ERROR IN EXPERIMENTS

Random Errors

-caused by unknown and unpredictable changes in the experiment. These changes may occur in the measuring instruments or in the environmental conditions.

-statistical methods may be used to analyze the data. 

-the mean m of a number of measurements of the same quantity is the best estimate of that quantity

-the standard deviation s of the measurements shows the accuracy of the estimate.

-The precision of a measurementis (which is limited by the random errors) is how close a number of measurements of the same quantity agree with each other and can be determined by repeating the measurements.

 

The Gaussian normal distribution. 

m = mean of measurements, s = standard deviation of measurements. 

68% of the measurements lie in the interval m - s < x < m + s; 

95% lie within m - 2s < x < m + 2s;  

99.7% lie within m - 3s < x < m + 3s.

 Examples of random errors are: 

1.electronic noise in the circuit of an electrical instrument

2.irregular changes in the heat loss rate from a solar collector due to changes in the wind.

Systematic Errors

-come from the measuring instruments cause by : 

1.something wrong with the instrument or its data handling system

Systematic Errors that occur with instruments having a linear response: 

i.Offset or zero setting error in which the instrument does not read zero when the quantity to be measured is zero. 

ii.Multiplier or scale factor error in which the instrument consistently reads changes in the quantity to be measured greater or less than the actual changes.

 

Systematic errors in a linear instrument (full line).
Broken line shows response of an ideal instrument without error.

Systematic errors also occur with non-linear instruments when the calobration of the instrument is not known correctly.

2.the instrument is wrongly used by the experimenter
i.errors in measurements of temperature due to poor thermal contact between the thermometer and the substance whose temperature is to be found

ii.errors in measurements of solar radiation because trees or buildings shade the radiometer.

The accuracy of a measurement (which can be reduced by systematic errors) is how close the measurement is to the true value of the quantity being measured. 

Systematic errors are difficult to detect even for experienced research workers.