1. Group A more likely to do X than Group B:
MY BRAIN: my mind interprets this as “A group is always doing this, while B group never does this.” I falsely assume that men are always dying on the job, women are always getting paid less, educated people all voted for Hillary (while the less educated voted for Trump), etc. But these sorts of natural mental jumps from 51% to 100% and from “more likely” to “this only happens to this group and not this other group” lead to quick stereotypes that are grossly inaccurate/ incomplete.
MATH: All these sorts of statistics actually mean is “there is a statistically significant difference between these two groups according to one study/ poll.” This does not give me a lot of information. Group A could be 5% more likely to do X, or 100,000% more likely to do X. That’s a pretty big range.
CONCLUSIONS: when statistics say something like this, I will either look up the details of the study to better understand what is actually going on or avoid repeating it to others.
This also applies to things like “the majority of people believe X” but to a lesser extent. That statistic still makes you assume “basically everyone believes that” even when it’s just a 51% majority- which any poker player will tell you is “basically a coin flip.” But this is not potentially as enormously misleading as “Group A is more likely than Group B to do X.” Because with the majority you at least narrow it down between 51% and 100%, while with Group A > Group B, you only know that it is between 0.0001% more likely (approximately) and INFINITELY more likely.
2. This Organization- blah blah blah- Some Big Amount of $$:
MY BRAIN: Wow, I could buy a lot with that money! Therefore, that government/ corporation/ institution is corrupt/ rich/ incompetent/ wasteful.
MATH: Organizations function differently than people, and when we instinctively compare “what we would personally do with X amount of $$s” with “what an institution does with such $$” we are comparing apples to oranges- or apples to “baskets of apples.” Replacing the federal government/ Exxon Mobil with you personally buying THOUSANDS UPON THOUSANDS of luxury Caribbean Cruises and Russian space vacations is not really a possibility here.
CONCLUSIONS: Numbers referencing large populations that we instinctively analyze from an individual/ small tribe perspective are often misleading UNLESS they are presented with a host of other relevant statistics. Knowing that the US Federal Government received about $3.3 trillion in revenue in 2016 starts to become much more useful when examined in tandem with other American statistics regarding federal expenditures, total population, labor force participation, personal income, etc.
This obviously applies to other numbers besides money that are presented alone without context for the purpose of producing shock or outrage. Statistics regarding violent crime, poverty, and unemployment are common examples.
3. Our economic growth rate/ mortality rate/ crime rate is “out of control” or “expanding rapidly” or “unbelievably high.”
Context free, non-mathematical terms such as these are useful when describing a swarm of approaching bees to fellow tribe members or a horde of the undead in a poorly written fantasy novel. However, their lack of specificity is not useful or informative when describing any measurable event in the 21st Century, and therefore should be avoided by people who don’t want to sound stupid.
That’s all I have to say about that.