Goodness of fit, Residual STD, chi square

In summary, the conversation discusses the use of CasaXPS software for modeling synthetic peak models in X-ray photoelectron spectroscopy data. The software provides a Residual Standard Deviation after each fit iteration, which is different from the more widely used Chi-square or Reduced-Chi-squares. The conversation also mentions the "Goodness of Fit" property and how it can be transformed into something statistically significant, which may require checking the software's manual.
  • #1
Dan Zar
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0

Homework Statement


Hello,

I am using CasaXPS to model synthetic peak models for X-ray photoelectron spectroscopy data. I am fitting.
The software has a lot of manuals online but they do not explain how they yield a Residual Standard Deviation, after each fit iteration. Most software use Chi-square or Reduced-Chi-squares, which I do not really understand either, but they are more widely used.
For example,
upload_2016-3-25_3-18-40.png

Whereas most softwares use Reduced Chi squares.
Lastly,Name Block Id Data Set Position FWHM Area St Dev Area %At Conc % St.Dev. Goodness of Fit
sp2 C1s 1-1 12 284.4560 1.1348 135.671 8.38179 54.79 286.976
sp3 C1s 1-1 285.0000 1.2000 89.8416 8.55699 36.28 286.976
sp2-Br C1s 1-1 285.6874 1.2000 14.7421 5.73433 5.95 286.976
C=P C1s 1-1 284.4843 0.9000 7.37342 2.8681 2.98 286.976 I get a report in which the "Goodness of Fit" equals 286.976, how do I transform this number into something statistically significant?
The examples they use on the manuals also happen to have high numbers for "Goodness of Fit"
Thanks a lot.
 

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  • #2
I think you'll have to check the manual how that property is defined.
 

Related to Goodness of fit, Residual STD, chi square

1. What is the "Goodness of Fit" test and how is it used?

The Goodness of Fit test is a statistical test used to assess how well an observed data set fits a theoretical model or expected distribution. It is commonly used to determine whether a sample of data is significantly different from a population or to compare multiple samples. The test involves calculating a test statistic, such as chi-square, and comparing it to a critical value to determine the level of significance.

2. What is Residual Standard Deviation (RSD) and how is it calculated?

The Residual Standard Deviation (RSD) is a measure of the variation of the data points around the regression line in a linear regression model. It is also known as the standard error of the estimate. RSD is calculated by taking the square root of the sum of the squared differences between the actual data points and the predicted values from the regression line, divided by the degrees of freedom.

3. What is the chi-square test and when is it used?

The chi-square test is a statistical test used to determine whether there is a significant association between two categorical variables. It is used when the data is expected to follow a specific distribution, such as a normal distribution, and the observed data deviates from this expected distribution. The test involves calculating a test statistic, chi-square, and comparing it to a critical value to determine the level of significance.

4. How do you interpret the p-value in a chi-square test?

The p-value in a chi-square test represents the probability of obtaining the observed data or a more extreme result, assuming that the null hypothesis is true. A low p-value (typically less than 0.05) indicates that the observed data is significantly different from the expected data, and the null hypothesis can be rejected. A high p-value suggests that there is no significant difference between the observed and expected data, and the null hypothesis cannot be rejected.

5. What are the assumptions of the chi-square test?

The chi-square test has several assumptions, including: the data must be categorical, the sample should be randomly selected, the expected frequency of each category should be at least 5, and the observations must be independent. If these assumptions are violated, the results of the chi-square test may not be accurate. Alternative tests may need to be used in these cases.

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