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# ACCURACY, RELIABILITY AND VALIDITY

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These three terms are often used when referring to experiments, experimental results and data sources in Science.

a) ACCURACY: Conformity to truth.

Science texts refer to accuracy in two ways:

(i) Accuracy of a result or experimental procedure can refer to the percentage difference between the experimental result and the accepted value. The stated uncertainty in an experimental result should always be greater than this percentage accuracy.

(ii) Accuracy is also associated with the inherent uncertainty in a measurement. We can express the accuracy of a measurement explicitly by stating the estimated uncertainty or implicitly by the number of significant figures given. For example, we can measure a small distance with poor accuracy using a metre rule, or with much greater accuracy using a micrometer. Accurate measurements do not ensure an experiment is valid or reliable. For example consider an experiment for finding g in which the time for a piece of paper to fall once to the floor is measured very accurately. Clearly this experiment would not be valid or reliable (unless it was carried out in vacuum).

b) RELIABILITY: Trustworthy, dependable.

In terms of first hand investigations reliability can be defined as repeatability or consistency. If an experiment is repeated many times it will give identical results if it is reliable. In terms of second hand sources reliability refers to how trustworthy the source is. For example the NASA web site would be a more reliable source than a private web page. (This is not to say that all the data on the site is valid.) The reliability of a site can be assessed by comparing it to several other sites/sources.

c) VALIDITY: Derived correctly from premises already accepted, sound, supported by actual fact.

A valid experiment is one that fairly tests the hypothesis. In a valid experiment all variables are kept constant apart from those being investigated, all systematic errors have been eliminated and random errors are reduced by taking the mean of multiple measurements. An experiment could produce reliable results but be invalid (for example Millikan consistently got the wrong value for the charge of the electron because he was working with the wrong coefficient of viscosity for air). An unreliable experiment must be inaccurate, and invalid as a valid scientific experiment would produce reliable results in multiple trials.

ACCURACY & PRECISION

Another term you will hear in relation to experiments and experimental results is the term precision. Precision is the degree of exactness with which a quantity is measured. It refers to the repeatability of the measurement. The term precision is therefore interchangeable with the term reliability. The two terms mean the same thing but you will hear & read both in relation to science experiments & experimental results.

The precision of a measuring device is limited by the finest division on its scale.

Note too, that a highly precise measurement is not necessarily an accurate one. As indicated in the first definition of accuracy above,accuracy is the extent to which a measured value agrees with the "true" or accepted value for a quantity. In scientific experiments, we aim to obtain results that are both accurate and precise. The section on errors below will hopefully further clarify the four important terms defined in these last two sections of notes - accuracy, reliability, precision & validity.

Errors occur in all physical measurements. When a measurement is used in a calculation, the error in the measurement is therefore carried through into the result. The two different types of error that can occur in a measured value are:

Systematic error – this occurs to the same extent in each one of a series of measurements eg zero error, where for instance the needle of a voltmeter is not correctly adjusted to read zero when no voltage is present.

Random error – this occurs in any measurement as a result of variations in the measurement technique (eg parallax error, limit of reading, etc).

When we report errors in a measured quantity we give either the absolute error, which is the actual size of the error expressed in the appropriate units or the relative error, which is the absolute error expressed as a fraction of the actual measured quantity. Relative errors can also be expressed as percentage errors. So, for instance, we may have measured the acceleration due to gravity as 9.8 m/s2 and determined the error to be 0.2 m/s2. So, we say the absolute error in the result is 0.2 m/s2 and the relative error is 0.2 / 9.8 = 0.02 (or 2%). Note relative errors have no units. We would then say that our experimentally determined value for the acceleration due to gravity is in error by 2% and therefore lies somewhere between 9.8 – 0.2 = 9.6 m/s2 and 9.8 + 0.2 = 10.0 m/s2. So we write g = 9.8+- 0.2 m/s2. Note that determination of errors is beyond the scope of the current course.

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Consider three experimental determinations of g, the acceleration due to gravity.

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 | 33 | 34 |

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