I’m never going to know the answer.
My laziness means I have to give up on getting facts or certainty, but hopefully I’ll end up with something that still reasonably helpful for making a decision.
I could still turn it into a reasonable action.
That is what the discipline of statistics is all about.
Something out of nothing?Some of you are hoping I’ll say, “With this magic formula, you can make certainty out of uncertainty!” No, of course not.
There’s no magic that makes something out of nothing.
When we don’t have facts, all we can hope for is combining data with assumptions to make reasonable decisions.
HypothesisA hypothesis is a description about how the universe might look, but it doesn’t have to be true.
We’ll be figuring out whether our sample makes our hypothesis look ridiculous to determine whether we should change our minds, but that wanders outside the scope of this blog post — pick up the thread here.
Here I am, uttering some uninformed garbage like “The true average height of all the trees is less than 20 meters.
” That’s a hypothesis.
You know the truth (I’m wrong!) because you’re omniscient in this example …but I don’t know anything.
My statement is a perfectly valid hypothesis, describing how reality might potentially look.
I’ll see how I feel about it after I get some data.
EstimateIf we knew the parameter, we’d be home right now.
It’s the fact that we’re looking for, but unfortunately facts are not always available.
Since we cannot compute the parameter, we can only make a best guess about it using a statistic.
An estimate is just a fancy word for best guess.
An estimate is just a fancy word for best guess about the true value of a parameter.
Let me show you that you are ready amazing at statistical estimation.
Ready?Let’s suppose that all you know is that one of the trees is 23m tall.
Can you please tell me your estimate for the true average height of all the trees?23m?.Yeah, me too!We’d have to guess 23m if this is our only information — if we guess anything else, we’re just makin’ stuff up.
23m is all we know, so we have to guess 23m.
To get something else, we’d have to be incorporating more information (which we don’t have in this example) or we’d have to make assumptions… at which point we’re again dealing with something other than facts.
All right, let’s try another one!.Say we have a sample and all we know about it is that it’s got an average of 22.
5m for the height.
What’s your best guess now?22.
5m?.Wow!.You’re so good at this!.You don’t even need a course!Here’s the punchline of several textbook chapters’ worth of statistics covering method of moments estimation, maximum likelihood estimation, and all their cousins: It turns out that the answer at the end of the proof rainbow is the same answer you just came to intuitively!.In 99%+ of cases you encounter in real life, just treating your sample as if it’s your population and going with whatever’s in it is how you get the best guess.
You don’t need any special courses.
Taa-daa, we’re done!It’s a lie that you always need statistics; you don’t.
If you’re just trying to make a best guess to get inspired, analytics is the best option for you.
Shrug off those p-values, you don’t need the unnecessary stress.
Instead, you can choose to live by these principles: More (relevant) data is better and your intuition is pretty good for making best guesses, but not for knowing how good those guesses are… so stay humble.
However, don’t for a moment think I’m bashing my discipline.
I’ve devoted over a decade to studying statistics and I like to think I’m not completely crazy.
When taking a statistical approach is useful, it’s very useful.
So when do you actually need it?.When will it prevent you from hurting yourself?.Read my “What’s the point of statistics?” to find out…Learn more about the difference between the subdisciplines in data science here.