164
11 Errors
count. Very large outliers can dramatically change your results, especially when you
are dealing with small sample numbers. If you have an unexpectedly small or large
result compared with the rest of the sample, you may wish to investigate why this
might be. Often it is an indication of an actual error (i.e., a mistake has been made)
rather than a true result. If you cannot find the mistake, you may exclude that result,
but you must note it in your results, as it might have been significant. In such cases it
may also be worth increasing your sample size to ensure that it is indeed a statistical
anomaly.
11.3.1 Systemic Errors
As stated above, there are two kinds of errors: random errors and systemic errors.
Systemic errors can also be divided into errors that can be addressed directly and
those that cannot. For example, the bias added during the read process is largely
unknown directly but is removed by the subtraction of a bias frame. Likewise, the
dark current is an offset that can be largely subtracted by the dark frame, although
there is an additional random element in the dark current. The nonuniformity of the
illumination of the CCD and the pixel sensitivity is largely constant over short time
scales and can also be considered in part systemic. Unfortunately, perfect flat fields
are extremely difficult to produce and quickly become dated as dust collects on the
optics. So although flat field subtraction deals with systemic errors, there is always
a degree of random error inside a flat, which, as we will see, can be significant.
However, systemic errors will always be of the same sign and magnitude for all your
readings.
There may well be other unadjusted or unknown systemic errors. For example,
the shutter on your camera might be sticking slightly so that your 1 s exposure is, in
fact, 1.01 s. This will increase the number of photons you detect in a 1 s exposure.
Likewise, you might be using a reference star to determine the magnitude of a star
with an unknown magnitude. If the magnitude of the reference star is overreported
by two magnitudes, you will have a two-magnitude systemic error.
Systemic errors are extremely difficult to detect. To avoid them, you should ensure
that your instrument is correctly calibrated. If you suspect that you might have a
significant systemic error, then compare your results with a known set. If your mean
results constantly appear outside of the uncertainty range of the known results, you
might well have an unknown systemic error, especially if they constantly appear on
the same side of the known result.
A tale of caution. In 2011, the OPERA experiment mistakenly announced that
they had observed neutrinos travelling faster than light. It turned out that an ill-fitting
fibre optic cable was causing a systemic error, and in fact, the results were entirely
consistent with previous experiments.
11 Errors
count. Very large outliers can dramatically change your results, especially when you
are dealing with small sample numbers. If you have an unexpectedly small or large
result compared with the rest of the sample, you may wish to investigate why this
might be. Often it is an indication of an actual error (i.e., a mistake has been made)
rather than a true result. If you cannot find the mistake, you may exclude that result,
but you must note it in your results, as it might have been significant. In such cases it
may also be worth increasing your sample size to ensure that it is indeed a statistical
anomaly.
11.3.1 Systemic Errors
As stated above, there are two kinds of errors: random errors and systemic errors.
Systemic errors can also be divided into errors that can be addressed directly and
those that cannot. For example, the bias added during the read process is largely
unknown directly but is removed by the subtraction of a bias frame. Likewise, the
dark current is an offset that can be largely subtracted by the dark frame, although
there is an additional random element in the dark current. The nonuniformity of the
illumination of the CCD and the pixel sensitivity is largely constant over short time
scales and can also be considered in part systemic. Unfortunately, perfect flat fields
are extremely difficult to produce and quickly become dated as dust collects on the
optics. So although flat field subtraction deals with systemic errors, there is always
a degree of random error inside a flat, which, as we will see, can be significant.
However, systemic errors will always be of the same sign and magnitude for all your
readings.
There may well be other unadjusted or unknown systemic errors. For example,
the shutter on your camera might be sticking slightly so that your 1 s exposure is, in
fact, 1.01 s. This will increase the number of photons you detect in a 1 s exposure.
Likewise, you might be using a reference star to determine the magnitude of a star
with an unknown magnitude. If the magnitude of the reference star is overreported
by two magnitudes, you will have a two-magnitude systemic error.
Systemic errors are extremely difficult to detect. To avoid them, you should ensure
that your instrument is correctly calibrated. If you suspect that you might have a
significant systemic error, then compare your results with a known set. If your mean
results constantly appear outside of the uncertainty range of the known results, you
might well have an unknown systemic error, especially if they constantly appear on
the same side of the known result.
A tale of caution. In 2011, the OPERA experiment mistakenly announced that
they had observed neutrinos travelling faster than light. It turned out that an ill-fitting
fibre optic cable was causing a systemic error, and in fact, the results were entirely
consistent with previous experiments.