Population, distribution sampled

The mean of a set of observed values is an estimate only of the mean of the underlying probability distribution or population. The sample mean, x, becomes a... 

Experiments were conducted in our laboratory to evaluate many of the dynamical expectations for rapid laser heating of metals. One of the aims of this work was to identify those population distributions which were characteristic of thermally activated desorption processes as opposed to desorption processes which were driven by nontbennal energy sources. Visible and near-infrared laser pulses of nominally 10 ns duration were used to heat the substrate in a nonspecific fashion. Initial experiments were performed by Burgess etal. for the laser-induced desorption of NO from Pt(foil). Operating with a chamber base pressure 2 x 10 torr and with the sample at 200 K, initial irradiation of a freshly cleaned and dosed sample resulted in a short time transient (i.e. heightened desorption yield) followed by nearly steady state LID signals. The desorption yields slowly decreased with time due to depletion of the adsorbate layer at the rate of ca. 10 monolayer... 

Estiinatiori of Sample Size when Form of Population Distribution is Unknown... 

The cdf of the empirical distribution converges in probability to the true cdf, as n increases. However, in small samples the empirical distribution may have some features that we do not want to extrapolate to the population. The empirical distribution is discrete (with positive probability only for observed values), whereas the population distribution may be conceived as continuous. With n too small there may actu-... 

The averages of random samples of a population are normally distributed. Therefore, the standard deviation of the population of sample means is the standard deviation of the population from which the sample is drawn divided by the square root of sample size. If we standardize the data to have a mean of 0.0 and a standard deviation of 1.0, then the standard deviation of the sample mean is 1.0 divided by the square root of the sample size. To be 95 percent confident that the incidence of insomnia in one group is smaller than the incidence in another group, the incidence in the first must be at least 1.64 standard deviations smaller than the incidence in the second. The sample size required to detect any given difference in means is approximately the square of 1.64 divided by the difference—in this case, (1.64/0.05) or 1,075.84. 

The extreme data point X is not an outlier and comes from a normally distributed population with sample mean X and standard deviation s... 

Experimental data obtained by any of the assay methods must be evaluated by someone. Judgements are commonly based on the experience of the analyst and accumulated laboratory data or published results. The evaluations range from comparison with a simultaneous standard to highly sophisticated statistical equations requiring many calculations. Evaluation of juice content should be considered as an estimate in the context of placing the sample somewhere in the natural population distribution, and the probability of that estimate should be reported. Unfortunately, many literature reports fail to mention or minimize the uncertainty of the estimate. In samples where the presence of foreign substances is proven, one can state with absolute certainty that the juice has been adulterated. 

As shown in Tables 5-2 and 5-3, the data on each group include survey period, geometric mean, population sample size, and the biomarker concentration at the 50th, 75th, 90th, and 95th percentiles of the population distribution. 

Point estimate uses the sample data to calculate a single best value, which estimates a population parameter. The point estimate is one number, a point on a numeric axis, calculated from the sample and serving as approximation of the unknown population distribution parameter value from which the sample was taken. Such a point estimate alone gives no idea of the error involved in the estimation. If parameter estimates are expressed in ranges then they are called interval estimates. 

Let the observed property of X elements of a population have a distribution determined by density function f(X). Let us randomly draw from this population a sample of... 

Student s t-test is frequently used in statistical evaluations of environmental chemical data. It establishes a relationship between the mean (x) of normally distributed sample measurements, their sample standard deviation (,v), and the population mean (p). Confidence intervals may be calculated based on Student s t-test (Equation 10). The upper limit of the confidence interval is compared to the action level to determine whether the sampled medium contains a hazardous concentration of a pollutant. If the upper confidence limit is below the action level, the medium is not hazardous otherwise the opposite conclusion is reached. 

Sample uncertainty is also referred to as statistical random sampling error. This type of uncertainty is often estimated assuming that data are sampled randomly and without replacement and that the data are random samples from an unknown population distribution. For example, when measuring body weights of different individuals, one might randomly sample a particular number of individuals and use the data to make an estimate of the interindividual variability in body weight for the entire population of similar individuals (e.g. for a similar age and sex cohort). 

A large sample of data (e.g. n = 1000) is obtained at random and represents a specific stratum of a population of interest, such as a specific age and sex cohort. The data represent observed interindividual variability (e.g. in body weight, in breathing rate). These data can be used to make a best estimate of the unknown population distribution, and conventional statistical methods can be used to infer confidence intervals regarding individual statistics (e.g. the mean) or for the entire observed distribution. 

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