# NSPS Model Standards Recommend 95% Confidence Levels

I have been doing some research on the NSPS Model Standards which were adopted in 2002 before the widespread use of 3D laser scanners. I think there is a need for an update to address the needs of the lidar industry. Let’s start by taking a look at confidence levels. Next time we will look at types of accuracy standards.

Most standards in use today are specified at the 95 percent confidence level. This means that if we have a measured distance of 1000 feet with stated reliability of plus or minus 0.10 feet at 95 percent confidence level we can be confident that a measurement of that line will be between 999.90 feet and 1000.10 feet 95 out of 100 times.

As an example, a Surveyor establishes two corners by a radial survey. The distance between the corners is computed and shown on the plat. As a check the Surveyor measures directly between the corners not once, but 100 times. The measurements are made on different days and under different conditions. If all corrections for systematic error are made, the average of those measurement probably approaches the correct length of that line and the standard deviation of those measurements is a good measurement of the accuracy of that distance.

If the value of the standard deviation is 0.05 feet, then we would say that the line length is equal to the average distance, plus or minus 0.05 feet at the 68 percent confidence level. In other words, of the 100 measurements there could have been 32 measurements that differed by more than 0.05 feet from the average. At the 95 percent confidence level we can expect that there will be 5 measurements that are 2 times 0.05 feet or 0.10 feet more or less than the average distance.

As a practical matter a Surveyor does not measure a line 100 times. The Surveyor makes one high quality check measurement. The Surveyor assumes that this check measurement is the correct value. The difference between the correct distance and the calculated distance is assumed to approximate the standard deviation. The 95 percent confidence interval value will be 2 times the approximate standard deviation. This double value is the value that is compared in the NSPS Standard. It must be pointed out again that the check measurements should be a very reliable measurement based on a specification that will provide accuracy above those being checked.

For many years experienced Surveyors have recognized a value that they considered an acceptable variation for their measurements in the field. This value is similar to the standard deviation, or a value at the 68 percent confidence level. Therefore, this value is ½ of the value at the 95 percent confidence level that is used in the NSPS Standards. In other words, if the Surveyor’s normally acceptable variation is 0.05 feet, that really is 0.10 feet at the 95 percent confidence level.