Forest Mensuration. Brack and Wood

Index Overview Help Types of error Describing error Error calculations |
## Error © |

An error may be defined as

the difference between the measured value and the true value.It is important for anyone involved in measurement to have a general knowledge of likely error sources, so that:

- errors can be controlled where possible or
- the effects of the error can be considered.

Errors arise from many sources. It pays the natural resource manager or scientist to determine as early as possible what are likely to be the **dominant sources of error** in the measurement task and to devote sufficient time to devising ways of reducing these errors. This is best accomplished by a preliminary trial - in short, a rehearsal. As well as providing a provisional estimate of the size of the various errors, the rehearsal enables one to check that the procedures are appropriate and sound.

There are four kinds of error:

- mistake
- accidental error
- bias
- sampling error

Accidental error can be reduced by using more accurate and precise equipment but this can be expensive. A competent scientist is expected to be able to assess in advance how good an instrument needs to be in order to give results of an accuracy sufficient for the task in hand. In other words, he / she is expected to make an appropriate choice from the equipment available (or to design a more appropriate instrument).

- flaw in measurement instrument or tool, e.g. survey tape 50 cm short;
- flaw in the method of selecting a sample, e.g. stocking counts - some observers always count the boundary tree, others always exclude it;
- flaw in the technique of estimating a parameter, e.g. stand volume : using a volume function or model in a forest without prior check of its suitability for applicationint that forest; inappropriate assumptions about formulae;
- subjectivity of operators.

- continual check of instruments and assumptions;
- meticulous training;
- care in the use of instruments and application of methods.

To avoid bias being introduced via faulty instruments, it is essential to check all instruments before one commences any important measuring project and re-check periodically during the course of the project.

- Accuracy - refers to
the closeness of a measurement or estimate to the true value

More broadly, accuracy is the degree to which a statement or quantitative result approaches the truth.**Accuracy refers to the size of the total error and this includes the effects of biases**. An estimated value may be inaccurate because of one or more kinds of error. - Precision - the definition has several variants depending on use:
- the fineness of a single measurement. Here precision refers to the resolving power of the measuring device and is ordinarily indicated by the number of decimal places in the measurements made with the device;
- the degree of agreement in a series of measurements;
- the clustering of sample values about their own average;
- the reproducibility of an estimate in repeated sampling.

- Accuracy = sqrt(Bias^2+ Precision^2)
- Accuracy and precision are not synonymous. An accurate measurement is one in which the systematic and random errors are small whereas a precise measurement is one in which the random errors are small.
- Precise measurements may not be accurate due to bias.
- Accuracy is freedom from all types of error whereas precision is freedom from variation - one does not imply the other!

- When A = B + C and the errors on B and C are
*b*and*c*, then the error (*a*) on A is given by:

*a*= sqrt(*b^2*+*c^2*) - When A = B x C, then the error (
*a*) on A is given by:

*a*/A = sqrt([*b*/B]^2 + [*c*/C]^2) - When A =K x C^n where K is a constant, then the error (
*a*) on A is given by:

*a*/A = n x*c*/ C

where

^n denotes raising to the power of n,

and sqrt(Y) denotes taking the square root of Y

**Note**: there is little sense in taking measurements in the field to a precision greater than needed for their ultimate use. Conversely, the precision of field measurements should not be less than that required for later computations.

http://online.anu.edu.au/Forestry/mensuration/ERROR.HTM

Cris.Brack@anu.edu.au

Sun, 11 May 1997