CHI Square test and a card shuffler

Hi There,

I was wondering if anyone was willing to help me explain how the chi square test works or knows a really good reference. The wikipedia definition seems a little confusing to me.

This is what I am doing:

I have a card shuffler that shuffles a single deck of cards in random order. I want to check for randomness to make sure that the shuffler is not biased in any way. The RNG is using a KISS RNG, which passes all the DIEHARD battery of tests if you know what those are.

Anyways, I have a spreadsheet with 100 columns and 52 rows, Each Column represents a shuffled deck. So I have 100 test samples. Since the likelyhood of drawing any one particular card is 1/52 then I would expect that card x should appear at the top position approximately 2 times in 100 shuffles, card y should appear at the top position approximately 2 times, etc. (note: I know 100 is extremely small sample size, but its not really reasonable to go over 100 trials)

At this point I do not know how to apply the Chi Square test to determine if my numbers are within acceptable limits.

Can anyone help or point me in the correct direction?

I appreciate it.

A \(\displaystyle {\chi}^{2}\) test is used to test whether a frequency distribution fits an expected distribution.

For example: Suppose a radio station says its listeners music preferences are as follows:

Classical 4%
Country 36%
Gospel 11%
Oldies 2%
Pop 18%
Rock 29%

You test the claim to see whether their claim is true or not.

\(\displaystyle H_{0}:\) The distribution of the music preferences is what the station says.(Claim)

\(\displaystyle H_{a}:\) The distribution differs from their claim.

You compare your data against theirs.


I really don't know about your card case, but do you know how to do a chi-square with Excel?. PHStat2 is a Excel add-on few seem to know about.
It has a great stats package. Besides, regular Excel has it too, only not as embellished.