Inverse Chi Square: Rejecting Null Hypothesis at α=5%, 9DF

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Discussion Overview

The discussion revolves around determining the smallest value of a χ² statistic necessary to reject the null hypothesis at a significance level of α = 5% for a distribution with 9 degrees of freedom. The context includes both theoretical and practical aspects of statistical hypothesis testing.

Discussion Character

  • Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant inquires about the smallest χ² statistic needed to reject the null hypothesis at α = 5% with 9 degrees of freedom.
  • Another participant questions whether the original inquiry pertains to the inverse chi-square distribution or the relationship between chi-square values and alpha levels.
  • A different participant suggests that knowledge of the probability density function (PDF) of the distribution is necessary for solving the cumulative probability value.
  • One participant acknowledges that their question required a table of corresponding χ² statistics and probabilities, which they did not have access to.

Areas of Agreement / Disagreement

Participants express uncertainty regarding the specific nature of the original question and whether it pertains to the inverse chi-square distribution or the standard chi-square distribution. There is no consensus on the approach to take or the necessary resources for answering the question.

Contextual Notes

Limitations include the lack of access to a table of χ² statistics and probabilities, which is essential for determining the required χ² value, as well as the ambiguity in the original question regarding the type of distribution being referenced.

MadViolinist
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How can I determine what the smallest value of a χ2 statistic must be to reject the null hypothesis at α = 5%, for a distribution with 9 degrees of freedom? Thanks in advance.
 
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MadViolinist said:
How can I determine what the smallest value of a χ2 statistic must be to reject the null hypothesis at α = 5%, for a distribution with 9 degrees of freedom? Thanks in advance.

It's not clear from your question whether you asking about the inverse chi square distribution or simply asking about how to determine the correspondence between the chi square value and alpha.

In the first case, there are two definitions of the inverse chi square distribution. One is the chi square of 1/X for \nu degrees of freedom and the second is the chi square of \nu / X for \nu degrees of freedom.
 
Hey MadViolinist and welcome to the forums.

Following on from what SW VandeCarr said, do you know the PDF of the distribution you are working with (chi-square if you are using a chi-square statistic) and how you solve (using a numerical routine) the value of a cumulative probability?
 
Hey all:
I just found out that the question I was asking required the use of a table of corresponding X^2 statistics and their probabilities (which I was not given). Thanks for your time anyway.
 

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