black swans.
There are only two types of theories.
- Theories that are known to be wrong as they were tested and adequately rejected.
- Theories that have not yet been known to be wrong but are vulnerable to being wrong.