Calculating Bin Center for Rate vs Energy Plot

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Discussion Overview

The discussion revolves around how to assign a bin center for a rate vs energy plot when combining data from two energy values, ##E_1## and ##E_2##, each associated with different counts and measurement times. Participants explore various methods for determining the appropriate energy to represent the combined data, considering factors like weighted averages and the implications of merging data points.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants suggest using a simple average of the two energies, ##(E_1 + E_2)/2##, while others propose a time-weighted average, ##(t_1E_1 + t_2E_2)/(t_1 + t_2)##.
  • One participant emphasizes the importance of keeping the two energies separate for accurate representation, questioning the validity of merging the data.
  • Another participant introduces the concept of using weighted averages based on the respective bin widths, arguing that the values of the data should not influence the averaging process.
  • There is a discussion about the physical interpretation of the graph and whether the energies are precisely measured values or averages over time intervals.
  • Concerns are raised about the potential loss of information when merging bins, particularly regarding the accuracy of counting rates associated with each energy.
  • One participant illustrates a scenario where combining counts from different bins could lead to misleading results if the rates are not normalized to the same counting time.

Areas of Agreement / Disagreement

Participants express differing views on how to assign the energy for the combined bin, with no consensus reached. Some advocate for merging methods while others caution against losing information and suggest maintaining separation of the data.

Contextual Notes

Participants highlight the need for careful consideration of the assumptions made regarding the data, including the precision of energy measurements and the implications of merging bins on the overall analysis.

  • #31
Events are suppose to be integers. You wave number differ by 0.000022% really.

Ok for me to proceed I have to have some confidence in this data. Can you explain exactly what and how you get this data and confirm the validity of the significant figures your present.
 
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  • #32
BvU said:
??

Total confusion. How do you count to 385.035301 ?
In my book 385 is followed by 386

[edit] Ah ! when you say "counts" you mean "rate" -- next time add a dimension to your data columns !

View attachment 251353

What on eart can move you to merge "bins" here ? You don't have bins, you have "energy settings".
I am sorry, yes I meant rate (to get counts multiply the first 2 columns, my bad!). Also I have few tens of thousands of points between 13252.3231 and 13293.9497 ##cm^{-1}##. Here I provided some randomly selected points just to give an example the kind of data that I have, but there is a peak when you plot everything (and you have something around 2000 counts around that freq value). So one of the reasons to merge bins, is that there might be an error associated with the freq measurement, so if I say 13252.74, if there was a miss reading, that might be actually a count belonging to 13252.75 or 13252.73. If we merge several bins, average the frequencies and quote the average as the center of the new bin (I am still not sure what kind of average would that be), we might be able to neglect that error when doing the fit. The main problem is that we know that the issue is there but we are not sure how to quantify it exactly yet. So averaging over several energies (assuming that the error goes like ##1/\sqrt(N)##) the error on each freq should be small enough such that we can ignore it. Also we are pretty sure that there is no fine structure in the peak, so doing this average should not hide some physics from us.
 
  • #33
BillKet said:
some randomly selected points
Ever see the end of the movie "A few good men" ? You could play Nicholsons role without having to audit !

Post your plot of ALL data. Counting rate vertically, cm-1 horizontally

If your counting times don't differ by more than 10%, don't even bother worrying about the effect on the error bar in individual measurements. Let alone trying to compensate.

BTW what's your energy resolution estimate ? Judging from your first two "some of the data" points it might be really good -- but by now I have trouble believing anything I read in this thread.

BillKet said:
Assuming that I want to rebin the data for some reason
Is that the lame reason 'misreading the frequency' ?

There can be no sensible argument concocted from that for rebinning. Or do you want to artificially 'improve' your observations in order to get a peak ?
 
  • #34
gleem said:
Events are suppose to be integers. You wave number differ by 0.000022% really.

Ok for me to proceed I have to have some confidence in this data. Can you explain exactly what and how you get this data and confirm the validity of the significant figures your present.
I made some clarifications in a post after, those are rates, not counts, I am sorry. So we used a laser to ionize some molecules and counted the number of ionized molecules for each laser wavelength. The laser (Ti:Sapphire)
wavelength was adjusted with a predefined schedule and when the wavelength was changed, the change was of about 0.02 ##cm^{-1}##. As I said above, we have some issues with reading the exact wavelength of the laser so 13252.7038 and 13252.7067 are probably the same value (which one of them is right, we don't know for sure), while 13252.7291 is the one after the increase by 0.02 ##cm^{-1}##. This is the raw data that we have from the software (including the decimals provided). As I said, this uncertainty about the actual freq, is the main reason why we want to do a rebinning.
 
  • #35
Don't rebin -- no reason. And show the plot -- I sure hope the peak isn't at 13252.7 :rolleyes:
 
  • #36
BvU said:
Ever see the end of the movie "A few good men" ? You could play Nicholsons role without having to audit !

Post your plot of ALL data. Counting rate vertically, cm-1 horizontally

If your counting times don't differ by more than 10%, don't even bother worrying about the effect on the error bar in individual measurements. Let alone trying to compensate.

BTW what's your energy resolution estimate ? Judging from your first two "some of the data" points it might be really good -- but by now I have trouble believing anything I read in this thread.

Is that the lame reason 'misreading the frequency' ?

There can be no sensible argument concocted from that for rebinning. Or do you want to artificially 'improve' your observations in order to get a peak ?
As I said I can't post my data. Also that peak is visible without rebinning, I am worried that the uncertainty in the freq measurement would add to the error of the actual peak center and I am not sure how to account for that yet.
 
  • #37
Wouldn't worry. Do the fit and look at the errors it comes up with. Rebinning should not affect the results and certainly shouldn't improve them.
 
  • #38
BillKet said:
I am worried that the uncertainty in the freq measurement would add to the error of the actual peak center and I am not sure how to account for that yet.

That is what we needed to know. You do need to know the uncertainty in the energy interval eventually. Why didn't set the laser to get definitively different wavelengths to start?

BillKet said:
I am worried that the uncertainty in the freq measurement would add to the error of the actual peak center and I am not sure how to account for that yet.

Yes you will need to deal with that but I agree with BvU that rebinning is not the way.
 
  • #39
gleem said:
That is what we needed to know. You do need to know the uncertainty in the energy interval eventually. Why didn't set the laser to get definitively different wavelengths to start?
Yes you will need to deal with that but I agree with BvU that rebinning is not the way.
So basically, whether the error on the freq is significant or not, rebinning will not help?
 
  • #40
You will need a reasonable estimate of the frequency uncertainty and combine it with the fitting uncertainty. As for significance it seems that you cannot determine if a change in frequency is actually a change if that is so I guess that the uncertainty would be it is close to the increment that you are making.

BillKet said:
As I said above, we have some issues with reading the exact wavelength of the laser so 13252.7038 and 13252.7067 are probably the same value (which one of them is right, we don't know for sure), while 13252.7291 is the one after the increase by 0.02 cm−1cm−1cm^{-1}.

So it looks like it is in the neighborhood of .02cm-1. Your going to have to understand your instrument and what it is telling you.
 
  • #41
I do not know what you are looking for or what you expect to see, but looking at the plot of the rate vs wave no. I see no peak only an outlier data point.
 

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