Statistical Test for X-Y Data with Error Bars

[natski]

Hi all,

I am hoping someone can recommend a useful statistical test. I have a set of data on an x-y plot which varies about the y=0 line in a seemingly random way. Each data point has a y error bar, which appears to be, in general, smaller than the standard deviation of the data.

I would like to apply a rigorous statistical test to calculate the probability that for the given individual one-sigma errors on each data point, the observed scatter about the y=0 line is plausible, or whether there is evidence for some kind of oscillation pattern?

A null hypothesis test was my first thought but this does not take into account the individual errors bars on the data points. Also I have noticed that many mathematicians don't hold the the null-hypothesis in much respect, nor does it offer a probability of the data points being randomly spread.

Thanks for any advise.

Natski

 

[ModernLogic]

It sounds like you're looking for a p-value, which is associated with null hypothesis testing. I would first use a computer and calculate the line of best fit through the data points. Let's call this line y = f(x). Then, your null hypothesis can be: "The equation which best models this phenomenon (or whatever it is) is f(x)." Your alternative hypothesis can be: "No. It's not."

Then for all the data points (X1,Y1)... (Xn,Yn), calculate ((Yi - f(Xi))^2)/(f(Xi)) for all i = 1, 2, 3...n. Add the numbers from these calculations up and that would give you a chi-square statistic. Using a table or calculator, you can find the p-value corresponding to this score. The p-value, or the probability of observing this data given the equation y = f(x) is the true model for this phenomenon.

Hope this helps.