There is no escaping it, you are going to have to know some stat stuff. Every now and then I will through in a blog post to cover some of this, its good for me to attempt to brain dump it, and its good for you to try and assimilate it. Nothing is going to make sense without it. It only hurts a little bit and I am going to try and give as many samples as possible and break down each concept as much as I possibly can. In the end you will be grateful for software, but stats came from long hand math calculations and have formulas that look like they could single handledly put a rocket in space.
If you are a RDBMS gal or guy some of the definitions will seem wonky, and if you are talking to an academic this will be the first communication breakdown, hopefully this will help.
Lets get some definitions out of the way, these are critical, it does not mean you need to question the lingo you use on a daily basis, but if you hear it from you statisticians or DS folks, make sure you are on the same page.
Population – A population is ALL THE DATA. As a data guy I lived in a world where if we were trying to make a decision we used all the data, this is why we had SQL performance problems, our customers sucked at statistics and did not know there was a way to sample a data set. That being said, i also would not like to check my bank account balance based on a sample. So, when you see a population referenced that means the entire data, all of it. If I am using a population of the United States, that means I am using all 330 million or so people in the US for my research. In Statistics, it is denoted as an uppercase N.
Census – A census is a study of EVERYTHING in a given population. Most countries have a census. One of the more popular results of the census is the American Community Survey, it frequently provides great statistical training and research material.
Sample – A sample is as it sounds, it’s a sample of a population, hence not all the data. There are sub-classes of samples we will get into later. But for now know that a sample is a portion of a population. In Statistics, it is denoted as an lowercase n.
Parameter – A parameter is a numerical quantity that tells us something about the population, such as quantity of a specific ethnicity, number high school graduates, proportion of singles. Do not confuse this with a numeric quantity of sample, that is called a statistic. Ah ha!
Variable – A variable in statistics is what most SQL Folks, me included call a column, there is a very long definition, they contain anything that describe a characterization, qualitative and quantitative.
Case – A case in statistics is a single row of data. You can imagine that if you have a patient, all of the columns(variables) will make up the data for that patient, hence it is called a case. So, if you hear this outside of academia see if they are discussing a row, or something else entirely. Usually, this terminology references something sciencey, less so outside of medical research or scientific fields. I have never heard a row of banking data referred to as a case.
Data – Plural for of data. Some get bent out of shape over the use of this, I find them more annoying than the usage, I mean its not like I am using there their they’re incorrectly.
Datum – Singular form of data.
Qualitative Data – In many respects this is an easy one, if its not Quantitative its probably Qualitative, another more familiar name for it is categorical or, a category. Categorical data is defined as which? Which color, which model of, which dog breed, which grade are you in.
If you recall, looking at the dataset we used for the Florida education choropleth you will recall that there was a variable called ruralurbancontinuum , though it was a number it was used as a categorical value. The values of this field are 1-9 and related to a category of population density used US wide. In this case no math could be done gainst the value even though it is a number, the Census could just have easily used A-I instead of 1-9.
Quantitative Data – This one is pretty easy if you remember that you can do math on a quantitative variable. Its is always a number. It can be my height, my weight, my pulse rate, the money in my checking account, my shoe size. If I have population or sample of these items I can average them, get a standard deviation etc. The word quantitative has a root of quantity, that should help you remember it.
To go a little bit deeper into the rabbit whole there are two types of Quantitative data, I know, I’m sorry… Hopefully looking at the root word of each will help.
Quantitative Discreet – Counting data. They ask How Many?
How many people on a bus?
-There are 20 people on the bus, not 19.5 or 20.5.
How many cars in my driveway?
-There are 2 cars in my driveway and one in the yard, though most of that on is missing it is still one car.
How many books do you own?
-I own 100 books, not 99.5, though an argument could be made for owning half a book, it is still one registered ISBN even if you do not have all of the book.
How many emails did you get to day?
-I received 50 emails today.
Quantitative Continuous – Measuring data, this asks How Much?
What is your height?
What is your weight?
What is the weight of a vehicle?
What ii the MPG of a vehicle?
The following sources help with statistics, FOR FREE
Khan academy of course, as well as;
Introductory Statistic, OpenStax
Australian Bureau of Statistics, Go figure, their definitions are too the point