# Accuracy and Precision

##

What's the Difference?

Up to this point, we have been studying the factors affecting
*our **confidence** in the correctness* of a
measurement - its precision.
In an experimental situation, however, we almost always will be
comparing a value that we measure (or calculate from our
measurements) with an "accepted value", or comparing 2 values from an
experiment. The degree to which 2 values agree is called **accuracy**.

Accuracy
and precision are not the same thing, although they are related. In
the diagram at right, the bullseye of the target represents an
"accepted value" of some measurement. To be very precise, your
measurements need to "cluster" within a small range, but to be highly
accurate, you need to "hit the bullseye" - the accepted value must
lie near your best estimate. A measurement can be precise withou
being accurate, and vice versa.

##

Comparing Two Measurements

Remember that lab to calculate the acceleration of gravity? You
got 10.3 m/s^{2}, when everybody knows your are supposed to
get 9.8 m/s^{2}. Conclusion? The experiment didn't work. Or what about
the lab where the kinetic energy here was supposed to equal the
potential energy there. You calculated 12 Joules for the kinetic
energy and 14 Joules for the potential energy - obviously not equal,
right? Another experiment that "failed".

Since measurements are not numbers but ranges of values, comparing
two measurements consists of comparing two ranges - not two numbers.
It is incredibly naive (I'm trying to be nice, here...) to expect to
get exactly the same numbers in two different situations. The
question is: "Do the ranges in which the values probably lie overlap
sufficiently to convince me that the two values are probably the
same?"

In
the diagram at left, the circle represents the best estimate of a
value, and the arrows represent the range of probable values. The red
measurement is compared to the blue measurement. If there is
considerable overlap of the ranges, as in the top picture, it is
reasonable to conclude that the two values are probably equal. All
situations are not quite so easy to judge - in the middle diagram
there is some overlap of the two ranges, so it is possible that the
two measurements are actually the same. In the bottom diagram, it is
highly unlikely that the two values are equal, since there is no
overlap at all in the two ranges.

last update August 17, 2006 by
JL Stanbrough