Post No.: 0264
In scientific experiments, take care with distinguishing between independent and dependent variables – for instance, individual fair dice rolls are independent from each other because the result of one roll has no bearing on the result of the next roll (despite some people’s superstitious beliefs sometimes!) But the opinions of individual children in the same class in school might be dependent on, rather than independent from, each other because they generally copy each other and will therefore likely create a clustering of data points.
If some variables are dependent on each other then (for a given sample size) raw positive results will be less statistically significant, hence the need to correct for clustering.
Take care with ‘multiple comparisons’ too – when lots of things are attempted at being measured within a single study, it increases the probability that we will find one or two positive results somewhere just by mere chance. This is akin to finding at least 1 six rolled somewhere by mere chance just by virtue of rolling a dozen dice at once, or eventually finding a string of 4 sixes rolled in a row by mere chance just by virtue of rolling a die hundreds of times – this won’t necessarily mean that there’s anything special to read into the dice, such as that they’re loaded.
Attempting to measure too many variables at once will also reduce the statistical significance of raw positive results, hence the need to correct for multiple comparisons.
There can be exceptional cases though. For example, if an independent variable does not offer a health benefit on its own, it might do so but only if combined with another independent variable i.e. there could be synergistic relationships rather than things working in isolation (e.g. extra intensive exercise is not going to be beneficial for one’s athletic performance without also adding extra nutrition and perhaps extra rest. Albeit one could argue that these particular variables are somewhat dependent on each other because doing more exercise can make one feel hungrier and sleepier). With so many different combinations of things in the world possible, it makes studying them all difficult hence why firm and concrete scientific conclusions are sometimes hard to come by in some areas of research.
There may also be bi-directional causes and effects too, so A causes B, and B causes A too, which would create a self-reinforcing positive feedback loop (e.g. sound is input into a microphone, which gets amplified and played though a nearby speaker, this microphone picks up the amplified sound from that speaker, which gets amplified and played through the speaker again, which gets picked up by the microphone again, which gets amplified and played through the speaker again, and so forth).
A double infant death occurring in a hospice – on the face of it – seems far less likely than a single infant death to be down to mere chance alone. It would seem like something seriously suspicious is happening at this place. But the odds of a double SIDS (sudden infant death syndrome) occurring is not the probability of one SIDS occurring multiplied by the probability of one SIDS occurring, as if they were ‘independent dice rolls’ and we’re trying to work out the probability of ‘rolling 2 sixes in a row’. This is because they’re not likely to be independent events. Thus to jump to conclusions and assume that a double infant death must be down to a double murder just because the odds of a double accident occurring is extremely low, would be fallacious. Besides, if the statistics of a double accident is extremely rare then bear in mind that the statistics of a double murder is possibly even more rare, thus – unless other non-circumstantial evidence is present – if one is merely arguing on the grounds of ‘prior probabilities’ (simplified, this is the probability assigned before any relevant evidence pertaining to the specific case is taken into account), the odds of the case being a double accident would possibly be greater than the odds of the case being a double murder. The main point is to not jump to conclusions.
A ‘one-in-a-million’ DNA match would actually mean thousands of people in the world would match that DNA because there are billions of people currently on Earth! And these thousands of people might not be evenly distributed around the world either since people sharing similar DNA will likely have come from the same geographic regions, hence some clustering should be expected too, despite humans being more mobile around the world nowadays. We must therefore be careful when trying to blame or convict someone based on prior probabilities and circumstantial evidence alone.
The number of accusations put forward against someone is also not by itself evidence of someone’s guilt. Historically ‘crying wolf’ (or the accusation of this) is not by itself evidence of someone’s guilt for a new specific case. This applies to praises as well as blames. One needs more than appealing to history – one needs non-circumstantial evidence specific to the current case in order to justly convict someone for this current case. (Yes I ate all the biscuits last time but I didn’t eat all the biscuits this time – woof. I’ve been framed. You gotta believe me… Burp. Okay, this is a bad example!)
And note that rare events do frequently happen around the world, such as people winning the lottery or getting struck by lightning. However, the media will typically actively seek out the stories of the lottery winners and actively ignore the millions of other people who’d also played but didn’t at least break even. That’s a massive skew or bias in reporting! This skew makes irrational risk-takers (of all kinds e.g. bankers and businesspeople who take overly-risky gambles) seem special when by far in most cases these types of people are not special – these relatively few individuals who win are just exceptionally lucky and that’s all; not skilled. For the media to focus on those who got exceptionally lucky is just like focusing mainly on the dice that rolled a six and ignoring all the (many more) others that didn’t, and then calling those dice that rolled a six special. This is not to say that business or investment requires no skill but luck is a key factor that often gets neglected. For sure though, there’s no skill involved in picking winning lottery numbers whatsoever if the game is fair.
Likewise, with people who get struck by lightning, they’re just exceptionally unlucky. When there are a lot of gamblers or lightning strikes, statistically one or two people will win or get struck now and again, but there’s nothing to read into these individuals – it’s just statistics and chance. (Well I guess avoiding being struck by lightning could be said to involve some skill, such as doing one’s best to not be a prominent electrical conductor when there’s a thunderstorm – but I’ll let others argue about the technicalities of how lightning picks its targets and paths.)
Media reporting, however, generally doesn’t care for accounting for statistical chance – it often just focuses on the unusual cases precisely because they’re unusual cases, rather than those cases that are more representative of the norm, and then seeks to find out what caused those cases to be ‘special’. We can sometimes learn something from unusual cases but we will logically learn more from more usual cases (e.g. that if you play casino games against a house, you’re going to likely overall lose in the long run, hence if some skill is involved – it’s the skill of choosing not to play these games in the first place!)
Another thing is that only the successful fund managers will typically wish to publicise themselves, whilst the losers in the game will typically want to keep their losses discreet to protect their reputations, hence a kind of ‘reporting bias’ again. Those with the lucky streaks (and statistically there’ll be a few by pure chance alone, like rolling a long string of sixes in a row) will be hailed as ‘rock star fund managers’, who’ll then be entrusted with even greater amounts of money, until they eventually end up losing a lot of other people’s money because their funds crash for the high risks they take. When experience is no guarantee of future performance, it’s not predominantly down to skill! Those who believe it is are basically behaving emotionally and irrationally.
Do also recognise the logic that for every stock market trader who bought low, another trader has just sold low; and for every trader who sold high, another has just bought high i.e. for every winner there is a loser; broadly speaking. So stock market traders, when averaged out, don’t have any special skills in predicting the future compared to chance. Investors can indeed help companies to carry out their projects by investing in them in return for shares. Regardless, value in the economy is ultimately generated elsewhere i.e. by those who actually create, invent, discover, extract or process things, not just merely swap things. There’d simply be nothing worth swapping (trading or investing in) without them! Portfolio optimisation involves diversification, and if one has a low risk appetite then one can get steady gains based on mirroring the health of the economy overall, which tends to steadily rise in the incredibly long-term.
So I hope you question results and patterns and wonder if variables are independent or dependent, and query whether any apparent ‘outlier’ outcomes are truly that amazing or can just be simply explained by the probabilities.