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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.
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.
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.
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.
Adel Ibrahim Bargal has written: 'Efficiency comparisons of goodness-of-fit tests for Weibull and gamma distributions with singly censored data' -- subject(s): Goodness-of-fit tests
There are Goodness-of-Fit tests that can be used. The choice of test will depend on what is known about the population and sample data.
There are various goodness-of-fit tests. The chi-square and Kolmogorov-Smirnoff tests are two of the better known of these.
There are many chi-squared tests. You may mean the chi-square goodness-of-fit test or chi-square test for independence. Here is what they are used for.A test of goodness of fit establishes if an observed frequency differs from a theoretical distribution.A test of independence looks at whether paired observations on two variables, expressed in a contingency table, are independent of each.
statistical goodness of fit test used for categorical data to test if a sample of data came from a population with a specific distribution. It can be applied for discrete distributions.
Normally never! I suppose that it could be used to test if the goodness of fit is too good to be true!
No, it cannot be used to measure that.
For goodness of fit test using Chisquare test, Expected frequency = Total number of observations * theoretical probability specified or Expected frequency = Total number of observations / Number of categories if theoretical frequencies are not given. For contingency tables (test for independence) Expected frequency = (Row total * Column total) / Grand total for each cell
Probably not.
Alois Starlinger has written: 'Parameter estimation techniques based on optimizing goodness-of-fit statistics for structural reliability' -- subject(s): Goodness of fit, Structural reliability, Weibull density functions, Parameter identification, Statistical tests, Ceramics 'Reliability analysis of laminated CMC components through shell subelement techniques' -- subject(s): Ceramic-matrix composites, Finite element method
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The coefficient of determination R2 is the square of the correlation coefficient. It is used generally to determine the goodness of fit of a model. See: http://en.wikipedia.org/wiki/Coefficient_of_determination for more details.