Statistics are important communication tools! They're a way for you to tell the reader how confident you are in your measurements and conclusions, and a way for you to tell us that you know how dodgy reality can be. Here, two topics are of importance: Propagation of Error and Regression. Since you've all taken your stats course already some details will be omitted.
A simple pump calibration experiment will be described to give us a data set to work with, and MATLAB will be used for all analyses and plotting. Consider an inexpensive, variable-speed pump that has a knob to adjust the flow rate, but the knob has tick marks of 1.0, 1.5, 2.0, ... 5.0 with no units (we call these nominal values). To translate from these values to a meaningful flow unit, we perform the following experiment:
Connect the pump to a reservoir so that water is pumped in a loop.
Set the pump knob to 1 and let the system stabilize.
Use a stopwatch (increments of 0.1 s) and graduated cylinder (increments of 1 mL) to measure the volume discharged in 10 s.
Repeat 2-3 for many knob settings.
After completing Step 4, we assemble the data as shown in Table 1. We'd now like to derive an equation to allow us to easily convert from nominal pump markings to volumetric flow rate. Towards that end we'll use statistical analyses to determine both the equation and our confidence in the equation.
Table 1. Experimental data for the pump calibration experiment.
0
10.1
0
1
10.0
23
2
10.2
43
3
9.9
71
4
9.9
83
5
10.1
120