The data reproduced by the model is to be fitted with the experimental data. The model has two parameters. Therefore when one is fixed the other is changed in such a way so that the chi-square/DOF will be minimum. Therefore the model has only one free parameter. The experimental data has 22 points and I normalize the data with the theoretical data at the first point. Therefore the remaining data points left are only 21. What will be the goodness of fit for such a fit?
The problem needs to be elaborated. Two examples are given below as illustrations
1. To test the goodness of fit of modal analysis data: The Singhbhum granite contains quartz, orthoclase, plagioclase and accessories in the ratio of 5:4:3:1. The modal analysis of 400 point count data indicates the volume percentages of these minerals to be 34.7%, 33.5%, 22.3% and 9.5% respectively. Statistically analyse the data and suggest if the thin section is of Singhbhum granite. In this case expected values of quartz, orthoclase, plagioclase and accessories are 154, 123, 92 and 31 respectively. The observed values of quartz, orthoclase, plagioclase and accessories are 139, 134, 89 and 38 respectively. Since the number of parameters are 04, the degree of freedom is 4-1=3
2. To test the paleocurrent data: Usually the paleocurrent data are grouped at 30 degree class interval resulting in 12 classes, 0 - 30, 30 - 60 .... etc, which are observed values. The expected number of data in each class in case of randomness of paleocurrent = (total no. of data/12), which is equal in all classes and are the expected values in each class. In this case the degrees of freedom is 12-1=11.
@Rabindra... actually I have a model that generates data(theoretical data). This generated data I compare with the given experimental data( with statistical errorbars also given). The model has two parameters. Therefore to find the best match of the theoretical data with the experimental data I need to find the chi-square and when this chi-square will be minimum the fit will be considered to be the best fit. Now I found the minimum chi-square per degree of freedom 1.43 with 21 data points. The total chi-square will be 30.03. How the goodness of the fit will be calculated.
1. If you have 21 experimental data and these are to be compared with 21 generated data; the Chi-square = ((O1-E1)^2/E1) + ((O2-E2)^2/E2) +........., where O1=observed data 1 and E1 is the expected data 1 ... etc then the Chi-square has 21-1 = 20 degrees of freedom.
2. If the data are in form of (x1,y1), (x2,y2) ......... and a model (regression equation) has been found out as "y = a + bx" type, for given values of xi, a set of yi are generated. In such a case F-test is necessary to find out best fit.
I have found chi-square...now I need to find the goodness of the chi-square fit. In calculating the chi-square I have used the same Pearson's chi-square test. The parameters are found by th minimization of chi-square. Now I have to find the goodness of the fit....please tell me if you have an idea
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