Professor Dave here, let's discuss accuracy and precision.
To do science, we must do experiments, and in doing experiments we must collect data.
If this data is quantitative, we will need to understand the concepts of
accuracy and precision in order to properly analyze the data. So let's
define these terms and discuss how they apply to sets of numbers. Under one
definition, we could understand that the accuracy of data refers to how close it
is to the true value of something. So if we measure the mass of an object that we
knew was precisely one kilogram, and we get 1.001 kilograms on
our balance, we could say that we got very accurate data. The word precision
refers to how closely a set of data correlates, so if we took this
measurement on many different balances and we got the following set of data, we
could say that it is a highly precise data set, because all of the values are
very close to one another. If there was much variance in the data we would say
it was imprecise. In this way, we can see that a data set can be both accurate and
precise, which means good measurement, accurate and imprecise, which may simply
be human error, inaccurate but precise, perhaps due to faulty calibration of an
instrument, or both inaccurate and imprecise, where everything goes wrong.
Once again, these qualities depend on how close they are to the true value and how
close they are to each other. We can use target practice as an analogy. If we
regard the bull's eye as the true value we can see how the following results
represent the different types of data sets we just discussed. Accuracy will
mean that a data point is close to the bull's eye and precision will mean that
data points are close to each other. Now that we understand accuracy and
precision in this context, let's learn about another context for the word
precision. We could also talk about the precision of an instrument. Let's say we
want to measure the length of an object in centimeters. This ruler displays
centimeters so we could say that this object is between these two centimeter
markings, and then we could estimate one more digit beyond that, the tenths place.
Let's say that the ruler also showed tenths of a centimeter, then we could
reliably report our value to the tenths place and now estimate the hundredths
place. This is because when taking measurements we always estimate one
digit beyond the scale that is reported on the measuring instrument. The more
digits there are in our measurement, the more precise it is, but no matter how
precise our measurement there will always be some uncertainty associated
with it. If we measure something as being 2.4 centimeters, that means that it is
really somewhere between 2.35 and 2.44, which will
round to 2.4, since the tenths place limits the precision of our
measurement. Even if it was 2.4187293
centimeters, there is still uncertainty associated with that final digit. The
precision associated with measurement is an important concept to understand
because we are limited by our five senses in the way that we interact with
the world, and therefore in how we do science, since analysis of the data we
collect is the only way we can do science in the first place.
We never want to report data to a higher degree of certainty than is appropriate,
so that previous measurement to the tenths place can only be to the tenths
place, as there is no way for our eyes to estimate with greater precision than
that. But this concept only applies to measurement. Counting numbers and defined
values have infinite precision, like the way that there are exactly 12
in a dozen, or exactly 1000 meters in a kilometer with no uncertainty of any
kind. The precision of measurements will affect the way we do calculations with
our data, but these infinitely precise values will not. At any rate, accuracy and
precision are important concepts to understand, because as we said,
measurement is the way we collect data, and the interpretation of this data is
what science is really all about. Let's check comprehension.
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