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Thread: Goodness of Fit Test

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    Goodness of Fit Test




    Hi,

    I am having trouble understanding goodness of fit tests.

    I am given the following data and want to determine if the suicide rate is constant.

    The question says to, under the latter hypothesis, model the number of suicides in each month as a multinomial random variable with the appropriate probabilities and conduct a goodness of fit test. Look at the deviations, O_i-E_i and see if there's a pattern.

    \begin{tabular}{lcc}
\hline
Month & Number of Suicides&Days in Month\\ \hline
January&1867&31\\
February&1789&28\\
March&1944&31
\end{tabular}

    There is more data, but think this will give you an idea of what I am doing.

    I calculated


    X^2=\sum_{i=1}^{12}\frac{(O_i-E_i)^2}{E_i} = 47.36533

    For the first, it was, \frac{31}{365}(23480)=E_1(\hat{\theta})\to \frac{(1867-1994.192)^2}{1994.192}

    I know that there are 12-1=11 degrees of freedom for the Chi-Square distribution, but what do I do next?

    Thank you!

    I'm in MathHelpForrum a fair amount and decided to try this site out!

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    Re: Goodness of Fit Test


    After you have computed the test statistic, with a given significance level, you just compare it to the critical value of the null distribution (\chi^2(11) this time). You reject the null hypothesis if the test statistic X^2 is larger than the critical value, as a larger test statistic indicate a larger "deviation".

    Equivalently you can compute the probability of the test statistic larger than the current observed one under the null distribution, which is the p-value and report it. Then each user may compare this p-value to their own, pre-specified significance level.

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