The general theory of resonance shifts is used to derive a general expression for the second moment Af of a polycrystalline paramagnetic sample and is specialized to Af.

Homozygous and heterozygous Af cells, Af and homozygous and heterozygous Af cells were used to test each sample ; ;

When paper electrophoresis was to be used for preparation, eight strips of a whole serum sample or a chromatographic fraction concentrated by negative pressure dialysis were run/chamber under the conditions described above.

Therefore, it is recommended that in such cases the sample be replaced, or if used, the results of dimensional change or dimensional restorability tests be considered as indicative only.

* Boolean analysis – a method to find deterministic dependencies between variables in a sample, mostly used in exploratory data analysis

* Principal component analysis – transformation of a sample of correlated variables into uncorrelated variables ( called principal components ), mostly used in exploratory data analysis

A common example used in undergraduate education is the determination of the amount of water in a hydrate by heating the sample to remove the water such that the difference in weight is due to the loss of water.

If the amount in the sample is below an instrument's range of measurement, the method of addition can be used.

The method of standard addition is used in instrumental analysis to determine concentration of a substance ( analyte ) in an unknown sample by comparison to a set of samples of known concentration, similar to using a calibration curve.

In analytical chemistry the technique is used for determining the concentration of a particular element ( the analyte ) in a sample to be analyzed.

Hardware from other vendors often used sample rates as high as 8192 Hz, often integer factors of video clock signals.

This sample was used to synthesize the element ununseptium for the first time in 2009 at the Joint Institute for Nuclear Research, Russia, after it was bombarded with calcium-48 ions for 150 days.

* whiff rate: a term, usually used in reference to pitchers, that divides the number of pitches swung at and missed by the total number of swings in a given sample.

* Analytical chromatography is used to determine the existence and possibly also the concentration of analyte ( s ) in a sample.

This motion causes the column to see one partitioning step per revolution and components of the sample separate in the column due to their partitioning coefficient between the two immiscible liquid phases used.

If are independent and identically distributed random variables, each with a standard Cauchy distribution, then the sample mean has the same standard Cauchy distribution ( the sample median, which is not affected by extreme values, can be used as a measure of central tendency ).

However, because of the fat tails of the Cauchy distribution, the efficiency of the estimator decreases if more than 24 % of the sample is used.

When a sample consists of more than one variable, descriptive statistics may be used to describe the relationship between pairs of variables.

* In rotary evaporation a vacuum distillation apparatus is used to remove bulk solvents from a sample.

The term " total DDT " is often used to refer to the sum of all DDT related compounds ( p, p '- DDT, o, p '- DDT, DDE, and DDD ) in a sample.

Filters can be represented by block diagrams, which can then be used to derive a sample processing algorithm to implement the filter with hardware instructions.

A subclass of this is focused ion beam milling, where gallium ions are used to produce an electron transparent membrane in a specific region of the sample, for example through a device within a microprocessor.

In another study, data from a sample of white, Christian men and women were used to test the hypothesis that traditional, church-centered religiousness and de-institutionalized spiritual seeking are distinct ways of approaching fear of death in old age.

This is the use of the factor n-1 in the denominator of the formula, rather than just n. This occurs when the sample mean rather than the population mean is used to centre the data and since the sample mean is a linear combination of the data the residual to the sample mean overcounts the number of degrees of freedom by the number of constraint equations — in this case one.

The first is a wide-ranging sample of successful tonal analyses.

The differentiation, however, is not very much greater, as shown by the fact that Athabascan shows 3.46 stems per meaning slot as against 2.75 for Yokuts, with a slightly greater number of languages represented in our sample: 24 as against 21.

Upon completion of the purging step, additional initiator appropriate for the molecular weight of the sample desired is added, and the system is then warmed to the polymerization temperature, at which the reaction is allowed to go to completion.

stereo BGS 5031 ) is a good sample of the special, elegant art of English madrigal singing.

The collection is often the sample space of an experiment.

If the list is a statistical sample, we call the resulting statistic a sample mean.

The arithmetic mean of a variable is often denoted by a bar, for example ( read " x bar ") would be the mean of some sample space.

A test result ( calculated from the null hypothesis and the sample ) is called statistically significant if it is deemed unlikely to have occurred, assuming the truth of the null hypothesis.

The expected value of F is ( where n is the treatment sample size )

Reporting sample size analysis is generally required in psychology.

Power analysis is often applied in the context of ANOVA in order to assess the probability of successfully rejecting the null hypothesis if we assume a certain ANOVA design, effect size in the population, sample size and significance level.

Power analysis can assist in study design by determining what sample size would be required in order to have a reasonable chance of rejecting the null hypothesis when the alternative hypothesis is true.

Eta-squared is a biased estimator of the variance explained by the model in the population ( it estimates only the effect size in the sample ).

To do so, a sample of the soil is mixed into a clear container with some water, creating an almost completely saturated liquid.

A formula for calculating an unbiased estimate of the population variance from a finite sample of n observations is:

note that the above online algorithm III is a special case of an algorithm that works for any partition of the sample into sets,:

Based on this sample, the estimated population mean is 10, and the unbiased estimate of population variance is 30.