Error, Accuracy, Precision and Correction

ERROR, SOURCES OF ERRORS, TYPES OF ERROR

Error: Error is defined as the difference between measured value (observed value) and the true value. No measurement in surveying is exact, no matter how carefully executed. So, the error always presents in the measurement.

Mathematically, Error = Observed Value – True Value

Error can be either:

1. Positive error: If observed value is greater than true value, the error is said to be positive. For e.g. If the person actual height is 180cm and the tape measure shows 185cm, then there is positive error of 5cm.
2. Negative error: If observed value is less than true value, the error is said to be negative. For e.g. If the person actual height is 180cm and the tape measure shows 175cm, then there is negative error of 5cm.

Sources of error

1. Instrumental errors: These are errors that arise due to imperfection or faulty adjustment of the instrument with which measurement is being taken. For example, a tape may be too long or an angle measuring instrument may be out of adjustment. Such errors can be corrected by calibrating or adjusting the instrument properly.
2. Personal errors: These are errors that arise due to human factors such as inattention, inexperience, carelessness, poor judgment or confusion in the mind of the observer. A surveyor may make a mistake in reading or recording a measurement due to carelessness or fatigue. This can lead to wrong calculations and erroneous results. To avoid this error, a surveyor should always check and verify the data before using it and use proper methods of recording and booking.
3. Natural errors: These are errors that arise due to variations in natural phenomena such as temperature, humidity, wind, refraction and magnetic declination. If they are not properly observed while taking measurements, the results will be incorrect. For example, a tape may be 20 meters at 20°C but its length will change if the field temperature is different. Such errors can be minimized by applying suitable corrections or using appropriate instruments.

Types of error

1. Mistake: A mistake is an error that arises from human factors such as inattention, carelessness, poor judgment or confusion. It does not follow any mathematical rule and may be large or small, positive or negative. It cannot be measured but can be detected by repeating the operation or checking the values by independent observations. If a mistake is undetected, it produces a serious effect on the final result. For example, writing 69 instead of 96, counting 8 for 3, forgetting a chain length or making mistakes in using a calculator are mistakes. Mistakes can be avoided by being careful, attentive, experienced and well-trained in surveying methods and instruments.
2. Systematic error (Cumulative error): A systematic error is an error that follows some definite mathematical or physical law and can be corrected by applying a known correction. It is of constant character and has the same sign and magnitude under the same conditions. It may arise due to instrumental, personal or natural causes. For example, a tape that is too long or short, an angle measuring instrument that is out of adjustment, variations in temperature, humidity, refraction etc. are sources of systematic errors. Systematic errors can be reduced by applying corrections based on calibration, adjustment, standardization or compensation of the instruments and measurements.
3. Random error (Compensating error): A random error is an error that occurs due to unavoidable circumstances that are beyond the control of the observer. It may be positive or negative and may change sign. It cannot be accounted for or corrected but can be reduced by taking multiple measurements and applying statistical methods. For example, errors due to imperfection of human sight, touch or hearing, variations in atmospheric conditions, vibrations or disturbances in the field are random errors. Random errors can be reduced by increasing the number of observations and using the mean or median value as the best estimate.

ACCURACY, PRECISION, PERMISSIBLE ERROR AND CORRECTION

Accuracy: Accuracy refers to how close a measured value is to the true value or the expected value. In other words, accuracy is a measure of how well a measurement agrees with the true or expected value. For example, if a person’s actual height is 170 cm and the tape measure shows 169.5 cm, the measurement is accurate. However, if the tape measure shows 165 cm, the measurement is inaccurate.

Precision: Precision refers to the degree of consistency or reproducibility of a measurement. It is a measure of how well repeated measurements of the same quantity agree with each other. For example, if a person’s actual height is 170 cm and three measurements with the tape measure give 164.5 cm, 164.4 cm and 164.6 cm, the measurements are precise. However, if three measurements give 160 cm, 165 cm and 169 cm, the measurements are not precise.

The idea of accuracy and precision can also be demonstrated using the dart system as shown.

 

 Relative Precision: It is the ratio of the standard deviation of the measurement and the meanof the measurement. Mathematically,R

elative precision = Standard deviation / Mean Value

For example: If standard deviation = ±0.1 and mean value = 500 then,

Relative precision = 0.1/500 = 1/500

Degree of accuracy: Degree of accuracy refers to the level of precision or closeness of a measured or calculated value to its true or accepted value. It indicates how well a measurement or calculation represents the actual quantity, with a higher degree of accuracy indicating a smaller margin of error.

For example: If a degree of accuracy is given as 1:2000, it means that for every 2000 units measured, there is an error of 1 unit.

Permissible error: Permissible error refers to the maximum acceptable deviation or discrepancy between the measured value and the true value of a specific quantity. The concept of permissible error is important to ensure that the measurements taken during surveying are within an acceptable range of accuracy, which is necessary for the proper design and construction of civil engineering projects.

For example: Permissible error for taping is 1:2000. It means for every 2000 unit measured; the error should be less than 1 unit.

Correction: A correction is a quantity that is applied to an observed value to reduce or eliminate the effects of errors and obtain an improved value of the observation or function. For example, a correction can be applied to a measured length of a line to account for the effects of temperature, tension, sag, alignment or slope. A correction can also be applied to a measured angle or elevation to account for the effects of refraction, curvature, collimation etc. Corrections are usually based on some mathematical or physical laws that relate the errors to the observed quantities or the conditions of measurement. Corrections can help reduce systematic errors and improve the accuracy and reliability of survey measurements.