Why do we reject null hypothesis of a Goodness of test when the Chi square statistic is more than the tabulated value of chi-square at say 5% level of significance and accept when it is less?

What does it mean to have a Chi-square value more or less than the value assigned to a certain level of significance?

  • $\begingroup$ The null hypothesis is usually set up as the uninteresting hypothesis. So we attempt to reject it. If we can't reject at a particular significance level that does not mean that we should accept it. $\endgroup$ – Michael R. Chernick Feb 8 '17 at 18:37
  • $\begingroup$ I didn't say that. My question is why accept when more and reject when less? May be you should consider rereading the query, my main question is the second one. $\endgroup$ – Tyto alba Feb 8 '17 at 18:55
  • $\begingroup$ What level of Type I error you will tolerate is a subjective economic decision. $\endgroup$ – Michael Hardy Feb 8 '17 at 19:42

To have a chi-squared value more than the value at a certain significance level means that under the null hypothesis the observed chi-squared value is more unlikely than your desired level of significance. A smaller chi squared value means the observed values are more likely under the null hypothesis. As the chi squared value gets higher, the likelihood of seeing your observations under the null hypothesis decreases, so rejecting the null becomes more and more attractive

  • $\begingroup$ Is this consistent with any type of test statistic, like goodness of fit and test for homogeinity of chi-square? $\endgroup$ – Tyto alba Feb 9 '17 at 5:00
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    $\begingroup$ Not sure if you are specifically discussing chi-squared type tests or other tests, but this is generally how things go. Your test statistic increases as the observations become less likely under the null hypothesis. $\endgroup$ – Conrad De Peuter Feb 9 '17 at 16:13

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