chi-square, regr.analysis, help please!

[valkovete]

Hi to all! I am answering some statistics questions from the course I have in statistics, and have some problems answering them. I thought somebody from the forum will volunteer to help, if s/he can, as I have to submit the answers to my teacher as soon as possible.
1. One of them is: whether a chi-square depends on the sample size or not, and why?

Well, I understood that chi-square uses counts and frequencies as data rather than standard deviations and means, and with it data is analyzed in categories, but I still cannot reach to a clear conclusion whether it depends on the sample size or not.

2. Another problematic question I have is: which null hypothesis does the regression analysis usually use?

As far as I know, there are two null hypothesis: a directional and a non-directional one. And I think that it is the non-directional null hupothesis, because it tests differences or relationships, and it is relationships between variables that a regression analysis tries to explore. But this is just my opinion and am not sure if it is really the case – If somebody is sure about the correct answer, please let me know

Thanks in advance!

[Dason]

Are these exactly how the questions are worded? Because they aren't very clear.

For the first question are you talking about a chi-square test of independence? A goodness of fit test? Just the distribution itself?

For the second question: Fitting a regression doesn't require any null hypothesis - it's when you do testing that you use a null hypothesis. What test are you talking about?

[jrai]

Assuming you mean chi-square test of independence, Chi-square statistic (technically Pearson's chi-square) is not reliable when the cell counts of the table are less than 5 or are inflated with zeroes. Then it is good to conduct Fisher's exact test or calculate the exact p-value of Pearson's chi-square statistic.

A quote:
"Exact statistics can be useful in situations where the asymptotic assumptions are not met, and so the asymptotic p-values are not close approximations for the true p-values. Standard asymptotic methods involve the assumption that the test statistic follows a particular distribution when the sample size is sufficiently large. When the sample size is not large, asymptotic results might not be valid, with the asymptotic p-values differing perhaps substantially from the exact p-values. Asymptotic results might also be unreliable when the distribution of the data is sparse, skewed, or heavily tied."

The routine p-values for the chi-square statistic are calculated using the asymptotic methods.

As Dason correctly mentioned: "Fitting a regression doesn't require any null hypothesis - it's when you do testing that you use a null hypothesis."
The packages by default test for the null hypothesis that the coefficient/parameter estimate/beta =0 & also conduct the F-test where null is that all the coefficients are simultaneously equal to 0.

[valkovete]

Hello Dason and jrai, firstly, thank you both for being kind to help, in particular with your remarks and clarifications. Though, I did not pose the questions correctly, I've at least now made a difference that an analysis and a test are two different things.
As to the asymptotic assumptions, I will need some more time to grasp this topic as I'm now entering statistics.

Secondly, I am obliged to apologize for wasting your time as I was in a hurry and did not precisely pose my questions in the forum (it's my lesson).

And now, I am posting them again, but the way they were exactly worded by my teacher:

1.Does the power of a chi-square test depend on the sample size? Why?

2.Which null hypotheses is usually a regression analysis testing?

I hope I will receive some other useful responses

Again, thanks in advance!

[Karabiner]

1.Does the power of a chi-square test depend on the sample size? Why?

You could take a careful look at the Chi² formula.

Kind regards

K.

[Dason]

As Dason correctly mentioned: "Fitting a regression doesn't require any null hypothesis - it's when you do testing that you use a null hypothesis."
The packages by default test for the null hypothesis that the coefficient/parameter estimate/beta =0 & also conduct the F-test where null is that all the coefficients are simultaneously equal to 0.

The omnibus F-test usually isn't that all the coefficients are 0. The intercept usually isn't included in that test.

[jrai]

Thanks for pointing that out.

[valkovete]

I've finalized my work with the questions asked above
I thank all who contributed to answering them.

Best wishes!