# The Scientific Method/Control of Measurement Errors

## Experimental Design

Perhaps the most important step in controlling experimental error is to design your experiments to produce as little systematic error as possible. In order to do this, it is important to know something about what you are measuring. As an example, suppose that you desired to measure the weight of the oxygen produced in the decomposition of hydrogen peroxide:

$H_2O_2(aq) \rightarrow H_2O(l) + \frac{1}{2}O_2(g)$

You would need to ask yourself: How would you separate the oxygen from the water and unreacted hydrogen peroxide? How will you prevent the oxygen from leaking? Do you want to measure the weight directly, or by calculating it from other values (such as pressure)?

Get into the habit of asking yourself, "what could go wrong with this experiment?" before you start the experiment. Then if you can, design it so that the things that could go wrong are as minor as possible, and then when performing it be as careful as possible to avoid what is left.

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## Calibration and Accuracy

All measurement instruments need to be calibrated in some way in order to ensure that the values that are read are near the true value of the property being measured. Rulers all are compared to a standard when they are made so that when an inch is marked on the ruler, it is truly an inch.

Many instruments lose their calibration, and hence their accuracy, over time. Therefore it is necessary to recalibrate them. Instruments are generally re-calibrated by measurement of a standard or several, which have well-defined properties. For example, a scale might be calibrated by weighing a 5g weight and adjusting a dial until the reading is 5.000 g. Follow the instrument manual closely for calibration procedures, so that any bias in measurement due to measurement inaccuracy can be mitigated.

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## Repeatability and Precision

Measurement instruments never will give you an exact answer. For example, if you are measuring the volume of a liquid in a graduated cylinder, it is necessary for you to estimate which of the hash marks on the instrument is the closest to the true volume (or to interpolate between them based on your eyesight). Most computerized measurement devices, such as many modern scales, take multiple measurements and average them to obtain accurate results, but these also have sensitivity limitations.

Manufacturers often report the precision of their instruments. The repeatability of an instrument is a measure of the precision, which is the similarity of successive measurements of an identical quantity to each other. Reproducibility is essentially the ability to, with all other conditions the same (or as close to the same as possible), achieve the same measurement value in an experiment. For example, you may measure the weight of an object with the same scale multiple times. If the reading is significantly different every time, it is possible that the instrument needs to be recalibrated or re-stabilized (for example, by cleaning out dust from the receiver, or making sure the setup is right). If it has been properly calibrated and set up and measurements still vary more than the precision claimed by the manufacturer, the instrument may be broken.

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## Reproducibility

Another way to control errors in measurement from experiment to experiment is to constantly assess the reproducibility of the measurements. Reproducibility is measured essentially by performing the same measurement multiple times while varying one part of the experiment. For example, if you are measuring the pH of a buffer as part of a process, you may assess the reproducibility of the buffer preparation by preparing the same sample several times, independently of each other, and measuring the pH of each sample. If the variance in the pH measurements is larger than the measurement accuracy (or repeatability) of the instrument, then it is likely that the preparation of the buffer is to blame for this error. Such tests can be performed on many parts of a larger process in order to pinpoint and remedy the largest control difficulties.

Another possible reproducibility test would be measuring the same sample with different pH meters. It is very important to test the compatibility of different measurement instruments before claiming that the results are comparable, and such reproducibility measurements are critical for determining the relationship between two instruments.

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