1. Introduction precision and accuracy
An Archery Example
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3. Accuracy and Precision

4. Accuracy- indicates the difference between measured value and the expected (true) value. If observed (measured) values are near the expected (true) value, the measurement has high accuracy.
Precision- indicates the differences among each measured value; if measured values are close together the measurement has high precision.

5. A Precise Score 4 Arrows from Contestant #2 14th Annual
Archery Contest
4 Arrows from
Contestant #1
The two contestants are highly precise, however, their accuracy is not very good. There is some subtle problem with their equipment or how they are using it.

6. A Precise and Accurate Score
14th Annual
Archery Contest
4 Arrows from
Contestant #3
The third contestant has a score that is precise and accurate.

7. Neither Precise nor Accurate Score
14th Annual
Archery Contest
14th Annual
Archery Contest
Neither Precise nor Accurate Score
Archery Contest
14th Annual
4 Arrows from
Contestant # 4
Archery Contest
14th Annual
The fourth contestant should not quit their other sport.
(This contestant needs to work on the concept of 4 arrows as well)

8. Accuracy of a measurement describes the difference between an observed value and the expected (true) value. If observed value is near the expected (true) value, measurement has high accuracy.
Precision of a measurement describes the differences among individual measurements themselves; if they are close together there is high precision.

9. Accuracy and Precision
How do we quantify these observations so that we can attach a number to the ideas of precision and accuracy of each event?
Accuracy and precision have no quantitative significance, and are used in a rough descriptive sense only.

10. Error and Deviation
Error expresses accuracy in the form of a number that relates the measured value to the true (expected) value.
Deviation expresses precision in the form of a number that relates the measured value to its closeness to other measured values.

11. Error
Error expresses accuracy in the form of a number that relates the measured value to the true (expected) value.
Error is the numerical difference between the observed value, xi and expected (true) value, .

12. Error
Error is the numerical difference between the observed value, xi and expected (true) value, .
For this case, the expected
position on the target for the expert is assigned the true (expected) score. This position is assigned a distance value of 0 and distance from this perfect score point on the target to an actual contestant point on the target is the error.

13. Error
Error is the numerical difference between the observed value, xi and expected (true) value, .
This is the center point that is used to measure a radius
to each of the 8 target points shown.

14. Error Contestant # 1 try # error 1 8.0 2 9.5 3 9.5 4 8.3
Error is the numerical difference between the observed value, xi and expected (true) value, . 11 9 7 4 6 10
Contestant # 1
try # error 2 6 1
8.0 2
9.5 3
9.5 4
8.3
This is the center point that is used to measure a radius
to each of the 8 target points shown.

15. Error Contestant # 2 try # error X5 ? 10.5 X6 10.5 X7 9.5 X8 9.5
In this example, the perfect score, , is equal to zero. A contestant's score, xi, is subtracted from to indicate the error. X5 ?
10.5 X6
10.5 11 X7
9.5 9 6 X8
9.5 7 5
= perfect score = 0
Error =(observed score, xi ) - 2
X = = 10.5
X = = 8.0
Error Calculation
X = = 9.5
X = = 9.5
X = = 8.3
X = =10.5
X = = 9.5
X = = 9.5 2
Contestant # 1
try # error X1
( ) = 8.0 X2
( ) = 9.5 X3 X4
( ) = 8.3 6 8 10

16. Deviation 11 9 6 7 5 2 2 6 11 6 8 10

17. Deviation Contestant # 1 1 8.0 2 9.5 3 4 8.3 try # Xi Score
One measure of precision is the numerical difference between the observed value, xi , and mean value for that group of measurements.
This is known as the deviation.
Deviation
Deviation Calculations X1
= - 0.8 = X2
= 0.7 X3 X4
= -0.5 11
Contestant # 1 1
8.0 2
9.5 3 4
8.3
try # Xi
Score X1 X2 X3 X4 9 6 7 5 2
Note: X1 = = 8.8 2 6 11 6 8 10
Mean score for contestant # 1
( ) n =
(X1 + X2 + X3 + X4)
(35.3) 4
(8.83)
X1 =

18. Deviation Contestant # 2 1 10.5 2 3 9.5 4 try # Xi Score X5 X6 X7 X811
Deviation Calculations 9 6 7 X5 = X2 = X7 = X8 = X6 5 2 2 6
Note: X2 = 10.0 8 10
Mean score for contestant # 2
( ) n =
(X5 + X6 + X7 + X8)
(40.0) 4
(10.0)
X2 =

19. Why? Who won? 14th Annual Archery Contest # 2 ?
Error and Deviation
Accuracy and Precision
Contestant # 2
Note: X2 = average score for contestant #2 = 10.0
Average Error
Average Deviation
10.0
0.1
14th Annual
Archery Contest 10 8 6 5 2 9 7 11
# 2 ?
Why is Contestant #1 average deviation = 0?
This person did not always hit the exact same spot on the target!
Why?
Who won?
Which contestant is
a better archer?
# 1 ?
Note: X1 = average score for contestant #1 = 8.8
Contestant # 1
Average Error
Average Deviation
8.8
0.0
Why are the average scores equal to the average errors?
How can we change the average deviation calculation so that a zero value only happens when all the arrows hit the same spot?
Does that always happen?

20. Accuracy and Precision
( a quick concept review)

21. Accuracy and Precision
( a quick concept review)

22. An example for Accuracy or Precision?
Accuracy and Precision
( a quick concept review)
An example for Accuracy or Precision?
An example for Error or Deviation?

23. Accuracy and Precision
( a quick concept review)

24. An example for Accuracy or Precision?
Accuracy and Precision
( a quick concept review)
An example for Accuracy or Precision?
An example for Error or Deviation?