4.3 Parameters of statistical analysis

Program gama-local uses two basic statistical parameters

• confidence probability P (default value is 95%, see parameter conf-pr) and
• actual type of reference standard deviation m0_a (parameter typ-m0).

Confidence probability determines significance level on which statistical tests of adjusted quatities are carried. Actual type of reference standard deviations m0_a specifies whether during statistical analysis we use a priori reference standard deviation m0 or a posteriori estimate m0'.

We can choose only the type of actual reference standard deviation (m0 or m0') but not its value. The value corresponds to a priori given value of reference standard deviation or to the results of adjustment. 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 used in the 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 quuantity is computed in dependence of the choice of actual type of reference standard deviation m0_a according to formula

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 probability P.