The typical development of an analysis system for
an experiment goes as follows:
- A simulation is created and it is checked thoroughly to insure
that it is performing correctly.
- The simulation is used to decide on the best way to design the
- The experimental data is compared to that from the simulation
to look for inconsistencies that could indicate problems either
in the experiment or in the simulation.
- A simulation may need to provide correction factors to the data,
such as corrections for acceptance losses due to dead spots in
- The simulation can help to estimate systematic errors.
Statistical errors are proportional to the amount of data taken
and are usually determined in a straight-forward manner. Systematic
errors, on the other hand, are less clear cut and can be difficult
to determine in a rigorous manner. A simulation can help by showing,
for example, the effects on the results due to faulty performance
of the instruments, mis-calibrations, different assumptions about
the performance of the instruments, etc. For example, suppose by
mistake one of the the sensors in our gravitational acceleration
experiment was far from its expected position due to faulty installation.
We can vary this in our simulation to see what effect it has on
the final results.
The Analysis Program
Ideally, the analysis program should treat simulated and experimental
data identically. This helps to find errors in the analysis code,
prevent inconsistensies in treatment of simulated and real data,
and it can also highlight problems with the analysis. For example,
the analysis of simulated data of particle collisions in an accelerator
experiment should return the same cross section used to produce
the simulated data originally.
Typically, the simulation would produce an output data file very
similar to that from the actual experiment. It might even simulate
"raw" data before any calibration corrections. For example,
values from an ADC (Analog to Digital Converter) typically requred
subtraction of pedestals (constant offsets) and slope corrections
in the input voltage to digital values. The simulated raw data could
include similar pedestals and slope variances.
In the dropped mass experiment program,
the analysis consisted of the histogram and a method to calculate
the acceleration. We can make this more modular by creating an analysis
class to which collected data is passed. The analysis code can then
be modified independently of the simulation code and could also
work on the real data.
In the following simulation we will use the least squares fitting
classes developed in Chapter
8: Physics to create our analysis code. We could have written
the simulation data to a file and then run the analysis separately.
But for convenience here we will keep combine the simulation and
analysis in the same applet/app.
Last update: Jan.28.04