Distributions, curves and statistics

Distributions and curves are some the most common statistical topics that you will use in electrophysiology analysis. Most statistics implicitly or explicitly use distributions. Distributions and curves help us model data. Modeling data helps us describe the data we have and simplify complex data. While this may sound complex or intimidating it is not. A simple linear regression is a model that is both a distribution and a curve. Distributions of our data are a model. Curve fitting is modeling. We have used these models in both the current clamp and mini analysis chapters but we will go more in-depth here to describe some of the underlying properties. Modeling can be divided into what, how and why models (see: https://compneuro.neuromatch.io/tutorials/intro.html for more). We will primarily focus on what models since these are the first step to using the other types of models. I rarely see what models discussed in patch clamp electrophysiology analysis, however I believe they are needed to analyze our data well. Lastly, this section will cover some statistical tests that you should use including heirarchical mixed models in R. In this next section we will cover distributions, curves and statistical tests. One thing to note is that some of the statistical testing (heirachical mixed models) will be covered using R. R is a statistical language which means it has the biggest breadth of stats packages and some very niche packages. Python has a decent statistical package (StatsModels) but really lacks a good heirarchical mixed model. The stastical testing we will cover is going to be frequentist. Python actually has a very good Bayesian statistics ecosystem which we will not cover here.

One thing I have noticed is that scientists are often criticized for using statistics poorly or incorrectly which I agree with. However, I have yet to have a stastics class that has been taught well. There two sides to this. I do think to many scientists are not interested in furthering their analytic skills and I think that there are very few good resources for learning statistics. I believe in a top down approach. Start with how to do things at surface level and then start to dive into the deeper levels. This section is an attempt at teaching statistics in a way that I believe is more useful that what we are typically taught.