What's the difference between systematic and random error?

Answer 1

Systematic errors bias the measurements in a reproducible (predictable IF we knew the cause) way. They do NOT have to be proportional, nor of the same sign. For instance if my tricorder (ala Star Trek) ignored values less than 0.001 and values greater than 1000 then the measurements would have a systematic bias if the actual readings should have been between 0.0001 and 2000. The net effect of this on the average would be impossible to figure out after the event.
"Random" error is by definition unpredictable. Often, random error is the result of multiple causes and so tends to have a "normal" (gaussian or boltzman) distribution which allows us, with enough measurements, to "average out" the error. Other types of random error (noise) known, see for example signal processing.

Answer 2

Systematic errors are cumulative in nature. They can be modeled by mathematical functions, and once their value is computed they may be corrected for. An example of a systematic error is a 100 foot steel tape that is 0.015 foot too long (measures short). A line that is measured as 1000.000 feet with said tape should be reported to be 1000.000 + (10 x 0.015) = 1000.150 feet long. The systematic error in the measured value is - 0.150 feet. It is important to realize that these errors cannot be "adjusted out" of a network; they must be removed from survey data before an adjustment is performed. Instruments that are out of adjustment are a source of systematic error.

Random errors, on the other hand, cannot be described by a predetermined mathematical model; rather, they obey the laws of probability. If an observation is repeated over and over many times these errors will tend to cancel each other. An example of random error is the error that comes from interpolation. Consider the surveyor who runs a differential level loop recording his observations to the nearest 0.001 foot while reading a rod graduated to 0.01 foot. Some of his estimates will naturally be too high while others will be too low. However, the laws of probability say that in the long run the highs will probably cancel the lows. All measurements, no matter how carefully made, contain random error. Random errors may be estimated and accounted for by least squares adjustment techniques.

Answer 3

Random errors cancel out, if there are lots of them. Some guesses are too large, some too small. The average still comes out near the true mean.

Systematic errors only go in one direction (all too high or all too low). The average of the guesses is quite different from the true mean.

Random errors can be lived with. Systematic errors are fatal for a study.

Answer 4

systematic errors are due to testing error biases. random errors are due to chance.

Answer 5

no clue