As a field of study, Statistics is essentially the study of how to make sense of data. It is full of formal, quantitative methods for dealing with uncertainty. There are fundamental questions that a successful analysis should touch upon. What do we know (the data)? What do we expect (our assumptions)? What should we expect given what we know (what does the data look like)? How does what we know affect the validity of the assumptions about what we expect (do the data seem excessively implausible given our assumptions)? The goal typically takes the form of setting up a fall guy (or gal) named Null Hypothesis and checking to see whether you can knock him (or her) down with your data. Traditionally, the null hypothesis is the enemy. If you are a drug company, the null hypothesis is that your drug is worthless (compared to the current standard of treatment).
On a structurally similar but less formal level, we’re all statisticians. We all compute our own personal statistics on a daily basis, using incredibly biased data derived from our muddled thoughts and our 5 senses. For instance, when I look myself over before I leave the house in the morning, I implicitly create an average rating of my appearance based on any number of specific observable data points. How’s my hair (when I have hair)? Are my teeth still crooked? Is my forehead doing that flaky, dry skin thing? Is my shirt suitably ironed? Does this stomach fat make it look like I have stomach fat?
All these things are weighted by importance and aggregated to create an overall “this is how I look” score. I then take this score and compare it to a null hypothesis about my appearance. My personal appearance null is usually “I look good” and I’m perfectly happy not knocking it down at all. Choosing a null for your personal appearance is a complicated process that incorporates your current state of mind and whole slew of conscious and unconscious thoughts based on a lifetime’s worth of accumulated experience.
So my perception of my appearance is my data. I use it to create an overall “this is how I look score”, which is then compared to what I’d expect the score to be if I looked okay (my null). This process is very sensitive to outliers. So if I looked like this guy, except that I had a giant, bulbous blister on my forehead, that blister would likely dominate my “this is how I look” score despite being a small, atypical portion of an otherwise magnificent package and I’d probably reject the null hypothesis that I look good.
The results of my personal appearance test have ramifications. Whether I decide that I look okay or not will partially determine how I interact with the world with me. It will inform my interactions with other people. During these interactions, I will be subconsciously gathering and aggregating more data and performing more informal statistical tests: Is this person listening to me? Do they understand what I’m talking about, or am I completely incoherent? Was that joke I told actually funny or was that laugh just a polite acknowledgment of attempted comedy? For each of these questions, I’d compare the person’s behavior (the data) with how I’d expect them to behave (the null) and draw conclusions accordingly.
If I feel especially dashing, then perhaps I’m slightly more apt to feel confident in my interactions with other people and this confidence can result in more positive ad hoc estimates of how well these interactions are going. These ad hoc estimates are data points that go into a running calculation of how well my day is going.
At the end of the day, I have all these internal data points describing the quality of my day. These too are then aggregated into a relative rating describing the overall quality of my day. If the average quality of my day seems especially good or bad (compared to my expectations), I might spend some time going through the data trying to figure out whether there was a specific event that made my day especially good or bad. Or, I’ll probably be asleep within moments of laying down.
I bet you do this too.
A lot of the time, this process is completely subconscious. One interesting thing you can do is try and figure out what your null hypotheses are and how they got to be that way. It can be enlightening to see how much of an effect things that happened ages ago can have in providing context for the decisions you make now.