We’re now to the point where we’ve taken measurements and analyzed our confidence and uncertainties. One of the most rewarding parts of experimental investigations is graphing and visualizing your hard work. Usually this will appear in the Results and Conclusions section of your report.

5. Results and Conclusions

What would someone take away from your report if they only read the introduction and skimmed ahead to the results and conclusions? Make sure you don’t let them miss your most important points and findings! When you skim through something what do you look for? Odds are headings and images.

Why the images?

They’re worth a thousand words… 900 of which are irrelevant. But what do they really tell us?

Comparing with visuals

When you look at the above graph, why have I chosen two y-axes to present both the heat capacities of hydrogen and the equilibrium fraction of spinning vs. non-spinning hydrogen at cryogenic temperatures? Because they are related. Graphs are great at showing how sometimes complex information is related, and changes, relative to another. Graphs compare and contrast.

Many will say that figures are a matter of taste and preference. That’s true to a point. However, you’ll find that good graphics will consistently do similar things. Here’s a few examples:

  1. What not to do: University of Wisconsin-Madison Professor Rod Lake’s abominable graphs website.
  2. What to do: here’s a very old standard on graphic design from 1914, but is still very relevant.

In general, the guidelines are pretty clear:

  1. Be empathetic to your reader.
  2. Focus on the relevant change or correlation you want the graphic to display.
  3. Give the titles, units, and digits when and where they are needed.
  4. Omit useless and repetitive words, digits, and space.

But you’ll need to practice to get good at it. The example above was of theoretical curves. Notice that they are smooth. The uncertainties in the predictions likely fall within the line-width. Experimental measurements are seldom this easy. The following figure¬†shows some raw measurement traces for when I measured the visco-plastic flow of solid deuterium. You can see in the figures when steady state was achieved at a given temperature, dynamic shear strength, and heat transfer measurement. At these steady state points I can average to obtain representative points.

Raw experimental measurements

Notice that I use the figure caption to describe what is displayed and do not repeat the information with a title above the graph. These graphs are all made with EES. The EES default graph is very clean and tends to work in most situations. Even for very large datasets like the one above. Plotting raw data like this can give people incredible confidence in your experiment. Can you estimate the precision error from the data traces? Does it look like I achieved steady state before moving to another data point?

With these raw datasets it’s straightforward to average the values to return points you want to report. Here’s an example with all of the points I measured for my Ph.D. dissertation.

Comparison plot

This single graph contains a considerable amount of information. This is a graph you want to close with. This one contains the visco-plastic flow measurements for hydrogen, deuterium, and neon. Can you compare and contrast? I even include the prior measurements, some with estimated uncertainty bars. Do the bars add important information when comparing to the correlations I developed (colored lines)?

In the end, spend time on effective visuals. The narrative that explains them is only necessary when your graphs are not completely obvious alone. Once finished, ask yourself what a person will take away from it. Is it what you want them to leave the report with? It should be. Make sure they can’t miss it.

From here, it’s easy to create bulleted lists summarizing the key findings from your report. With all of the key portions of your reports and presentations covered, it’s time to revise, polish, and practice!