5.3 Parameters of statistical analysis

Program gama-local uses two basic statistical parameters

• confidence probability P (default value is 95%, see input XML parameter conf-pr) and
• actual type of reference standard deviation m0_a (parameter sigma-act).

Confidence probability determines significance level on which statistical tests of adjusted quantities are carried. Actual type of reference standard deviation m0_a specifies whether during statistical analysis we use an a priori reference standard deviation m0 or an a posteriori estimate m0’. On the type of actual reference standard deviation depends the choice of density functions of stochastic quantities in statistical analysis of the adjustment.

• A priori reference standard deviation m0 is an estimate of the standard deviation of an observation with the unit weight. Numerically it is a scaling factor used in calculation of the weights. If we change m0, only the sum of weighted residuals squares is changed and all adjustment results remain the same (there is just one least squares solution). m0 can be selected in cases when we know its value in advance and with sufficient reliability. Another situation when m0 is used are networks with low number of degrees of freedom (poorly overdetermined systems) or when veen degrees of freedom is zero. Examples may be analysis of network models etc.
• A posteri estimate of reference standard deviation m0’ is used in cases when a priori value of reference standard deviation m0 is not known and when degrees of freedom is sufficiently high and reliable for empirical estimate of m0’.

The standard deviantion of an adjusted quantity is computed in dependence of the choice of actual type of reference standard deviation m0_a according to formula

m0_a sqrt(q)

where q is the weight coefficient of the corresponding adjusted unknown parameter or observation. Apart from the standard deviation, program gama-local computes for the adjusted quantity its confidence interval in which its real value is located with the probabilityP.

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