I want to apply the chi square goodness of fit test to evaluate the quality of fit of wind direction data. I have a dataset with measurements of wind direction and some corrections are applied to this to predict the wind direction in another location. The method of prediction is not important here what is important is how to evaluate the fit. My approach:
The data is classified in different wind direction bins of for example 30 degrees width and compared with the dataset of predicted directions.(same number of categories)
Then the statistics of the chi square is calculated (Oi-Ei)**2/Ei and compared with a critical value.
This is what I understood about the critical value calculation.
It depends on the significance level (0.05 in my case) and the degrees of freedom.
With (k − c) degrees of freedom where k is the number of non-empty cells (bins in my case?) and c is the number of estimated parameters (1?). If my understanding was correct for this example 12-1=1, and then critical value around 19.675
Is my approach correct?
Why the values are different if you use counts or percentage of data? I know that using percentages is not correct.
What is the difference between Chi square goodness of fit and reduced chi square goodnes of fit? When should I apply the second one?
