Are you confused about the meaning of ‘statistic’ in statistics?
You’re not alone. Many blogs and posts on the internet use the term loosely.
In statistics, a statistic is defined at a sample level, whereas a parameter is defined at a population level. To estimate the parameter, we use a statistic.
One of the mental models that I use to get these concepts right is to think of these concepts in the form of Matryoshka dolls (a.k.a Russian nested dolls).
Please note that barring the first doll (Population and sample), I don’t intend to showcase them in a way that one is smaller than the other.
Rather I would want the readers to see the emphasis on identical nature of the dolls.
Why focus on that ?
Well lets start with the first doll (Population-Sample). To me this image clearly conveys the point that the sample is representative of the population.
This is very important because only when your sample is representative of the population, you can make inferences that generalizes at the population level.
Once your sample is representative of the population, you can then try to estimate your population parameter through the sample statistic.
For example you can estimate your population mean through sample mean.
Further this Matryoshka doll mental model also would allow you to see the statistical model and ML models from a new perspective.
For example, these dolls help me think that the model (small doll) is an abstraction of reality (the bigger doll).
If your model is well specified, it will look more like the reality you are trying to model.
This could be Marketing Mix model trying to capture the marketing reality or any model trying to abstract the reality.
