Experimental Errors

It is impossible to make an exact measurement. Therefore, all experimental results are wrong. Just how wrong they are depends on the kinds of errors that were made in the experiment.

Be careful! Wrong doesn't mean bad!

We're using the word "wrong" to emphasize a point. All experimental data is imperfect. Scientists know that their results always contain errors. However, one of their goals is to minimize errors, and to be aware of what the errors may be. Significant digits is one way of keeping track of how much error there is in a measurement.

Since they know that all results contain errors, scientists almost never give definite answers. They are far more likely to say: "it is likely that ..." or "it is probable that ..." than to give an exact answer.

As a science student you too must be careful to learn how good your results are, and to report them in a way that indicates your confidence in your answers.

There are two kinds of experimental errors.

Random Errors

These errors are unpredictable. They are chance variations in the measurements over which you as experimenter have little or no control. There is just as great a chance that the measurement is too big as that it is too small.

Since the errors are equally likely to be high as low, averaging a sufficiently large number of results will, in principle, reduce their effect.

Systematic Errors

These are errors caused by the way in which the experiment was conducted. In other words, they are caused by the design of the system.

Systematic errors can not be eliminated by averaging In principle, they can always be eliminated by changing the way in which the experiment was done. In actual fact though, you may not even know that the error exists.

It is not easy to discuss the idea of systematic and random errors without referring to the procedure of an experiment. Here is a procedure for a simple experiment to measure the density of rubbing alcohol (iso-propanol).

Materials:

digital electronic balance that can be read to 0.01 g
100 mL graduated cylinder, marked every 1 mL
iso-propanol

Procedure:

Find and record the mass of the empty, dry graduated cylinder.
Fill the graduated cylinder about 3/4 full of the alcohol. Record the volume of the alcohol in the cylinder.
Find and record the mass of the filled graduated cylinder

Some possible random errors in this experiment	Some possible systematic errors in this experiment
slight variations in the level of your eye while reading the meniscus in the graduated cylinder vibration in the floor or air currents that cause fluctuation in the balance	a mis-calibrated balance will cause all the measured masses to be wrong. alcohol evaporates rapidly. During the period of time required to measure its mass, some of the alcohol will evaporate. density depends on temperature. The temperature was not specified or controlled.

Notice that the random errors can't really be eliminated. If you honestly (and that is the catch – it is psychologically very hard for us to do so) read the graduated cylinder two or more times, you should get slightly different readings. However, if we made lots of measurements, and averaged them, the mean would be an estimate of the real measurement. It is just as likely for your eye to be slightly above the meniscus as below it, so the random errors will average out.

The systematic errors are caused by the way we did the experiment. Unlike random errors, these errors are always in the same direction. A mis-calibrated balance will always give results that are too high (or too low, depending on the direction of mis-calibration). Evaporation of the alcohol always causes a mass that is lower than it should be. We could get rid of these systematic errors by calibrating the balance properly, or using a cover to prevent evaporation.

Click for more details about systematic errors

What about human error?

There is also something students want to call an error that is not an error at all, and that is human error. If you mean the kind of error that is caused by your eye's inability to read the exact level of liquid in a graduated cylinder, then that is a random error. If you mean the kind of error that is caused by a poor design of the experiment – after all a human designed it – then that is a systematic error. These two kinds of errors are the only errors you should ever have in your experimental results.

What students seem to mean by human errors are really mistakes. Spilling part of a solution, dropping part of a solid from the weighing paper, or doing a calculation wrong are blunders, not errors. They can be avoided by being careful. If you know that you have made such a mistake – a "human" error – you simply cannot use the results. You must discard the measurements if you know that these kinds of mistakes have happened and redo the observations, or redo the calculations properly.

You should always make sure to include "human error" in your lab writeup?

Never report these things as "human error". They are mistakes that should not have happened.

spilling, or sloppiness, dropping the equiment, etc.
bad calculations, doing math incorrectly, or using the wrong formula
reading a measuring device incorrectly (thermometer, balance, etc.)
not cleaning the equipment
using the wrong chemical
not following the planned procedure

Which of the following are characteristics of random errors? Check all that apply.
a) doing several trials and finding the average will minimize them b) the observed results will usually be consistently too high, or too low c) proper design of the experiment can eliminate them d) there is no way to know what they are

Which of the following are systematic errors in measuring the density of a liquid as described in this procedure? Check all that apply.
a) your eye level will move a bit while reading the meniscus b) some of the liquid will evaporate while it is being measured c) air currents cause the balance to fluctuate d) the balance may not be properly calibrated