Question: Is there a way to statistically define change in min-max diagrams?

[Wouter Penris]

Dear all,

 

I am currently writing up my MA thesis in Applied Linguistics on Measures of Complexity, Accuracy and Fluency, from a Dynamic Systems View Perspective.

 

We often use min-max diagrams to indicate whether there are periods of high or low variability, like this:

 

"To identify periods with different degrees of variability within the variables, moving min-max diagrams were created, where the minimum and maximum values of 5 instances was taken, as the following example shows:

 

            min(t1...t5), min(t2...t6), min (t3...t7), etc.

            max(t1...t5), max(t2...t6), max (t3...t7), etc."

 

Here is one of the resulting diagrams:

 

<link removed for privacy reasons> --fuzzy

As you can see, there are periods of high and low variability, but I want to know whether these changes are significant. Could I do something with surface change over time? Say, when the average surface of a min-max diagram over 5 t units decreases or increases by at least 50 percent for 5 subsequent t units, then there is a significant change? Or are there some traditional statistical measures to calculate this? I know of the way devised by Van Geert (1997) to use resampling and Monte Carlo analyses to find if the differences found in a set of data are significant, but that is only very rarely significant...

 

I am not an expert on Math at all, so I hope you will have some ideas.

 

Best,

 

Wouter

Edited June 14, 2013 by fuzzylogician
edited for privacy

[DMX]

bootstrapping will work

[cyberwulf]

bootstrapping will work

 

Not necessarily. The bootstrap can do a pretty bad job of estimating distributions of extreme order statistics (i.e., min and max).

 

I can't think of an obvious way to do this; perhaps the reason that Van Geert's technique rarely yields a small p-value is because it (correctly) accounts for the unstable behavior of mins and maxes.