As part of each experiment you are required to submit an analysis to your TA which will be graded for completeness and used to provide feedback during your subsequent post meeting. The question of what exactly do we mean by an “analysis” is sometimes a source of confusion for students. Literally speaking the analysis is all of the calculations, plotting and fitting of data, error propagation, etc., which you do to arrive at your final results for the experiment. There is however no definitive guide for what goes into your analysis writeup, nor is there a template or example which we can provide. Part of the reason for this is that everyone does their analysis differently, different groups will perform the same experiment differently, and the analysis will look different from one experiment to the next.

What we wish to teach you is not a recipe to follow for writing up an analysis, rather we want you to learn how to figure this out for yourself. In this section we walk you through a thought exercise which can be applied to any of our experiments.

We will begin by assuming that you have collected your data and analyzed it to the point at which you can draw conclusions about how and where your data agree or disagree with the predictions of the Thompson model. Furthermore we will adopt a top down approach by starting with the final result of the analysis and using that to determine what needs to be included in your analysis writeup.

This implies that the end product of your analysis should be a comparison of your measured values of $\sigma(E)$, with uncertainties, with the values predicted by the Thompson model. This comparison could be done either by plotting both the measured and predicted values together, fitting your measured values to the functional form of the model, or even a simple table. Thus we start our analysis writeup with such a plot and or table along with a sentence stating that this is our final result.

What you don't have to discuss in the analysis are your conclusions, details of how you took the data, etc. Those things will go into your final report.

Since you likely did this for about half a dozen different energies it is not unreasonable to include the plot of the fitted data for each energy, along with the mathematical form of the fit function used, the returned fit values and your calculation converting linear attenuation coefficient into cross section. Maybe a table showing the linear attenuation coefficients along with their uncertainties as returned by the fitting algorithm and the goodness of fit parameters for each plot. You can include a note in this section indicating that this is how you extracted the linear attenuation coefficients from the data.

This suggests that we should show how the rates were calculated for each energy and thickness. This required determining the total number of counts recorded in some time interval.

Perhaps we got the total counts by fitting the photo-peak in each pulse height spectra to a gaussian function plus a background term and then integrating the area under the gaussian. At this point there were likely too many peaks fit to reasonably include a plot showing each fit, possibly as many as 10 thicknesses for 6 different energies would result in 60 plots! All we really need to do here is to show the TA how we handled this part of the data analysis, so a reasonable thing to do might to to include one representative plot of the fit for each energy gamma along with the mathematical form of the fit function. If different energy peaks required background terms, a listing of the fit functions used for each energy would be appropriate to include. A table could be used to provide the results of all of the fits along with the uncertainties and goodness of fit values. The details of the calculations involved are the same for each peak that was analyzed, so one example of the calculations will be good enough. Such a sample calculation should include details on how the uncertainties were propagated.

The time interval for each spectra is just the live time value from the USX software, so a table of these values with uncertainties for the different energies and absorber thicknesses is sufficient. Include a caption with the table stating what the numbers relate to.

Lastly you would have had to divide the total number of counts by the time interval to get a rate, and the uncertainties would have to be propagated. Thus you would want to show the full calculation, including the error propagation formula used, for one peak.

Absorber thicknesses are easy to include. Probably you measured them with a caliper and estimated the measurement uncertainty. There is no need to describe how this process was carried out, that will take place in your Report. Instead a table of absorber thicknesses, including appropriate units and uncertainties will be completely sufficient.

Note that it is perfectly acceptable to write up your analysis back to front like this, and doing so helps prevent your analysis from becoming a stream of consciousness recitation of what you did in the lab as you did it.

In general there should be just enough text to describe what the plots, calculations, etc. represent and how they fit together. Keep in mind that the TA grading your analysis knows what the experiment is about, what data is required and what needs to be done with that data. So all you need to do is provide enough description to make it easy for them to follow what you did and how you did it.

When you proceed to write your final report is when you will discuss your conclusions in detail, along with how the data were collected, issues which may have arose that impact the interpretation of your results, etc.