Sources of Error

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• I can identify the types of experimental errors and their sources.

• I can explain how these errors can be reduced.

There are two kinds of numbers in the world;

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1. Exact numbers - (those whose values are known exactly)

EXAMPLE: There are exactly 12 eggs in a dozen.

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2. Measured numbers - (those whose values have some uncertainty)

EXAMPLE: Height of student, Temperature of student.

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• Accuracy refers to the closeness of a measured value to a standard (known or true) value

• Precision refers to how closely individual measurements agree with each other.

Measurement Error (also called Observational Error) is the difference between a measured quantity and its true value. It includes random error and systematic error.

• Systematic Errors - Systematic errors arise from incorrect procedure, incorrect use of instruments, or failure of some value to be what it is assumed to be

• This type of error is repeated consistently every time the instrument is used or the method is followed, which affects the accuracy of all readings obtained example making observations too low.

• To reduce systematic errors:

  • Instruments should be recalibrated, or different instruments should be used

  • Corrections or adjustments should be made to the technique

• Personal Errors - personal bias of the observer in reading, recording of observation or following a method.

  • to reduce this error, one must observe with proper caution and disregard personal biases

• External Error is caused by external conditions such as temperature, pressure, wind or humidity.

  • to reduce this error, one must improve the experimental techniques, use calibrated instruments​

• Random Error - is one in which positive and negative errors are equally probable This is due to unknown factors and unpredictable variations in an experiment usually beyond the control of the observer.

• ​Random errors cause unpredictable fluctuations in an instrument’s readings as a result of uncontrollable factors, such as environmental conditions

• This affects the precision of the measurements taken, causing a wider spread of results about the mean value

• To reduce random error:

  • Repeat measurements several times and calculate an average from them or apply descriptive measures

• Central tendency or location is a value around which the observations tend to cluster and which typifies their magnitude.

  • The arithmetic mean or average, median and mode are descriptive measured under this class.

• ​Dispersion or variability is the scattering of the values of a set of observations from the average value.

  • Some of the statistical tools that measure the dispersion or variability are the deviation, average deviation, variance, and standard deviation.

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• ​Percentage error is defined as the difference between the experimental value and the standard value, divided by the standard value, multiplied by 100 percent.

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• The percentage difference is used when neither of the quantities may be taken as a “standard value”. In such cases, their average or mean value (𝑥) may be used in place of a standard value.

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