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# Samples

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# Large number of samples

In case n is greater than or equal to 30 are valid the expressions of the normal distribution and of the lognormal distribution.

If we talk about compensated or uncompensated strengths from direct measurements and in the considered limit state is involved a high volume of soil (eg. in shallow foundations or in a landslide the volume affected by the failure surface is very large) is run a conservative estimate of the average value of geotechnical parameters.

In the case of small volumes of soil, when direct measurements are performed outside of the significant volume and we speak about uncompensated strengths from measurements extrapolated in the calculation of the characteristic value it's estimated a value close to the minimum measured.

In the geotechnical field is quite often met the need to perform some checks in the presence of limited data. This generally happens in projects of modest importance when performing surveys with SPT or laboratory tests on samples extracted, of which only a few affecting the homogeneous layer or the thickness of influence of the limit state. A frequent objection to the statistical treatment is that this can not be done with a few data. On the other hand, using the discrimination and technical judgment and a priori regional and local knowledge, a statistical treatment is possible even in the extreme case of only one data available (or, at least, no data available, in this case by relying solely on prior knowledge).

# Small number of samples

If n is comprised between 5 and 30 are valid expressions of the Student's t-distribution (Gosset, 1908).

For uncompensated strengths from extrapolated measurements can be used the rule of three-sigma replacing, in the calculation of the standard deviation of the population, at the value 6 of the denominator a variable, function of the number of measurements.

# Very small number of samples

If n is between 1 and 5 it will be used the Student's t-distribution (Gosset, 1908).

For uncompensated strengths from extrapolated measurements we estimate the coefficient of variation. The values ​​of the coefficients of variation can be obtained from the scientific literature. The higher the value of the C.O.V. the greater the dispersion of the data, and therefore the lower the minimum value of the parameter estimated.

# Unit sample

In the case of the unit sample is assumed that the single measurement represents the average value having an approximate idea of the variability of the parameter in the considered soil.

In this case it is applied the Bayes' theorem.

# Null sample

In this case we refer to measures available in areas close to the one investigated, considering soils with similar geotechnical characteristics.

For the estimation of m and C.O.V. are used the specifications provided by Orr and Cherubini C. (1999):

with a minimum estimated value of x, b estimated as most probable value of x, c estimated as maximum value of x.

# Outliers

In the presence of values ​​much lower or much higher than most of the data, the determination of the characteristic parameters can be altered significantly. Is therefore necessary to eliminate these extreme values ​​(outliers) before calculating characteristic values​​.