Where Theory Meets Practice Archives
Surveying Statistics
The t Distribution, Part 2 In the previous article (July 2015), I introduce the concept of sampling distributions and the need to use these distributions to analyze small samples of data. In surveying, observing small samples is typical where angles are often observed only two or four times, and repeated distance observations simply means pushing […]
Sampling Statistics
The Chi-squared Distribution In my most recent article (August 2015), I discuss Student’s t distribution and how its properties can be used to isolate blunders in observations. Another sampling distribution that is commonly used in least squares adjustments is the χ2 (chi-squared) distribution. It appears in the form of what is typically called the “goodness of fit” […]
A Correctly Weighted Least Squares Adjustment, Part 1
Problems from using computed standard deviations. According to the 2011 Minimum Standard Detail Requirements for ALTA/ACSM Land Title Surveys, “‘Relative Positional Precision’ means the length of the semi-major axis, expressed in feet or meters, of the error ellipse representing the uncertainty due to random errors in measurements in the location of the monument, or witness, […]
A Correctly Weighted Least Squares Adjustment, Part 2
Estimating Uncertainties In the previous article (January 2016), I point out the unreliability of sample standard deviations as estimates for population standard errors when the number of repeated observations is very small, which is typically the problem in surveying. In this article I look at how we can estimate the standard errors for observations based […]
A Correctly Weighted Least Squares Adjustment, Part 3
Estimating Standard Errors in Angular Observations In the previous articles (January and February 2016) I discuss the unreliability of standard deviations when they are computed from a small sample of observations, as well as how to estimate errors in centering an instrument over a well-defined point and how to estimate the standard error for electronically […]
A Correctly Weighted Least Squares Adjustment, Part 4
Correct Weights In previous articles (January, February, and April 2016) I discuss the unreliability of standard deviations when they are computed from a small sample of observations and their use in developing the stochastic (weight) model for a least squares adjustment. This is followed with how to: (1) estimate errors in centering an instrument over […]