Explain why the chi-square independence test is always a right...

Question

Explain why the chi-square independence test is always a right-tailed test.

Accepted Answer

Hello there. Today we're gonna solve the following practice problem together. So first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. Which of the following best describes the rejection region or the test statistic in a G2 test of independence? Awesome. So it appears for this particular prompt that we need to take our multiple choice answers and we need to determine which of our multiple choice answers best describes the rejection region for the test statistic in a T squared test of independence. So now that we know what we're ultimately trying to solve for, let's read off our multiple choice answers to see what our final answer might be. A is the left tail of the distribution, B is the center of the distribution, C is the right tail of the distribution, and D is both tails of the distribution. Awesome. So our first step that we need to take in order to solve this problem is we need to recall and use the equation for the G squared test statistic. Which states that G2 is equal to the sum of, so when you take the sum. Of parentheses 0 minus E, or rather minus E. So once again G2d is equal to the sum of O minus E in parentheses squared divided by E. Which is always non-negative, so this is non-negative, so I'll call it NN for short, or N hyphen N, so it's non-negative. So, our second step now is we need to recall a note that small values of g squad mean observed and expected frequencies are smaller, which supports the null hypothesis. Our thirdly large values of G squared, as we should recall, will indicate significant differences which suggests dependence. Fourthly, The rejection region is in the right tail where the T squared value is large. So, 5th and finally, therefore, as a result, the rejection region for the T2 test of independence is always in the right tail, which this corresponds to multiple choice answer letter C, which once again is the right tail of the distribution, and that's it. We've officially solved for this problem. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

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Explain why the chi-square independence test is always a right-tailed test.

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