Chi-square distribution is a probability tool used in hypothesis testing. In the case of least squares adjustment, original observations are compared to adjusted observations and evaluated in terms of how widely these observations vary with respect to each other.
The following formula is used to calculate X2, the chi-square value:
where
- m = the number of observation equations
- vi = the residual value from the V matrix
- pi = the corresponding weight from the P matrix
The X2 value is small if the adjusted observations are close to the corresponding measured observations. This is referred to as a "good fit." A goodness-of-fit test is then conducted in which the X2 value is compared to those from a table of critical values of chi-square distribution at the 5% level. A X2 value below that listed in the table passes, while a larger X2 value than that listed fails, indicating possible blunders in the initial surveying measurements.