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

In summary, the conversation discusses determining the smallest value of a χ2 statistic needed to reject the null hypothesis at a significance level of 5%, for a distribution with 9 degrees of freedom. It is mentioned that there may be two definitions of the inverse chi square distribution and that knowing the PDF and using a numerical routine may be helpful in solving for the cumulative probability. However, it is ultimately discovered that a table of corresponding X^2 statistics and their probabilities is needed for this task.
  • #1
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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  • #2
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 [itex]\nu[/itex] degrees of freedom and the second is the chi square of [itex] \nu / X[/itex] for [itex]\nu[/itex] degrees of freedom.
 
  • #3
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?
 
  • #4
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.
 
  • #5


To determine the smallest value of a χ2 statistic that would reject the null hypothesis at α = 5% for a distribution with 9 degrees of freedom, you can use a chi-square table or a statistical software. These resources provide critical values for different degrees of freedom and alpha levels. In this case, you would need to look for the critical value for 9 degrees of freedom at an alpha level of 5%. This value would represent the smallest χ2 statistic that would lead to rejecting the null hypothesis at α = 5%. Alternatively, you can also use the Chi-Square Distribution Calculator, which allows you to input the degrees of freedom and alpha level to determine the critical value.
 

1. What is inverse chi square?

Inverse chi square is a statistical test used to determine whether there is a significant relationship between two variables. It involves calculating the inverse of the chi square statistic, which is used to measure the difference between the observed and expected values in a contingency table.

2. How is inverse chi square calculated?

The inverse chi square statistic is calculated by taking the sum of the squared differences between the observed and expected values, divided by the expected values. This result is then compared to a critical value from a chi square distribution table to determine if the null hypothesis should be rejected.

3. What does it mean to reject the null hypothesis at α=5%, 9DF?

This means that there is a 5% chance of obtaining the observed result if the null hypothesis is true. The 9DF refers to the degrees of freedom, which is the number of categories or variables in the contingency table minus 1. If the calculated inverse chi square value is higher than the critical value at α=5%, then the null hypothesis is rejected.

4. What is the significance level in inverse chi square?

The significance level, denoted as α, is the probability of rejecting the null hypothesis when it is actually true. In inverse chi square, a significance level of 5% is commonly used, meaning that there is a 5% chance of rejecting the null hypothesis even if it is true.

5. What are the assumptions of inverse chi square?

Inverse chi square assumes that the sample is representative of the population, the variables are categorical, and the expected values in the contingency table are greater than 5. It also assumes that the observations are independent and that there is no significant relationship between the variables.

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