# Talk:Introduction to statistics

## Experiments, Outcomes and Events - difficult to understand if not already familiar with symbols

It would be nice if each symbol could be named, or a reference to the name could be provided. I managed to find omega right away, but the other symbols (the ${\displaystyle \cup }$ symbol and the ${\displaystyle \cap }$ symbol, for example) were difficult because they are represented graphically when vieweing the page (not in edit mode).

Additionally, it would be good to narrate each equation. For example:

${\displaystyle N(A\cup B)=N(A)+N(B)}$

Could be narrated as:

"The number of times A union B occurs equals the number of times A occurs plus the number of times B occurs."

Despite the simplicity of this equation, it took me a while to figure out the meaning simply because I am not yet familiar with the ${\displaystyle \cup }$ symbol.

Despite these criticisms, I find this page to be well written and extremely useful. I would just like to see it updated for dummies like me :-).

--Jimmytharpe 19:04, 19 January 2007 (UTC)

to Introduction to statistics -- Jtneill - Talk 05:02, 18 March 2008 (UTC)

Are courses that are more than just a module or project in the themselves like proper titles that should be capitalized? [1] [2] In my experience the course titles that I see are usually capitalized. I'm not sure we have built consensus around this specifically, unless it falls under the umbrella of what exists at Wikiversity:Naming_conventions. There seems to be inconsistency at Category:Introductions for example. --Remi 05:10, 18 March 2008 (UTC)
If you feel there is consensus on the issue, I wouldn't object to it being moved. What do others think/feel about the issue?

## Bayes' Theorem

I think the formula for Bayes' Theorem on this page may be wrong. In the proof, we are given
${\displaystyle P(A\cap B)={\frac {P(A|B)}{P(B)}}}$
However, in the section immediately previous we are given
${\displaystyle P(A|B)={\frac {P(A\cap B)}{P(B)}}}$
This previous statement gives
${\displaystyle P(A\cap B)=P(A|B)P(B)<>{\frac {P(A|B)}{P(B)}}}$
So we have an internal inconsistency.
In addition, the Wikipedia statement of Bayes' is
${\displaystyle P(A|B)={\frac {P(B|A)\,P(A)}{P(B)}}\,\!}$
Which is NOT equivalent to the statement here that
${\displaystyle P(B|A)={\frac {P(A|B)P(A)}{P(B)}}}$
Wikipedia's proof seems internally consistent.

Yeah, reading through this I had to reread through the Bayes' Theorem proof many times because I couldn't figure out why it worked. The answer? The proof is messed up. I have edited the page so that it contains a valid proof 71.222.89.18

The proof of Bayes's Theorem needs to be expanded here, I think. You start off with: ${\displaystyle P(A)=\sum _{n=1}^{k}P(A|B_{n})P(B_{n})}$, but where does this come from? Because ${\displaystyle B_{i}}$ are disjoint, the student can understand that for any one of them, the left-hand side of the conditional probability equation, when the ${\displaystyle P(B)}$ term is brought over to it, matches what you have in the summation. And that, therefore, equals the right-hand ${\displaystyle P(A\cap B)}$ term of conditional probability.

But you haven't explained multiplication of probabilities anywhere in this article. And there is no explanation, within the context of this proof and the Bayes's Theorem section, of the relationship between A and B. Given that the Bayes's Theorem presentation says ${\displaystyle P(B_{i}|A)}$, we can assume that there's an interesection. I'd just like to see more explanation.

Ah...I see that this is a citation of the total law of probability, as shown in the "Extended Form" of Bayes's Theorem on Wikipedia. This is an introductory module. Don't you think you should start off with the basic version of things?

Remember, this is Wiki_versity_, not Wikipedia. The goal is to teach, not cite, right? :)

## Cross links between here and Intro to Statistical Analysis?

I recently created another course on statistics over at Introduction to Statistical Analysis. I was originally going to call it Introduction to Statistics but then discovered this project by the same name. I think both projects are great and actually seem to cover some different ground. Anyways, I just wondered if it was worth maybe adding links between the two, maybe at places where one has additional content building on or explaining the other. Wanted to see what contributors here thought. MyNameWasTaken 16:59, 11 January 2012 (UTC)