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Types of Errors in Measurement. Accuracy vs. Precision

SECTION 1 - Foundations of Chemistry

When discussing the differences and definitions of Accuracy and Precision, we must first introduce the two main types of errors in measurement.

Types of Errors in Measurement

There are two types of measurement errors...

1. random errors (human errors)
2. systematic errors (instrumentation errors)

Random Errors 

Random error = measurement errors that have an equal probability of being too high or too low, too long or too short, etc.

   ➞ usually "human errors."

Haphazard, whoops, random experimental and/or measurement mistakes.


Systematic Errors 

Systematic error = measurement errors that tend towards being consistently too high or too low, too long or too short, etc.

   ➞ usually "instrumentation errors."

An example of instrumentation error would be an analytical balance that is not calibrated correctly and consistently gives mass readings that are too high.


Accuracy vs. Precision

Now that we know about the two types of errors in measurement, we can discuss the differences between Accuracy and Precision.

Let's first define the two terms...

Accuracy = how well a measurement agrees with the true value.

Precision = how well a series of measurements agree with each other, regardless of what the true value is.


If a measurement is accurate, it agrees with the true or accepted value.  If a series of measurements are precise, their values "agree" with each other.

Let me explain using a dartboard analogy with four different situations...

ex:  Dartboard Analogy.  A dart represents the results of a measurement or experiment. The bulls-eye represents the true value of the measurement or experiment.

Accuracy vs. Precision

Left dartboard - our results are not accurate and not precise.

We've got a lot of human mistakes in our technique (random errors), and it's too difficult to tell if we have any instrumentation errors (systematic errors).

Middle dartboard - our results are precise, but not accurate.

We are making few (if any) random errors, but something is wrong with our procedure, or our measurement devices, etc. We are experiencing only instrumentation error (systematic error).

Right dartboard - well done! Our results are both precise and accurate.

Very few (if any) human errors or instrumentation errors.


ex:  Is it possible to be accurate without being precise??

   ➞  YES. See below:

Accuracy without Precision

As you can see in the dartboard above, the average of the 5 measurements or experiments end up being the bulls-eye!

This is an example of "accuracy without precision."


ex:  A student performed an analysis of a sample for its calcium content and got the following results:

14.92%     14.91%     14.88%     14.91%

The actual amount of calcium in the sample is 16.25%.

What conclusion can you draw about the accuracy and precision of these results?
Answer:  we are precise, but not accurate. Since we are precise, we are not making any human errors (random errors).

But... because our experimental results do NOT agree with the "true value," an instrumentation error or errors (systematic errors) is/are occurring.


One last note about systematic error (instrumentation error). 

Having a "wrong" or "bad" experimental procedure would also be an example of systematic error. 

The same improper procedure gives the same inaccurate results - every time.


Next up in SECTION 1 - Foundations of Chemistry we'll discuss: 

Significant Figures in Calculations and Dimensional Analysis.

Important stuff in the early stages of any Chemistry class or course!