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June 5th, 2016, 11:58 AM  #1 
Newbie Joined: Jun 2016 From: Seattle Posts: 7 Thanks: 2  Determining ChiSquare test confidence
I tried this problem in the basic statistics forum but none there responded, so perhaps it's an advanced statistics problem. To set the stage, lets set up a typical sample problem: A group of people are categorized by gender and also by political affiliation, and we wish to test the hypothesis that there is a relationship between the two categorizations. \begin{array} {rc cc} gender & republican & democrat & total\\ \hline male & 30 & 20 & 50 \\ female & 20 & 30 & 50 \end{array} \begin{array}{r l} H_0 &: \text{gender and political affiliation are independent variables} \\ H_1 &: \text{gender and political affiliation are related} \\ \text{degrees of freedom} &: (rows  1) \times (columns  1) = 1 \end{array} If the two dimensions were independent then we would have an expectation of equal portions in each of the four table entries \begin{array} {rc cc} gender & republican & democrat & total\\ \hline male & 25 & 25 & 50 \\ female & 25 & 25 & 50 \end{array} The test statistic $\chi^2$ is calculated by summing a computation for each cell of the table $$\chi^2 = \sum{\frac{(observed  expected)^2}{expected}}= \frac{(3025)^2}{25} + \frac{(2025)^2}{25} + \frac{(2025)^2}{25} + \frac{(3025)^2}{25} = 4 $$ At this point we compare $\chi^2$ to a reference value $\chi^2_a$ drawn from a precalculated table for some confidence level $a$ in the appropriate number of degrees of freedom, and reject the null hypothesis $H_0$ if $\chi^2 > \chi^2_a$ Question Is there a way to determine the value $a$ at which $\chi^2 = \chi^2_a$ ? 
June 5th, 2016, 09:53 PM  #2 
Senior Member Joined: Dec 2012 From: Hong Kong Posts: 853 Thanks: 311 Math Focus: Stochastic processes, statistical inference, data mining, computational linguistics 
You need a computer to do that, though a would not be not be the confidence level any more  it would be the pvalue. If you determine the confidence level after computing the chisquare statistic, this is data snooping and not good science, so you probably should not regard a as the confidence level.

October 26th, 2017, 01:29 PM  #3 
Newbie Joined: Oct 2017 From: US Posts: 11 Thanks: 0 
The a value is just the p value of chisquare test here, I used this chisquare calculator to get a p value of 0.0455. Usually, the threshold is set at 0.05 or 0.01. For this chisquare test with a p value of 0.0455, it is statistically significant at p<0.05 level, but NOT at p<0.01 level.


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