chi-squared - philosophy styles - straight up

[th!nkstyle]

alright, I seem to be one of the ones that like s to bring up the topic of how rediculous it is that people accept math at face value; here is the latest.

This one is a competition per se. What is YOUR definition of what Chi-squared really is. Don't copy paste things from wikipedia or anything, if you really get it, skip the jargan, and give it to people straight up.

My question for now is: as the degrees of freedom increases, the Chi-squared tends to look more and more like a t-test graph. what is the relation here? Secondly- is there a relation between the peak of chi-squared and the inflecion point on a normal graph?

Why can no source tell this shit straight up? Everyone always hides behind "intelectual definitions" and half understandings.

Likewise if you sort of understand it, but not quite, feel free to reply to this thread stating whatever!

word out.

[Misazeno]

This is the part where I ball my eyes out and cry about how I don't know anything about what your talking about...

:cry: :cry: :cry: :cry: :cry:

[Pooja]

the chi-square test is a sort of "litmus test" in stats needed to see if you should rejuct or accept the null hypothesis... Generally, if you're able to show that the null hypothesis has less than a 5% chance of being 'correct', then you can reject it.
About the deg.s of freedom... isn't the formula for that (1-#of rows)*(1-# of columns)?

[Hypnos]

This one is a competition per se. What is YOUR definition of what Chi-squared really is. Don't copy paste things from wikipedia or anything, if you really get it, skip the jargan, and give it to people straight up.
I don't understand the entirety of your post, but I can tell you how I use the chi-squared test in the context of my work: it is a positive-definite figure of merit for how far away from the hypothesized behavior a data sample is, weighted by the spread due to sampling and measurement error. If the underlying process is not normally distributed (e.g., small numbers), it becomes more heuristic.


My question for now is: as the degrees of freedom increases, the Chi-squared tends to look more and more like a t-test graph. what is the relation here? Secondly- is there a relation between the peak of chi-squared and the inflecion point on a normal graph?
Well, both the chi-squared and t-test distributions approach the normal distribution, though the chi-squared does very slowly. No deep connection between the two is required. Any normalizable distribution (goes to zero at +/- infinity, positive) will be dominated by the first odd moment (the mean) and the first even central moment (the variance) as the sample size/# of trials increase. The picture is of stuff piling up: stuff in the middle will increasingly dwarf over stuff at the tails.

If I am wrong or off-base, I'd like to know, for work.

[th!nkstyle]

Let me rephrase myself.

I know how to use it, and even when to use it. im more interested in the essence of what it really means. for example: why is it not scewed the other way? what is the significance of the peak of chi squared? why does the peak more to the right as the sample gets bigger? I am looking for "deeper" analysis. why is it used to test the null? Why exactly does it represent something that is random? What is the exact relation between chi squared and the essence of variance? etc etc.

Basically anything that is NOT discussed in most stats book would be very interesting, for Ive read a bunch, but am looking to reasure my inutititve understanding, which i ofen can not really explain in words, nor in math.

[Hypnos]

So take one variable distributed normally. What is the distribution of Y^2? You can imagine taking all the samples from the Gaussian and squaring them, then seeing where they fall -- you get something like a decaying exponential with a sharp peak at x=0. Indeed, if you calculate it with a delta function, that's what you get.

Now let's take the sum of two copies of Y^2. First you, expect the peak away from 0 and some spread, as the Y for one Y^2 doesn't have to be the same as Y from the other.

Repeat ad infinitum, and you get a Gaussian with a mean at x=r, where r is a really large number of degrees of freedom, for the reason I described in my last post.

Your two questions: why does this test the null hypothesis, and why does this say about variance? On the latter, i think the picture I paint above works. For the null hypothesis, it's because you expect your measurements to be independent and repeatable between different experimental parameters, and for these independent measurements to approach a normal distribution after many trials with mean given by physical law.

[Star Cannon]

I think you both just lost the contest. I couldn't understand ANYthing you just said.
So, uh, factor labeling any one?

[th!nkstyle]

So take one variable distributed normally. What is the distribution of Y^2? You can imagine taking all the samples from the Gaussian and squaring them, then seeing where they fall -- you get something like a decaying exponential with a sharp peak at x=0. Indeed, if you calculate it with a delta function, that's what you get.

Now let's take the sum of two copies of Y^2. First you, expect the peak away from 0 and some spread, as the Y for one Y^2 doesn't have to be the same as Y from the other.

Repeat ad infinitum, and you get a Gaussian with a mean at x=r, where r is a really large number of degrees of freedom, for the reason I described in my last post.

Your two questions: why does this test the null hypothesis, and why does this say about variance? On the latter, i think the picture I paint above works. For the null hypothesis, it's because you expect your measurements to be independent and repeatable between different experimental parameters, and for these independent measurements to approach a normal distribution after many trials with mean given by physical law.

individually most sentances make sense, as a whole you lost me (or at least didnt convince me). im sure there is an easier way to explain this with terms that anyone that hasnt even taken a stats course in university could still understand... or maybe i am being optimistic?