Issue with Mass Loss in Experiment

[lapo3399]

Hi,

I am doing a chemistry lab writeup, and I have an issue with my loss in mass. I measured the mass lost by plastics exposed to various pH levels (sulfuric acid conc's) and I have conclusive results. The expected patterns are visible in the results; however, since the pieces of plastic were weighed using a milligram balance, and the maximum mass loss is around 0.007g, the uncertainties outweigh the observable patterns. Thus, if I am to use significant digits and show all of the uncertainties, the patterns will not show up and will make the results inconclusive, even though I know they are not. What exactly should I do? All help is immensely appreciated.

M.

[GCT]

Why don't you show us an example?

[lapo3399]

The following is a grpah showing the data (not plotted using significant digits). You can see the patterns in mass loss for PETE and its fabric especially; however, if the graph were plotted with values with appropriate significant digits, the relationship would not be as pronounced. As well, the uncertainty is around 0.003 g, so it outweighs the actual data produced. My questions are a) Do I graph using non-significant digits and b) do the uncertainties matter if the relationship is visible?

http://img90.imageshack.us/img90/6876/untitledro1.jpg (http://imageshack.us)

Edit: oops, messed up my chart title :S

[Hurkyl]

Thus, if I am to use significant digits and show all of the uncertainties, the patterns will not show up and will make the results inconclusive, even though I know they are not.
How do you know they aren't inconclusive? Eyeballing the data isn't good enough.

Anyways, a more precise way to present your data is to actually plot the range of uncertainty. Instead of a bar graph, plot something that indicates the value you measured and the range of uncertainty about it, such as:

.....(---*---).....
..(---*---)........
.........(---*---).
.....(---*---).....

(I've rotated 90 degrees and made up the data to make it easier to draw in text)

[lapo3399]

The error is a constant +/- 0.006g for all the values. I think that a bar graph is appropriate for this situation, as I am comparing values, not using time as one of the variables. As the error is so large compared to the values, they seem inconclusive... although calculations that ignore the uncertainties show that the results are not. I think the reason this has happened is that I used a milligram balance (+/- 0.001 g), so that, even if my data seems conclusive, the uncertainty caused by the measuring device overrules it. Is that true?

[lapo3399]

I just thought of something: If the the sum of the three trials was used for data analysis instead of the average, wouldn't the number be around three times larger but have the same uncertainty?

[Bystander]

Mass loss per how much mass per sample?

[lapo3399]

Mass loss per whatever the sample's mass was... e.g. the sum of three samples' (trials) masses was initially 0.182g, and lost 0.009g. I still think that finding the sumof the 3 trials per pH per polymer is a good idea, because it keeps the same uncertainty as an average yet still displays the relationship.

[DaveC426913]

As per Hurykl's ? in post 4, I am curious as to how you rationalize ignoring the error factor in concluding that there was indeed mass loss.

[Hurkyl]

If I remember correctly, the rough rule of thumb is that when you add two quantities with uncertainties m and n, the uncertainty of the sum is \sqrt{m^2 + n^2}. (Of course, that's still an relative improvement in precision)