and t95%n-2 is Student's t-value for (n - 2) degrees of freedom at the 95% confidence level. The worked examples in Section 5.7 illustrate the use of these equations in practice.

5.5.4 Dealing with small data sets

The techniques discussed above may be used to determine the characteristic value of a geotechnical parameter, provided there is sufficient data to justify the assumptions made. Others28 have argued that statistical methods could be used when the number of data points n is greater than 13 (but we rarely have this much data) and, when the number is less than 13, a pure statistical approach is too pessimistic to be of practical value.

A simple way to estimate the characteristic value from limited knowledge of the ground properties is to assume:29

X, = mx + 'f - [ Xmi" + 4X6mod- + X- ) + 2(Xmax - Xm, )

where mX and sX are the mean and standard deviation of X; Xmin and Xmax are the estimated minimum and maximum values of X; and Xmode is the most likely value of X. The term for sX assumes that Xmax and Xmin are three standard deviations above and below the mean value mX, and hence are extreme values not normally measured in field or laboratory tests.

This formula is valid when assessing characteristic values of independent soil samples, for which their autocorrelation1 may be neglected. In practice, samples may be considered independent when their locations differ by more than the so-called 'auto-correlation distance', which is typically 0.2-2m vertically (depending on depositional history) and 20-100m horizontally.30

An alternative to the above approximation, assuming Xmax and Xmin are two standard deviations above and below mX, is:

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