By the time big data sets are filtered down to the type of matter that is relevant, sample sizes may be too small and measurements may be exposed to potentially
large sampling errors.
Even with 61,000 interviews the estimates for each local authority are potentially subject to quite
a large sampling error.
Not exact matches
However, the three - point difference from the national average was within the range of
sampling error, suggesting that their likelihood of experiencing a dissolved marriage is the same as that of the population at -
large.
Results for the full
sample have a margin of
error of plus or minus 3.9 percentage points; the margin of
error is
larger for subgroups.
«By acquiring a
large amount of data, our system can significantly reduce the
error involved in analyzing the physiological status of a crop and the monitoring efficiency of crop growing conditions, without requiring repeated
sampling,» said Li.
(As always with polling data and reporting subgroups, some caution should be taken when making comparisons of subgroups having smaller
sample sizes — and hence,
larger margins of
error — than the total national
sample.)
The results presented for subgroups within the
sample have
larger margins of
error, depending on their actual size.
Sampling can sometimes result in quite
large tracking
errors in annual returns, especially in volatile markets like the ones we experienced in 2008 and 2009.
The
error bars in state - of - the - art SST compilations take into account such
sampling uncertainties, and indeed they become
larger back in time, especially the earliest decades (1850s - 1870s) in part due to the fact that there is substantial eddy variance.
The
sampling error can be
large as results from realistic ocean model consistently show.
«Estimating
sampling errors in
large - scale temperature averages.»
We have constructed four different chronologies to illustrate some of the issues associated with chronology
sampling error and bias, and to compare these between a single - site chronology and a chronology developed from a much
larger region.
This issue arises in tree - ring chronology construction too, balancing the inclusion of more data to reduce the noise (i.e. the
sampling error) against the inclusion of data from too
large an area such that the signal becomes ambiguous or even incompatible.
Errors in these adjustments can be
large and could well be systematic, meaning they don't average out with multiple
samples.
Hence, it possible for a
large number of measurements at different locations to result in a meaningful reduction in the level of
error of a quantity, provided that the value of the quantity does not vary much across the
sample space.
Cogley (1999) pointed out that with a measurement network spaced at 50 - 100 m apart the
largest source of uncertainty is the
error in actual point mass balance measurement (> 0.05 m), and
sampling error is negligible.
Measurement and
sampling errors (derived in part 1) are
larger than in previous analyses of SST because they include the effects of correlated
errors in the observations.
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.
The PDF has been computed in the same way (apart from the reciprocal relationship) as the climate sensitivity PDF in Figure 2 in the original paper, using the same data and
error distribution assumptions but with a
larger number of random
samples to improve accuracy.
A
large sample and thin margin of
error.
These biases are both substantially
larger than
sampling errors estimated in Lyman et al. [2006].»
Frequentists are comfortable dealing with PDFs that are computable from a
large number of
samples and estimates of
error.
As to how fractions of a degree are measured, I would strongly suggest looking at the Central Limit Theorem and the reduction of
errors and deviations with
large sample numbers.
Doing multivariate analysis with underspecified models, small
samples and metrics with
large error terms is questionable at the best of times.
These biases are both substantially
larger than
sampling errors estimated in Lyman et al. [2006], and appear to be the cause of the rapid cooling reported in that work.
For example, when fitting a trendline with random walk
errors (H = 1), the intercept is unidentified and hence has an effective
sample size of 0, while the slope is identified with a finite (though perhaps
large) standard
error.
-- It is
error to regard a random
sample from a population as highly representative of the total population (part of the law of
large numbers);
I2 was 81, indicating that a
large proportion of the observed variance in effect sizes may be attributable to heterogeneity rather than to
sampling error.
Multivariate hypotheses control the Type I
error rate and have a
large sample chi - square distribution (Raudenbush & Bryk, 2002).
However, the ABS acknowledges that non-sampling
errors due to the
large level of undercoverage in the 2008 NATSISS may introduce bias, if, for example, the estimated 31 % of Indigenous people screened in areas other than discrete Indigenous communities who did not identify as Indigenous were different from those who did identify and so could participate.16 Similarly, those excluded from the
sample because they were not usual residents of private dwellings (eg, visitors and people in hostels, caravan parks, prisons or hospitals) may have responded differently to those who were included.
Effect sizes were weighted by the inverse of their variance (i.e.,
sampling error), so that effect sizes derived from studies using
samples of
larger size contributed more to the overall effect size estimate than effect sizes derived from studies using
samples of smaller size.
Although SEM is traditionally utilized with
large samples, bootstrap analyses allow model testing with small
samples by utilizing the actual data to estimate standard
error (Shrout & Bolger, 2002).
Mplus v7.11 was used for all analyses.23 SDQ items were treated as ordinal, with weighted least - squares means and variance — adjusted estimation used.23 Given the χ2 statistic's propensity to reject good models when
samples are
large and / or complex, the comparative fit index (CFI) and root mean square
error of approximation (RMSEA) were used to assess model fit.
In this respect, Maas and Hox (2005) found that level 2
sample sizes exceeding 30 (i.e., 136 in our study) are sufficiently
large to produce unbiased estimates and accurate estimations of standard
errors and fixed effects.
The significant results found in the Pereira et al. (2012) study may in part be due to the
large sample size (N = 291) which may have been sufficient to detect subtle associations between CSA and parenting stress in the community
sample and protect against type II
errors.