Re: chi-square test goodness of fit

From: D. Touie (dtouie_at_tscnet.com)
Date: 12/27/04 

Date: Mon, 27 Dec 2004 10:06:37 GMT

On Sun, 26 Dec 2004 21:08:27 -0500, Richard Ulrich
<Rich.Ulrich@comcast.net> wrote:

>On Sat, 25 Dec 2004 03:05:20 GMT, D. Touie <dtouie@tscnet.com> wrote:

UR
This note was written so strangely that it is hard to respond to.

It seems to be a response to my note, but it deleted 100%
of my words, while saving what I quoted -- I have replaced
what I quoted, with what I replied.

DT
Yes, I did delete your words. I was probably tired. Seen now in pure
message isolation it seems odd to me too.

UR
Also, what D. Touie is describing seems confused to me.

<snip>

DT
> I did do some due diligence research before posting my "complaint."
>
> Left over from the dozen or so statistics texts I used to keep on
> hand, I have two basic books left. Both have Chi-square probability
> transformation tables. One reads from right-to-left, the other
> left-to-right.

UR
"Transformation tables"? Okay, not necessarily distribution tables.

DT
For me the tables serve the primary purpose of transforming
(converting?) accumulated chi-square sums into probability amounts. Of
course the table are based on the chi-square distribution so they
could also be termed distribution tables.

UR
I don't understand right-to-left and left-to-right, but that
sounds like opposite approaches.

DT
They both express the same relationship between accumulated chi-square
sums and their probability amounts. They merely do it in opposite
directions on their pages.

DT
> I also consulted my nearly new TI-89 Titanium calculator. It
> Chi-square functions work as "cumulative distribution functions"
> rather than as tables. It produces the same probability
> transformations as my two basic book tables.

UR
Confusion? Aren't the two books different?
TI-89 gives a label of "cumulative distribution function"
and yet, approaches zero for large values?

DT
As I hope you can see by now, my book tables and my TI-89 evaluate
larger chi-square sums as higher probability amounts. This is opposite
what Excel does, and what you suggest is proper practice.

> Since I posted my "complaint," I thought of a simple experiment. I
> tried it out this morning in my Excel work***. I entered 10 made-up
> coin-flipping results into 2 two-bin Chi-square vectors. In the first
> vector I made all 10 results heads. In the second I made it 5 heads
> and 5 tails. I then evaluated the two vectors with the uncorrected
> Excel "Chidist()" function at 1 degree of freedom.
>
> 10 heads = Near zero probability.
>
> 5 heads & 5 tails = Exactly 1 probability.
>
> Are these the results you non-amateurs expect?

Another poster took me to task about this question. If this Excel
evaluation reflects current proper chi-square distribution tail
direction, my nit pick is the 5 heads & 5 tails probability amount
should be near 1, not exactly 1.

I did some more looking. This time on the Internet. I found four
sites, including NIST's, that plot the chi-square distribution tails
your (and Excel's) way.

My conclusion is I can evaluate either way with impunity. But it does
seem to me that what is proper practice here is wholly dependent on
what authority I rely on.

UR
2) Excel does not appeal to statisticians. It is hard to
use Excel as evidence for proper practice. -- Especially,
considering this --

DT
I used Excel in this instance to do a quick and dirty answer to the
original poster's question.

UR
Jack Tomsky posted an earlier reply to DT's first note,

  "I have found that Excel's rule for the probability tail differs
  according to the distribution. Each time I use it, I have to check
  whether I need to modify their result. "

Surely, even non-statisticians will detect a problem here....

DT
I entirely agree.

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