4.2 Accuracy, Precision, and Error Types
Key Takeaways
- Accuracy is closeness to a true or accepted value; precision is repeatability; resolution is the smallest increment the instrument or dataset can record.
- Systematic errors bias every observation the same way, random errors scatter about a mean, and blunders are mistakes. Planning cannot average out a bias you never check.
- Allowable survey error is set by the use of the data—design grade, earthwork, or mapping—not by the finest digit the data collector can display.
- Map, construction, and control products have different accuracy orders. FGDC NSSDA reporting and Caltrans survey-manual classes are professional-practice examples, not Board-published CES numeric cutoffs.
- Redundant observations reveal blunders and reduce random error of the mean. If a pad must finish within 0.05 ft, a one-third survey budget points to about 0.02 ft shots on control several times tighter, with spacing dense enough to catch grade breaks.
The 2022 CES test plan groups accuracy and precision with data collection, measurements, errors, and the application of the data. That last phrase is the planning key. You do not start from the prettiest instrument specification sheet. You start from what the design, earthwork, or map must support, then specify control, methods, redundancy, and spacing so the delivered dataset can actually be used.
Accuracy, precision, and resolution
Accuracy is closeness to a true or accepted value (a published benchmark, a calibrated baseline, or a higher-order check survey). Precision is the scatter of repeated measurements—how tightly they cluster, whether or not that cluster sits on the truth. Resolution is the smallest increment the instrument, rod, or digital elevation model can record or display (0.01 ft on a data collector, 0.001 m on a digital level, a 1-m DEM cell).
A total station that repeats 142.18, 142.19, 142.18, 142.19 ft is precise. If the true distance is 142.05 ft, the set is not accurate; a scale, prism-constant, or calibration bias is sitting in every shot. Displaying 142.184 ft does not create 0.001-ft accuracy; that extra digit is resolution, not a proven error budget.
On a map, resolution also appears as pixel size or DEM cell size. A 1-m cell cannot faithfully locate a 0.3-ft curb face even if the lidar RMSEz looks attractive in open terrain. Planning must name all three: how close to truth, how repeatable, and how fine the sampling is.
| Term | Question it answers | Planning failure if ignored |
|---|---|---|
| Accuracy | How close is this to the datum or check survey? | Beautiful contours that are 0.4 ft high as a set |
| Precision | How much do repeats disagree? | A single lucky shot treated as a benchmark |
| Resolution | What is the smallest stored increment or cell? | 1-ft design grades interpolated from a 2-m DEM |
Systematic error, random error, and blunders
Systematic error is a consistent bias: collimation on a level, an uncorrected prism constant, EDM scale from temperature and pressure, a geoid model that does not fit the project, or refraction that always lifts long trig sights. Repeating the same setup does not cancel a systematic error. You remove it by calibration, reversal (double centering, balancing foresights and backsights), formulas, or a better model.
Random error is the leftover scatter after you have attacked the bias: small pointing differences, momentary refraction, rod bubbles a little off. Random error is reduced by redundancy—more independent observations—and is described with standard deviation or RMSE, not by the single smallest residual you happened to see.
A blunder is a mistake: reading 5.12 instead of 6.12, occupying the wrong hub, using the wrong target height, or coding a flowline as top of curb. Blunders are not 'large random errors.' They are found by checks: closing a loop, repeating a critical invert, comparing an independent method, or looking at a shot that violates gravity (water running uphill on the map).
Planning implication: a scope that says 'one GNSS occupation on the site benchmark' has no check against a blunder. A scope that says 'closed level loop plus two independent GNSS ties' can expose the blunder before design uses the number.
Allowable error comes from the use of the data
The same total station can support a planning exhibit, a mass-grading model, or a building-pad spec. The allowable survey error is not the instrument's advertised accuracy. It is a fraction of the construction or mapping tolerance so that survey error, interpolation, and construction process still fit inside the specification.
Typical uses, as professional judgment rather than Board numeric cutoffs:
- Mapping / exhibits: contour interval and smallest plotted feature set the need. A 2-ft contour exhibit does not justify 0.01-ft pad procedures over 80 acres.
- Earthwork: volume is sensitive to a systematic vertical bias. A 0.10-ft high existing-ground model on a 10-acre cut is a real money error even if precision looks tight.
- Design grade / drainage: inverts, pad elevations, and flowlines need hundredths of a foot relative to project control, plus shot density at breaks.
- Construction staking: the layout must be tighter than the installer can use, or the survey consumes the entire spec.
A useful planning split, used in many offices and consistent with ASPRS-style 3:1 thinking for check control, is to keep the survey contribution to about one-third of the construction tolerance, keep control several times better than the shots, and spend the rest on interpolation and construction. That split is not a BPELSG-published CES cutoff. It is how you keep 0.05 ft from being eaten twice—once by the survey and once by the grader.
Map versus construction versus control (conceptual orders)
Think in orders of product, not in a fake Board table of millimeters.
Control is the skeleton. Horizontal and vertical control are planned to be substantially better than the mapping or layout they support, so control error is a small term in the budget. Transportation agencies publish control orders and closure limits in survey manuals. Caltrans Surveys Manual classes and similar agency tables are contract and professional-practice examples. They are not Civil Engineering Surveying cut scores.
Mapping products are often specified with RMSE or with 95-percent accuracy in ground units. The Federal Geographic Data Committee National Standard for Spatial Data Accuracy (NSSDA) is a reporting standard: compare the dataset to independent higher-accuracy check points, compute RMSE, then report 95-percent accuracy. Under the usual NSSDA assumptions, horizontal accuracy at 95% ≈ 1.7308 × RMSE_r and vertical accuracy at 95% ≈ 1.9600 × RMSE_z. NSSDA does not tell you the pass/fail number; the project owner does. Older National Map Accuracy Standard (NMAS) language (for example, 90 percent of tested elevations within one-half contour interval) still appears in textbooks; know it as a mapping idea, not as a hidden CES formula.
Construction accuracy is relative to project control and to the feature being built. A curb stake can be 'good' at 0.02 ft in elevation on the job datum even if the job datum is 0.15 ft off a distant NAVD88 benchmark the contractor will never use. Mixing map-absolute language with construction-relative language is a classic planning error: you either over-specify a citywide geodetic campaign or under-specify the pad.
ASPRS positional accuracy standards similarly expect the check-point survey to be about three times more accurate than the geospatial product being tested. Again, that is professional practice for specifying airborne mapping, not a Board CES numeric spec.
Propagation at the planning level
If independent error sources combine, a planning-level root-sum-square (RSS) model is:
σ_total ≈ √(σ_control² + σ_instrument² + σ_setup² + σ_interpolation²)
If each of four similar sources is 0.01 ft, the combination is about 0.02 ft—not 0.04 ft, and not 0.01 ft. If one source (a 0.05-ft GNSS vertical) dominates, buying a 0.003-ft digital level for the same points does not rescue the budget.
Redundant observations matter for two different reasons:
- They detect blunders. A loop that miscloses by 0.18 ft is a warning, not a number to bury in an unadjusted map.
- They reduce random error of the mean. Averaging n independent, similar observations cuts the random component by about √n. Averaging does not remove systematic scale error, and it does not legalize a misidentified point.
Planning therefore specifies: close the level loop; occupy GNSS control twice or tie to a second mark; turn angles by repetition or direct-and-reverse; shoot critical inverts twice. Side shots with no check are the weakest points in the network even if the instrument is expensive.
Worked example: a pad that must be within 0.05 ft
Survey share, control, RSS, and spacing
A building pad must finish within 0.05 ft of design elevation. That 0.05 ft is a construction specification. It is not the survey's entire budget.
Step 1 — survey share. Using a one-third planning split (professional practice, not a Board cutoff), the survey contribution target is about 0.05 / 3 ≈ 0.017 ft, commonly rounded to 0.02 ft for shots used to check grade relative to project control.
Step 2 — control. If shots need ~0.02 ft, a 3:1 control-to-product idea puts vertical control near 0.02 / 3 ≈ 0.007 ft on the project datum. That is differential leveling from a nearby benchmark (or a very short, carefully run trig scheme tied to a level), not a single RTK shot under a tree. GNSS may still bring a datum onto the site, but the pad control itself is leveled.
Step 3 — RSS check. Suppose control σ = 0.007 ft, instrument-and-rod σ = 0.012 ft, and interpolation/spacing σ = 0.010 ft. Then
σ_survey ≈ √(0.007² + 0.012² + 0.010²) = √(0.000049 + 0.000144 + 0.000100) = √0.000293 ≈ 0.017 ft.
That leaves roughly 0.03 ft of the 0.05-ft spec for grading equipment and inspection—tight, but coherent. If you instead allow 0.05-ft GNSS shots on 0.05-ft control, RSS already exceeds the construction spec before the blade moves.
Step 4 — shot spacing. Accuracy of each shot is useless if the high spot is between shots. On a 150 ft × 150 ft pad, a 50-ft grid is only a 4 × 4 edge pattern (16 points). A mound 0.10 ft high in the center of a panel interpolates as 'on grade' if you only hold the corners. A 25-ft grid (7 × 7 = 49 points) plus edge breaklines is a planning response to that interpolation risk, not a decoration. Add extra shots at suspected high/low points, inlets, and slab edges. If the surface is a true plane and the contractor will proof-roll it, you can justify a slightly coarser grid—but you write that assumption down.
Step 5 — method. From Section 4.1, this pad is not an ALS-only job. Level the control, shoot the pad with a total station or short-range level, and use ALS or photographs only as surrounding context.
Exam traps: treating resolution (0.001 ft displayed) as accuracy; calling a tight cluster 'accurate' when it is biased; citing a made-up BPELSG millimeter table; giving the entire 0.05 ft to the survey; spacing shots so far apart that interpolation is the largest error source.
A total station repeatedly measures the same distance as 142.18, 142.19, 142.18, and 142.19 ft, but an independent calibrated baseline shows 142.05 ft. This pattern is best described as:
Design of a building pad requires finished grade within 0.05 ft of design elevation. Using a planning error budget that assigns about one-third of the construction tolerance to survey (an office split, not a BPELSG numeric spec), the grade-check shots should target about:
Why do survey plans specify redundant observations such as a closing level loop, direct-and-reverse angles, or a second GNSS occupation on a control mark?