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Nordic and Baltic GeoGebra Conference 2022�Jackknife resampling �measuring errors in fitted parameters�

Jonas Hall / The Mad Mathematician�jonas.hall@norrtalje.se

Swedish GeoGebra Institute�https://geogebra.se

Mattecentrum Stockholm �https://www.mattecentrum.se/

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What is jackknife resampling?

Resampling methods are for large data sets: Select many small samples and do your statistics on the samples rather than on the original data.
Jackknife resampling is the simplest possible resampling method: Works even for small data sets.
Aim is to find statistics such as error estimates, bias etc with very little effort.
Or, in our case, because it is the only realistic way to do it in a high school class, since GeoGebra does not produce error estimates of fitted parameters automatically (hint, hint, Markus!)

Typical physics experiment

How to do jackknife resampling?

Remove 1 data point and record calculated value of g
Repeat this with all data points. If you had 8 data points, you now have 8 values of g
Calculate standard deviation of these values

Normal distribution reminder

Jackknife statistical quirks

This factor can be ignored since we’re only doing rough estimates of error sizes.

Some results in class

One class (yr10/11) have done 3 labs using this method
First time difficult, each group needed hands-on help even though written instructions were at hand. Lots of aha:s when we did a class summary afterwards.
Second time, after further instructions, went smoother.
Third time they really knew the method.
Important to tell them that this is a standard method to be used by them many times in the future.

Some results of simulations

Comparing this method to the ”usual” covariance matrix method in Python shows that it works.
Different data sets gives different ”offsets” from covariance method.
Running large numbers (1000) of random simulations of linear data show some residual errors in the order of 6-7 % in the intercept and �1-2 % in the slope.