Table 2 lists the most common terms used to estimate errors in surveying and mapping. Probable error is the term used to describe the probability, or the confidence level, that 50% of the errors fall within, while 95% errors represents the confidence level that 95% of the measured error values fall under.
| Error | % Error | Constant wrt σ |
|---|---|---|
| Probable Error | 50 | 0.6745 σ |
| Standard Error | 68.27 | 1.000 σ |
| 90% Error | 90 | 1.6449 σ |
| 95% Error | 95 | 1.9599 σ |
| 3σ Error | 99.73 | 3.0000 σ |
The different confidence levels (50% to 99.73% or 3 sigma) listed in Table 2 can be used to express the same accuracy level. For example, accuracy expressed via RMSE and at the 95% confidence level essentially reflects the same accuracy, differing only in their statistical confidence assignments.
To clarify these distinctions, consider the following example: In Figure 5, colored balls symbolize errors identified during an accuracy assessment using independent check points. Ball diameters indicate varying error magnitudes for each check point, while the funnel’s spout diameter corresponds to the maximum allowable error for each statistical metric—50%, 90%, 95%, and 97.73% confidence levels. For instance, Funnel D’s larger spout accommodates the greatest error, representing the 97.73% confidence level.
If users unfamiliar with these statistical terms are presented with various accuracy figures, they would likely select the smallest value—in this case, 6.74 cm associated with the 50% confidence level—as it suggests tighter accuracy. Conversely, producers might prefer the larger value of 30 cm at the 97.73% confidence level, anticipating greater flexibility. However, both selections are based on a misunderstanding: both values reflect the same underlying accuracy, differentiated solely by the proportion of checkpoints meeting that threshold. Specifically, for the 6.74 cm figure at the 50% confidence level, only half of the check points must meet this criterion, whereas at 30 cm and the 97.73% confidence level, nearly all must comply.
This nuanced distinction often leads to confusion among end users, prompting the decision to remove the 95% confidence level and rely exclusively on RMSE in the latest version of the accuracy standards of the American Society of Photogrammetry and Remote Sensing (ASPRS), which provides a clearer and more consistent metric for accuracy.
