Lately, I’ve been trying to learn some things about trade, economics, and statistics. Every once in a while when I find myself stuck, I go online to look for help. For several years now, I have made it a habit when researching any particular topic to start with Wikipedia and see if it can help me with basic information and direct me to better sources.
But with these kinds of mathematics-related topics, I’ve found that more often than not, the Wikipedia article goes way over my head and offers nothing that would help me understand and apply basic techniques at a beginner’s level.
For example, these articles –
I find that doing searches for professor’s lectures and other basic course materials are much more helpful in learning basic principles and how to apply them.
But I have this idea that a Wikipedia article about scientific or mathematical subjects should be more like a basic introductory textbook or class lecture. Otherwise, who’s it for?
I find Wikipedia to be a godsend at times. When it comes to advanced mathematics, a good many authors write so cryptically it’s damn near impossible to figure out what they’re trying to say. My feeling is that when professors write a math textbook, they’re trying to impress other professors with their knowledge, and don’t have the potential student in mind at all.
There have been many times where I’ve tried to decipher WTF the author is talking about, then I look it up on Wiki to find that the subject is described in plain English. Well, to me, a math grad student, that is.
ETA: The topics you list aren’t beginning topics. These are things that would most likely be introduced in a second stats course. Not sure if that helps, but I thought I’d mention it.
I suspect that this is one of those areas where it would be hard write an article that would satisfy both the person starting on the topic and the grad student who just wants to be reminded abut the details.
There is one online specialist encyclopedia that I’ve found very useful: Wolfram Mathworld. Its articles are often at an easier level than Wikipedia’s – though it still won’t be elementary enough for many users.
Yeah, this is a real problem with Wikipedia. Technical articles are usually, well, too technical. New article authors want to get all the cool stuff down, and worry about the intuitive explanations (which are usually harder to write!) later. Most of the time, this never happens, though.
I only looked at the article on regression but I thought it was a good overview.
The problem with trying to make a topic like that simple is that it isn’t simple.
It’s certainly not an extremely advanced subject but unless you have sufficient background you’re just not going to understand it. I like to think of math as a language in some ways. I can count to 10 in German but that doesn’t make me ready to study a treatise on the Bauhaus movement in it’s original German – I’m just not equipped to handle it. Math is similar in that a strong understanding of the underlying concepts is required to move forward confidently, you can’t just skip over a couple years of study and expect to jump in and understand.
I agree, Wikipedia is not usually the best place to go to understand a mathematical topic.
I think part of the problem is that Wikipedia is about presenting information, whereas you’re looking for explanation.
And part of the problem is, as others have noted, that a description that is correct and complete enough to satisfy someone who already knows something about the topic is going to be over the head of a beginner.
And in some cases, part of the problem is that the people who understand a topic well enough to write a Wikipedia article about it aren’t necessarily good at describing or explaining it to someone who doesn’t already understand it.
I am a high school math teacher. I can testify that I teach regression, coefficient of regression, and confidence intervals in my statistics class. I first learned those things during my high school statistics class and covered them again as a freshman in college.
Mathematical topics are presented to students in a certain order because the human mind functions in certain ways, and finds certain things easier to understand than others. In the case of the three things that the OP linked to, we always begin by teaching them as they apply to a linear regression model and then advance from there to other statistical models. Trying to introduce those things by presenting the most general case is a recipe for failure.
Here’s my opinion, which is not necessarily shared by every sentient being in the universe. Wikipedia looks like a collection of webpages written piecemeal by anonymous internet users without any attempt at consistency, meaningful standards, or editorial control. Which is no surprise because that’s what it is. Some Wikipedia articles are correct and useful. Some are technically correct but so poorly written and poorly organized that they’re useless. Many are just plain wrong. There are other websites for mathematics that do a better job, such as Wolfram (already linked by Giles), but they still leave a lot to be desired. If you truly want to learn statistics or any other branch of mathematics, forget the internet and start reading books. If you go to the bookstore you can find plenty of books that are above the For Dummies level but below a college textbook. That’s where you’ll find well-written explanations of these things.
I should have written that better. I didn’t mean to imply that these are advanced topics, just that they aren’t the first things taught in a statistics class. I was first introduced to these topics during the second quarter of a two-quarter Intro to Statistics sequence, that’s all I meant by a “second stats course.”
Honestly, if what you’re looking for is a quick overview of a great many mathematical and statistical topics, it’s hard to do better than Wikipedia; many of its editors really do know their stuff. But to provide a tabula rasa introduction to every topic is too much to expect and, frankly, wouldn’t really be in keeping with the goals of Wikipedia (to serve as an encyclopedia).
For instance, there’s just no way to explain in detail what a confidence interval is to someone who doesn’t (at least) have some idea of basic statistics and probability – random variables, mean, variance, preferably normal approximations. And there’s probably not a whole lot of value in telling someone what a confidence interval is until they know that stuff.
Eh. Your general notions of the overall value of Wikipedia are showing. Although allowing anyone to edit articles has risks, many of the (relevant) editors are working mathematicians, and I’ve found the rate of actual errors to be very low. Additionally, Wikipedia usually gives a much broader amount of information on a particular topic than MathWorld (which often goes too far in the opposite direction than that desired by the OP).
More along the lines of advice to the OP: you’re doing exactly what I’ve found most helpful (searching for course lecture notes). One thing I like to do is do a google search something like “probable-course-name syllabus”, to get recommended readings and find course websites. Blackboard is a horrible, horrible development for the autodidact.
But there’s probably no better way to get acquainted with these topics than slogging few a couple textbooks. Schaums guides are cheap and practical; they have beginning statistics and econometrics books which would probably get you to the point where you could easily understand materials you find around the net, such as Wikipedia. If you’re really serious about economics and statistics, I’d recommend some calculus as well, because you’ll be coming up on that rather quickly.
These topics were all topics in a ridiculously easy stats course I took in high school. I would definitely call them beginning topics (after the super basic stuff that everyone covers in middle school.)
I hope ITR champion won’t disagree with me when I add that, if you truly want to learn statistics or any other branch of mathematics, you have to do more than read; you have to do the exercises, work things out for yourself.
For some highly technical subjects, Wikipedia does have a simpler version. If you are having a problem understanding a particular entry, you can look at the language list to see if there is an option for “Simple English”
But, since it’s goal is to be an encyclopedia, it should be. The point of an article is not to satisfy the people who already understand the topic.
The actual reason for the overly technical articles is that they require you to provide sources the easier explanations–and those are hard to find. They’ve recently created an expert program that will let some certified experts do it, but not many know about it, and it is the rare expert that is good at dumbing down their expertise.
And, no, it’s not hard to write an article that is good for the layman and the professional. You just have multiple sections.
I had to do this to prep for business school (actually, I had to do it to apply). I just signed up for courses at UCLA extension. If you have the discipline, you could probably just buy yourself some textbooks.
The internet stuff was sort of incomprehensible except for econ.
