I obtained one loop Nyquist plot for my one layer coating, so I used an electrical equivalent circuit of (Rcoat-Ccoat) to fit EIS plots. The fitting results are Ok but not very well, and chi-square goodness of fit is 0.03. If I add (Rct-Cdl) in the circuit, it fits so well and chi-square goodness of fit is 0.002. But I can't explain this result. My question is "is 0.03 is acceptable for chi-square goodness of fit?"
In chi-square goodness of fit test, the degrees of freedom is (k-1) where k is the number of categories you are comparing. you need to see critical value of chi-square at the desired level of significance for the calculated degrees of freedom and compare it with the value of chi-square you got. Now, the real issue is you much significance level you want. Best regards. P.Ganguly
A p value = 0.03 would be considered enough if your distribution fulfils the chi-square test applicability criteria. Since p < 0.05 is enough to reject the null hypothesis (no association), p = 0.002 reinforce that rejection only.
If the significance value that is p-value associated with chi-square statistics is 0.002, there is very strong evidence of rejecting the null hypothesis of no fit. It means good fit.
Assumption of Normality is a requirement for the chi square test. It is applicable for large samples. One can confirm with non-parametric methods too (rank tests, permutation tests and the bootstrap).
I am sorry but the chi-square test does not require any assumption of Normality; it is based on the chi-square distribution and has its own applicability criteria. However, it is possible to use exact methods instead.
Apologies with the long reply.
For the chi-square approximation to be valid, the expected frequency should be at least 5. This test is not valid for small samples, and if some of the counts are less than five (may be at the tails). The reason is Central Limit Theorem, chis-square distribution approaches standard normal distribution for large degrees of freedom.
I agree with Dr Alvarez that exact tests are appropriate if Dr Trang knows the appropriate distribution of the variable (i.e., layer coating). I have assumed the variable as 'layer coating' and as a continuous variable, if I am wrong please ignore my opinions.
One of the reasons, why the p-values are different, may be because of choice of bins. Chi-square goodness of test is sensitive to the choice of bins. There is no optimal choice for the bin width (since the optimal bin width depends on the distribution). Most reasonable choices should produce similar, but not identical, results. If the distributional assumption is not justified, a non-parametric or robust technique may be required.
Chi-square goodness of fit is a non-parametric test. It does not require normality assumptions.It is rather used for categorical variable. The test criteria(Q) suggested by Pearson(1900) is the sum of squares deviations of expected and observed frequencies normalized by the expected frequency. The probability distribution of Q is approximately chi-square with k-1 degrees of freedom. for large samples. For continuous variable kolmogorov-Smirnov(K-S), Lilliefors tests and Anderson-Darling(A-D) is preferable to chi-square test. which eliminates the chances of arbitrary selection of bins in chi-square test.
Dear
Trang Thi Phan,
Are the values mentioned by you the test statistics values or p-values, In case of good fit you get smaller test statistic value and bigger p-value(e.g >.05) whereas in case of poor fit you get larger test statistic value and smaller p-value( e.g< .05)
I'm sorry for not seeing your helps sooner. I don't work in statistic so I don't really undestand your answers. I obtained a diagrams by Electrochemical Impedance Spectroscopy, then I determined some parameters using a simulation sofware and a equivalent electric circuit. Result shows simulation diagrams, parameters values, errors and chi-square goodness of fit. As giving errors for each parameters is too much in the data table, many articles in my domain gived only chi-square value to show goodness of fit. But they only said that smaller chi-square value is, better diagrams fitting is. And their chi-square values are often < 0.001. So I really don't know if my chi-square 0,03 is enough good.
Anyway, thanks so much for your helps.
Yes. 0.03 is good enough for Nyquist plot.
You may overlap your original data with the fitted curve. I think it is quite good.
Similar question: The data I obtained for the glassy carbon electrode fits perfectly for the following circuit but the chi square is 0.12. Is it acceptable?
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