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Generally, an instrument does not directly give the required information. In

most cases, several measurements are combined to obtain the needed value. For

example, in tracer gas measurements, several concentrations, gas ﬂows, time

and volume measurements are combined in equations that are solved to get

the airﬂow rates. The errors accompanying the measured values propagate

through the interpretation formulae and ﬁnally give a probable error on the

ﬁnal result.

In this chapter, some methods for estimating the error on the result are

presented. Note that only the instrumental and random errors are treated

here. Bias caused by misuse of the instruments or by a lack of precautions is

not discussed here.

Deﬁnitions

Let x be the result of a measurement. If several measurements of the same

physical quantity are made, the results, x

, of these measurements will not be

all equal, but nearly all of them will be within some interval. The conﬁdence

interval with a probability, P, has this probability to include the actual value.

In practice, about NP results out of a large number, N, of measured values

of the same quantity should be included in the con ﬁdence interval.

The conﬁdence interval or the probable error can be expressed by two

ways:

1 The absolute error is expressed in the same units as the phy sical quantity:

Measurement ¼ x  x ½unitð7:45Þ

and the conﬁdence interval goes from x  x to x þ x.

2 The relative error is the ratio of the absolute error to the measured value:

" ¼ x=x ð7 :46Þ

which can be expressed in per cent by multiplying " by 100.

The inverse relation is:

x ¼ x" ð7:47Þ

The results should always be given with their conﬁdence interval (or with an

estimate of the possible error) and with the unit used. The digits in the results

should all be signiﬁcant:

Correct: length ¼420  10 mm or 420 mm within 2 per cent;

Not coherent: length ¼421:728  9:511 mm or 421.728 mm

within 2.255 per cent.

A few statistics

Error analysis cannot be done well without using some basic statistical theory.

There are simpliﬁed methods, which unfortunately often give too large an erro r

154 Ventilation and Airﬂow in Buildings

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Sharp JX-9400 Technical Information Seite 175