1. CENTENNIAL COLLEGE SCHOOL OF ENGINEERING & APPLIED SCIENCE VS 361 Introduction to GIS ERROR, ACCURACY & PRECISION COURSE NOTES 1

2. Understanding Mapping precision and accuracy imprecise and inaccurate Precise and accurate Precise but inaccurate imprecise but accurate 2

3. Understanding mapping Accuracy and Error with the scale Precision and accuracy are functions of how data are produced or gathered The perfect map is not 100% accurate or precise. It is FIT FOR PURPOSE 3

4. ACCURACY ERROR, ACCURACY & PRECISION... ‘Accuracy is the relationship between the value of a measurement and the “true "value of the dimension being measured’ Geomatics, Kavanagh. The “true "value is a concept as no measurement can be performed perfectly without error. The objective is to minimize error to acceptable levels. My definition : Accuracy is how close a measured value is to the actual (true) value. 4

5. Accuracy is the degree to which information on a map or in a digital database matches true or accepted values. Accuracy is an issue pertaining to the quality of data and the number of errors contained in a dataset or map. In discussing a GIS database, it is possible to consider horizontal and vertical accuracy with respect to geographic position, as well as attribute, conceptual, and logical accuracy. –The level of accuracy required for particular applications varies greatly. –Highly accurate data can be very difficult and costly to produce and compile. 5

6. PRECISION ERROR, ACCURACY & PRECISION... ‘Precision describes the degree of refinement with which the measurement is made’ Geomatics, Kavanagh. Repeatability Confidence levels, I.e. 90% probability. My Definition : Precision is how close the measured values are to each other. 6

7. Any given measurement is precise only to the degree of accuracy with which it was made Precision is a function of the repeatability of a measurement. How precise a measurement can be made using the ruler below? 7

8. Precision refers to the level of measurement and exactness of description in a GIS database. Precise locational data may measure position to a fraction of a unit. Precise attribute information may specify the characteristics of features in great detail. It is important to realize, however, that precise data--no matter how carefully measured--may be inaccurate. Surveyors may make mistakes or data may be entered into the database incorrectly. –The level of precision required for particular applications varies greatly. Engineering projects such as road and utility construction require very precise information measured to the millimeter or tenth of an inch. Demographic analyses of marketing or electoral trends can often make do with less, say to the closest zip code or precinct boundary. –Highly precise data can be very difficult and costly to collect. Carefully surveyed locations needed by utility companies to record the locations of pumps, wires, pipes and transformers cost $5-20 per point to collect. 8

9. Low Accuracy & High Precision Low Accuracy & Low Precision High Accuracy & High Precision Target or Origin So, if you are playing soccer and you always hit the left goal post instead of scoring, then you are not accurate, but you are precise! 9

10. Low Accuracy & Low Precision High Accuracy & Low Precision Low Accuracy & High Precision High Accuracy & High Precision Accuracy And Precision 10

11. Finally......in Statistics explanation........ Origin How close to the origin...... How close measured Values to each other..... 11

12. ERROR Often overlooked and misunderstood. The objective is to minimize error to acceptable levels. The error inherent in a GIS is fundamental to capacity of the system. Error is unavoidable, but must be acknowledged, quantified and planned for. The spatial analysis power of GIS makes the system and results of analysis dependent on the amount of error equated with each and every data se t. ‘An error is the difference between a measured, or observed, value and the true value’. Geomatics, Kavanagh. 12

13. Types of Error in GIS Positional accuracy and precision Attributional accuracy and precision Conceptual accuracy and precision Numeric accuracy and precision 13

14. Positional accuracy and precision…….. Positional accuracy is the expected deviance in the geographic location of an object from its true ground position Applies to both horizontal and vertical positions. Accuracy and precision are a function of the scale at which a map (paper or digital) was created. The mapping standards employed by the United States Geological Survey specify that: "requirements for meeting horizontal accuracy as 90 per cent of all measurable points must be within 1/30th of an inch for maps at a scale of 1:20,000 or larger, and 1/50th of an inch for maps at scales smaller than 1:20,000." Accuracy Standards for Various Scale Maps –1:1,200 ± 3.33 feet –1:2,400 ± 6.67 feet –1:4,800 ± 13.33 feet –1:10,000 ± 27.78 feet –1:12,000 ± 33.33 feet –1:24,000 ± 40.00 feet –1:63,360 ± 105.60 feet –1:100,000 ± 166.67 feet 14

15. Scale is expressed as a ratio : 1:500 means that for every unit of measurement on the map represents 500 units on the ground. Scale = Ground Distance Map Distance Ground Distance = Map Distance x Scale Positional accuracy and precision……… 15

16. Typically large scale data sets typically have more vertices and are greater file sizes. Large scale data can be used at smaller scales, but smaller scale data cannot be used at larger scales. Using data (plotting/overlays) at scales beyond the data’s design does not make the data more accurate--it increases the risk! Typical mapping standards employed by government agencies specify that: ‘requirements for meeting horizontal accuracy as 90 percent of all measurable points must be within 0.5mm for maps at scales of 1:500 or smaller’. Positional accuracy and precision……………….. 16

17. Attribute accuracy and precision The non-spatial data linked to location may also be inaccurate or imprecise. Inaccuracies may result from mistakes of many sorts. Non-spatial data can also vary greatly in precision. Precise attribute information describes phenomena in great detail. For example, a precise description of a person living at a particular address might include gender, age, income, occupation, level of education, and many other characteristics. An imprecise description might include just income, or just gender. The non-spatial data linked to location may also be inaccurate or imprecise. Inaccuracies may result from mistakes of many sorts. Non-spatial data can also vary greatly in precision. Precise attribute information describes phenomena in great detail. For example, a precise description of a person living at a particular address might include gender, age, income, occupation, level of education, and many other characteristics. An imprecise description might include just income, or just gender 17

18. Conceptual accuracy and precision GIS depend upon the abstraction and classification of real-world phenomena. The users determines what amount of information is used and how it is classified into appropriate categories. Sometimes users may use inappropriate categories or misclassify information. - For example, classifying cities by voting behavior would probably be an ineffective way to study fertility patterns. Failing to classify power lines by voltage would limit the effectiveness of a GIS designed to manage an electric utilities infrastructure. Even if the correct categories are employed, data may be misclassified. A study of drainage systems may involve classifying streams and rivers by "order," that is where a particular drainage channel fits within the overall tributary network. Individual channels may be misclassified if tributaries are miscounted. Yet some studies might not require such a precise categorization of stream order at all. All they may need is the location and names of all stream and rivers, regardless of order. 18

19. Computers can only perform numeric calculations out to a certain number of decimal places before introducing rounding errors Since GIS process data digitally, numeric errors may be inserted at the conversion process – A drawing may be put together very precisely and accurately, but not only is that precision and accuracy lost in translation, but likely not accounted for by how the computer stores the resultant data. Numeric Accuracy and Precision 19

20. Different types of mapping handle map distortion differently Conformal maps can be used to describe shape well, but not area Equal distance maps compromise everything but distances Azimuthal maps protect angles Mapping Error........ 20

21. distortion is not constant Azimuthal projections distort from the centre Cylindrical projections distort from the equator Scale is only exact on OS mapping at 2 central axes 180km either side of the central meridian 180 KM W 180 Km E Error at central meridian = !:0.9996 Error = 1:1 Error increases as a function of distance from the equator Mapping Error................. 21

22. The point is that the geo-spatial footprint necessarily contains error. It can’t be avoided, but can be managed. This impacts on any questions we ask of our GIS and the nature of the answers that we get back. Error.... For mapping to be useful certain known elements of the world are discarded. The greater the scale, the more is discarded. Shape, direction and connection may be lost. 22