# Statistics summarized Unlike [calculus](math-calc.md), which represents the highest form of abstraction, statistics most closely resembles reality. - All [natural phenomena](reality.md) ends up clustering in statistical patterns, with a heavy centralized grouping and unlikely instances moving outward from all measurements on a bell curve. This means statistics is probably the most useful form of math possible for most advanced applications, and can track the following: - How far someone can throw a ball - A rocket's likely trajectory - Radioactive chemicals' half-life - [Social trends](people-trends.md) - How we change [habits](habits.md) - How we [make decisions](mind-decisions.md) when we are [in groups](groups-member.md) ## How statistics are gathered Statistics is a relatively simple concept: 1. Find many similar things to measure (e.g., a population of people). 2. There's usually a *ton* of those things, so figure out how many of that thing to measure to give it [scientific rigor](science.md) without wasting too much time or money on it. 3. Pile up that information until it shows a bell curve across a numbered range. 4. Calculate the center of that bell curve, then determine where most of those things sit from that center, which is the "standard deviation". A standard deviation (σ, or sigma) can be low or high, and determines how spread-out the samples sit from the average. In a normal distribution you can expect a few numbers to arise: - 1 standard deviation will cover ~68% of the values (~34% on each side of the bell curve) - 2 standard deviations will cover ~95% of the values - 3 standard deviations will cover ~99.7%. ## Statistics vs. perception Normally, we interpret [certainty](understanding-certainty.md) in our minds through convictions grounded in [experiences](understanding.md). Statistical systems, however, create an anomaly to that mode of reasoning: 1. Gathering statistics requires heaping up [stories](stories-why.md), but only for specific and measurable elements of those many, many stories, without any consideration of other things that aren't being measured. 2. All [analysis](logic.md) derived from the results can't naturally regard the qualitative experiences that were trimmed during collection. 3. Since we all need stories to [understand](understanding.md) reality, most statisticians easily interpret cause-and-effect through correlation. ## Statistics for decisions Statistics are tracking reality, and reality is [uncertain](understanding-certainty.md), so all statistics are always a little uncertain. - They're alarmingly accurate (when measured correctly) at determining correlation, but only in a broad sense. Statistics, however, can *only* demonstrate correlation. Any causation only comes through how the information is [interpreted](stories-why.md): - People in the 1980s who ate hot breakfasts more often than cold were dramatically more likely to have Alzheimer's Disease. We [tend](habits.md) to eat what we ate when we were kids, and cold cereal took off in [popularity](people-trends.md) in the 1950s. - Crime statistics *always* go up when cities expand their police forces. Technically, crime statistics are only measuring *caught* crimes. - The [culture](people-culture.md) of most of the world aligns with anthropology studies of the West, representative by data. Most anthropology data is gathered near Western universities. - People who saw the 1984 Ghostbusters movie are more likely to die than people who saw the 2021 Ghostbusters movie. This is simply because of age-related facts. APPLICATION: A statistical report is a statement of curated observations and is as trustworthy as the [group](groups-small.md) it came from. There's lots of [money and power](power.md) if someone can [prove](influence.md) they're not biased (which isn't [possible](mind-bias.md)), so the people who create statistics often [have something to lose](power-types.md) by stating that they're not precisely accurate. Statistics don't fit our [intuition](mind-feelings.md) for a few core reasons: - When there are different sample sizes from different groups (e.g., populations of various districts in a country), the less-populated groups are *guaranteed* to have more high/low extremes, simply from having fewer numbers. - Observing statistical anomalies (e.g., very unusual height) creates more engaging [stories](stories-why.md) and spurs the [imagination](mind-imagination.md), and it requires training to *not* [feel](mind-feelings.md) the outliers more than the norm. - Possessing information on a chart doesn't explain anything directly. It indicates a connection, but that connection has to [stay unknown](unknown.md) for us to be accurate, and [we *hate* not knowing](purpose.md). - When we experience the [possibility](mind-imagination.md) of a [risk](safety.md), we only [feel](mind-feelings.md) comfortable when its chances become 0%. For that reason, we tend to obsess about the smaller risks (which can theoretically be eliminated) at the opportunity cost of managing the larger ones. - Over time, statistical things [trend](people-trends.md) back to normal from extremes (e.g., high-performing athletes, extremely depressed people). Without measuring what normally happens, we can imagine that a statistical change was caused *by* a measured element included in it. ## Statistics for influencing When we hear a statistical result, it takes lots of training to *not* inserting our [explanation](logic.md) on the [causes or effects](stories-why.md) of the information. Our only hope to gain full [understanding](understanding.md) lies in forced [uncertainty](understanding-certainty.md), which requires directing our thoughts toward the specific [purpose](purpose.md) of suspending judgment, which requires tremendous effort to maintain. APPLICATION: We can never expect something to go *precisely* how we envision it because we always gain 1 sample of a statistical range at any given time. All we can do is [change our statistical likelihoods](success-2_attitude.md) whenever possible. Very frequently, statistics [hide lies](people-image-distortion.md) by making the statistician appear more credible. The value of the statistical [analysis](logic.md) comes from the [value](creations.md) of the raw data, which comes from the [quality](values-quality.md) of the data collection. APPLICATION: Claiming statistical analysis is immaculate requires faith in a [community's](groups-member.md) collective [understanding](understanding.md). Nothing is all/nothing, but statistics provide the opportunity to make a clear [story](stories-why.md) of reality, even if it's not precise. However, most [younger people](maturity.md) can be [influenced](influence.md) to [believe](understanding-certainty.md) statistics more than its truth.