FALL 2023

184
THE DISTRIBUTOR’S LINK
ROB LaPOINTE FASTENER SCIENCE PRECISION, ACCURACY AND SIGNIFICANCE IN MEASUREMENT from page 168
While measuring the table in Figure 4, if we
upgrade our meter stick to one with better resolution,
we can make a more precise measurement. Let’s
upgrade to millimeter resolution like the instrument
in Figure 5, and we can add a thousand times
greater precision to our measurements. Assuming the
accepted dimensions of the table are exactly 2 meters
and 1.5 meters, our new measurements should be
2.0000 meters by 1.5000 meters. Writing this in
millimeter units, these same measurements would
be 2000.0 mm and 1500.0 mm. You can see that
these measurements have the same precision as the
measurements made in Figure 5.
This is really cool, because whenever we see a
measurement, whether it’s the length and width of
a table or the magnetic moment of an electron, we
know the precision of the instrument used to make the
measurement. By the way, the magnetic moment of an
electron is now measured to a precision of 1.3 out of
10 trillion. As you can imagine that level of precision
required an expensive meter stick.
Accuracy
Accuracy is how close a measurement is to an
accepted value. At first, this may sound similar to
precision, but it’s really very different. Although the
measurement of the magnetic moment of the electron
is both very accurate and very precise, it is only by
comparison to a theoretical standard that enables us to
see its accuracy. The magnetic moment value can also
be derived from theory (Quantum Electro-Dynamics) and
the measured value can be compared to the theoretical
value.
Can measurements be precise and not accurate?
Yes! Figure 6 shows an example using darts. We can
interpret the clustering of the darts as precision. The
tighter the cluster, the higher the precision. The distance
between the darts is like the distance between marks
on our meter stick. Closer spacing means greater
resolution. Figures 6B and 6D both have high precision,
with 6D being slightly better than 6B. But what about
the accuracy of 6B and 6D? That depends on what is
accepted as the correct value of the measurement. If
the accepted value is the center of the dartboard, then
clearly, 6D has both high precision and high accuracy.
If the accepted value was the upper-left section of the
dartboard, then 6B would have both high accuracy and
high precision.
What can we learn from figures 6A and 6C? It is
easy to see that neither 6A nor 6C have high precision
because the darts are spaced far apart. But what about
their accuracy? If the accepted value is the center of
the dartboard, then 6C is highly accurate, although with
low precision. 6C is highly accurate because the darts
are evenly spaced around the accepted value and thus
indicate correctly what the accepted value would be.
Using the center of the dartboard as the accepted value,
figure 6A is neither accurate nor precise.
Significance
Now that we understand a little about precision and
accuracy, we have some context to understand what
significance is as it relates to measurement values used
in calculation.
FIGURE 6 ARRANGEMENT OF DARTS TO ILLUSTRATE
PRECISION AND ACCURACY
FIGURE 7 A CIRCLE SHOWING THE PROPERTIES OF DIAMETER,
RADIUS, AND CIRCUMFERENCE
CONTINUED ON PAGE 189