My Math Forum Determining Chi-Square test confidence

 June 5th, 2016, 10:58 AM #1 Newbie   Joined: Jun 2016 From: Seattle Posts: 7 Thanks: 2 Determining Chi-Square 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} {r|c c|c} 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} {r|c c|c} 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 $$\chi^2 = \sum{\frac{(observed - expected)^2}{expected}}= \frac{(30-25)^2}{25} + \frac{(20-25)^2}{25} + \frac{(20-25)^2}{25} + \frac{(30-25)^2}{25} = 4$$ At this point we compare $\chi^2$ to a reference value $\chi^2_a$ drawn from a pre-calculated 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, 08:53 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 p-value. If you determine the confidence level after computing the chi-square statistic, this is data snooping and not good science, so you probably should not regard a as the confidence level.
 October 26th, 2017, 12:29 PM #3 Newbie   Joined: Oct 2017 From: US Posts: 13 Thanks: 1 The a value is just the p value of chi-square test here, I used this chi-square calculator to get a p value of 0.0455. Usually, the threshold is set at 0.05 or 0.01. For this chi-square 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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