This could be random variation of the atmosphere over a short period, or
random measurement error, or some combination.
Nondifferential misclassification because of
random measurement errors, especially for VCAM - 1, may have attenuated the observed associations.
If we have inadequate sampling, and short time intervals, the statistical uncertainties from random fluctuations and
random measurement errors can be large, but would tend to cancel out as the number of observations and length of time increases.
Lots of factors make measuring global temperature a difficult task, such as sparse data in remote places,
random measurement errors and changes in instrumentation over time.
Estimates of biases from the literature are typically of order 0.1 degC and
random measurement errors for ship data are typically estimated to be around 1 degC.
Not exact matches
To correct the dietary questionnaire data for
measurement errors, intake data were calibrated with standardized 24 - hour dietary recall interviews on administered to a
random sample of 8 % of the cohort.
The
measurement errors on the two tests, taken months apart from each other, are unlikely to be related (after all, these are
random influences).
Such results can be a real systematic effect, e.g., cooling by planted vegetation or the movement of a thermometer away from the urban center, or a
random effect of unforced regional variability and
measurement errors.
The variance in individual samples is not a result of
measurement errors with known Gaussian
random noise.
But the SEM is standard deviation of the results divided by the number of
measurements... so your individual
errors are indeed accounted for, whether they are
random or are from other sources.
However, these
measurements contain non-negligible
random errors and biases owing to the indirect nature of the relationship between the observations and actual precipitation, inadequate sampling, and deficiencies in the algorithms.
The principal scientific objective is to make global SSS
measurements over the ice - free oceans with 150 - km spatial resolution, and to achieve a
measurement error less than 0.2 (PSS - 78 [practical salinity scale of 1978]-RRB- on a 30 - day time scale, taking into account all sensors and geophysical
random errors and biases.Salinity is indeed a key indicator of the strength of the hydrologic cycle because it tracks the differences created by varying evaporation and precipitation, runoff, and ice processes.
Increasing the number of
measurements in this case, does decrease the
random component of the instrumental
error by 1 / SQRT (n) where n is the the number of observations.
It is closer to the 0.5 / sqrt (25) = 0.1 cm uncertainty that one would expect if there were
random errors in the
measurements.
Human
error,
random fluctuations, biases, varied weather conditions at times of
measurement, limited geographic coverage, missing data...... etc..
Now, as you say, there are all sorts of problems with the historical records of sea level but — just as with temperatures — it is likely that
measurements from the satellites will be more accurate and less prone to
random variation and sampling
error than
measurements from ground based sensors.
It is certain that they made plenty of mistakes, introducing a large degree of
random error into the
measurements.
The math behind the Law of Large Numbers goes back to Jacob Bernoulli in 1713, and is based on the statistics of
measurements and
random errors.
Later, when the signal is extracted from the
random noise, from the
measurement error and the deliberate
measurement errors, and all of that extracted from the millennium temperature changes, can the «chicken and egg» relationship be considered.
When I simulated how many times would actually measured
random value would be indeed true highest value (sd = 0.7 was 0.7 for value and 0.5 for a
measurement error, both normally distributed), I've got the following results (Number of years, being highest percentage): 2, 0.801146 10, 0.532256 20, 0.46076 50, 0.384286 100, 0.338422 135, 0.32037 200, 0.30028 1000, 0.232482 10000, 0.165234 I am not sure, but can we conclude that 38 % likelihood was actually not that small?
For independent
random errors with the same mean (i.e., no drift), the accuracy increases with the square root of the number of
measurements.
Uncertainties associated with «
random errors» have the characteristic of decreasing as additional
measurements are accumulated, whereas those associated with «systematic
errors» do not.