## Chi-Squared Tests (Pearson)

For the discussion of math. Duh.

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GTM
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### Chi-Squared Tests (Pearson)

Okay, I don't have a strong background on this but I just don't understand the theory when I read up on it, it's a lot of blah blah.

So you calculate an X2 value from your observed data. And you compare it to a chi squared value you get from calculating the integral (knowing k, degrees of freedom, and x, which is...?) The process is all fine and dandy.

But what does the second chi-squared value mean? How does it relate to the observed data? For example, if we assume there are 10 plants total, I assumed that 95% of the ways that you can classify the 10 plants would result in a chi squared lower than the critical value (and 5% of the ways would result in a chi-squared value higher). Is that a correct assumption? If it is, how (and why) does the chi squared function know that?

I'm just completely lost here. Thanks in advance.

Dason
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### Re: Chi-Squared Tests (Pearson)

It sounds like you're talking about a specific example without providing the actual context.

The chi-square test is an asymptotic test as well. So for small samples the sampling distribution of the test statistic might not actually be chi-squared but as the sample size increases the sampling distribution gets "closer" to a chi-square distribution.

But providing more context and asking your question more clearly might result in better responses.
double epsilon = -.0000001;

GTM
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Joined: Tue Nov 10, 2009 4:53 am UTC

### Re: Chi-Squared Tests (Pearson)

I wasn't using a specific example but I can try to reword it so it is.

Say plants can have 1 leaf or 2 leaves. This is 1 degree of freedom. I have 10 plants, I calculate the chi squared value, I get 2.5. Looking at a lookup table with alpha = 0.05, the critical value is 3.81. What does this value intuitively mean and how do you get it?

My assumption was for every possible distribution with 1 degree of freedom, if you calculate the chi-squared value for all of them, 95% will have a chi squared value of less than 3.81. 5% will have a value greater than 3.81. Is this correct?

Since 2.5 is less than 3.81, the test concludes nothing. Is there anything we CAN say? Like can we say "using a chi squared test, there is no reason to believe the actual distribution didn't come from the stated distribution" or something?

Thanks.

Izawwlgood
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### Re: Chi-Squared Tests (Pearson)

I'm not sure if this is a well known stats joke, but my biostats professor only called it a 'Chi Chi Rodriguez' test, which I thought was pretty funny.
... with gigantic melancholies and gigantic mirth, to tread the jeweled thrones of the Earth under his sandalled feet.