Ai52487963 said:Simple question: can a chi-squared be represented as a gaussian distribution? I'm wondering if I can take some chi-squared numbers that I have and represent them as increasing/decreasing widths of FWHM of a gaussian. Can I?
The chi-squared test is a statistical test used to determine whether there is a significant difference between the expected and observed frequencies of data. It is often used to test the goodness of fit of a model to observed data. Gaussian curves, also known as normal curves, are commonly used to model continuous data and can be used in the chi-squared test to determine the expected frequencies.
The chi-squared value for a gaussian curve is calculated by summing the squared differences between the observed and expected frequencies, divided by the expected frequency for each category. This calculation is then compared to a critical value from a chi-squared distribution to determine the significance of the results.
No, the chi-squared test is most commonly used with categorical or discrete data. However, it can also be used with continuous data if the data is grouped into categories.
If the chi-squared value calculated is greater than the critical value, it indicates that there is a significant difference between the expected and observed frequencies, and the gaussian curve does not fit the data well. If the chi-squared value is smaller than the critical value, it suggests that the gaussian curve fits the data well.
In theory, it is possible to have a perfect fit between a gaussian curve and observed data. However, in practice, there is always some level of error or deviation from the expected frequencies, and a perfect fit is rare. The aim of the chi-squared test is to determine whether the level of deviation is significant enough to reject the fit of the gaussian curve to the data.