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Is the chi-square goodness of fit a one-tailed test with the rejection region in the right tail?
true
What is the purpose of Chi Square Analysis?
Chi-square is mainly used for a goodness of fit test. This is a test designed to assess how well a set of observations agree with what might be expected from some hypothesised distribution.
What do you mean by expected frequencies in chi square test?
Expected frequencies are used in a chi-squared "goodness-of-fit" test. there is a hypothesis that is being tested and, under that hypothesis, the random variable would have a certain distribution. The expected frequency for a "cell" is the number of observations that you would expect to find in that cell if the hypothesis were true.
How is the chi square independence test similar to the goodness of fit test how is it different?
With either test, you have a number of categories and for each you have an expected number of observations. The expected number is based either on the variable being independent of some other variable, or determined by some know (or hypothesised) distribution. You will also have a number of observations of the variable for each category. The test statistic is based on the observed and expected frequencies and has a chi-squared distribution. The tests require the observations to come from independent, identically distributed variables.
What is difference between chi square and reduced chi square?
A reduced chi-square value, calculated after a nonlinear regression has been performed, is the is the Chi-Square value divided by the degrees of freedom (DOF). The degrees of freedom in this case is N-P, where N is the number of data points and P is the number of parameters in the fitting function that has been used. I have added a link, which explains better the advantages of calculating the reduced chi-square in assessing the goodness of fit of a non-linear regression equation. In fitting an equation to the data, it is possible to also "over fit", which is to account for small and random errors in the data, with additional parameters. The reduced chi-square value will increase (show a worse fit) if the addition of a parameter does not significantly improve the fit. You can also do a search on reduced chi-square value to better understand its importance.
