Efforts were made to take the grab samples at random periods so that the mass of data could be treated as a 6-hr. composite sample.

While this loss of precision may be tolerable and viewed as a minor flaw of Algorithm I, it is easy to find data that reveal a major flaw in the naive algorithm: Take the sample to be ( 10 < sup > 9 </ sup > + 4, 10 < sup > 9 </ sup > + 7, 10 < sup > 9 </ sup > + 13, 10 < sup > 9 </ sup > + 16 ).

* 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

Originally it was headerless, being simply 8-bit µ-law-encoded data at an 8000 Hz sample rate.

All fields are stored in big-endian format, including the sample data.

When reconstructing the data, owing to the evaporation of successive layers of material from the sample, the lateral and in-depth reconstruction values are highly anisotropic.

Descriptive statistics are distinguished from inferential statistics ( or inductive statistics ), in that descriptive statistics aim to summarize a sample, rather than use the data to learn about the population that the sample of data is thought to represent.

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.

and n is the number of data points in the sample.

Kuiper's test is used in statistics to test that whether a given distribution, or family of distributions, is contradicted by evidence from a sample of data.

Denote the sample of data which are independent realisations of random variables, having F as their distribution function, by x < sub > i </ sub > ( i = 1 ,..., n ).

Additionally, concerns over the sample populations used were later addressed by the Kinsey Institute, and the conclusion was that none of Kinsey's original estimates were significantly affected by these data sources.

In response, Paul Gebhard, Kinsey's successor as director of the Kinsey Institute for Sex Research, cleaned the Kinsey data of purported contaminants, removing, for example, all material derived from prison populations in the basic sample.

The strong likelihood principle applies this same criterion to cases such as sequential experiments where the sample of data that is available results from applying a stopping rule to the observations earlier in the experiment.

and the ML estimator of the covariance matrix from a sample of n observations is

which is simply the sample covariance matrix.

Define a data matrix, X < sup > T </ sup >, with zero empirical mean ( the empirical ( sample ) mean of the distribution has been subtracted from the data set ), where each of the n rows represents a different repetition of the experiment, and each of the m columns gives a particular kind of datum ( say, the results from a particular probe ).

Postulated migration of proteins in a Laemmli gel system A: Stacking gel, B: Resolving gel, o: sample application c: discontinuities in the buffer and electrophoretic matrix

The Cholesky decomposition is commonly used in the Monte Carlo method for simulating systems with multiple correlated variables: The correlation matrix is decomposed, to give the lower-triangular L. Applying this to a vector of uncorrelated samples, u, produces a sample vector Lu with the covariance properties of the system being modeled.

If the measures of correlation used are product-moment coefficients, the correlation matrix is the same as the covariance matrix of the standardized random variables X < sub > i </ sub > / σ ( X < sub > i </ sub >) for i = 1, ..., n. This applies to both the matrix of population correlations ( in which case " σ " is the population standard deviation ), and to the matrix of sample correlations ( in which case " σ " denotes the sample standard deviation ).

The more extensive the conversational sample, the more accurate and reliable is the " translation matrix ," enabling instantaneous conversion of verbal utterances or written text between the alien language and American English / Federation Standard.

Given any set of points in the desired domain of your functions, take a multivariate Gaussian whose covariance matrix parameter is the Gram matrix of your N points with some desired kernel, and sample from that Gaussian.

Data of this type is very common in chemistry, for example a liquid-chromatography / mass spectrometry ( LC-MS ) system generates a large matrix of data ( elution time versus m / z ) for each sample analyzed.

The Wishart distribution arises as the distribution of the sample covariance matrix for a sample from a multivariate normal distribution.

If we take the matrix V above to be, not a variance of a random vector, but a sample variance, then it may have a Wishart distribution.

In such applications typically the statistics of matrices is known in advance and one can take as approximate eigenvalue the average eigenvalue for some large matrix sample,

* S / SL ( Split / Splitless ) injector ; a sample is introduced into a heated small chamber via a syringe through a septum – the heat facilitates volatilization of the sample and sample matrix.

Vox format files are similar to wave files except that the vox files contain no information about the file itself so the codec sample rate and number of channels must first be specified in order to play a vox file.

) Diffracted x-ray or neutrons beams cannot be focused to produce images, so the sample structure must be reconstructed from the diffraction pattern.

While there is a real theorem that a random variable will reflect its underlying probability over a very large sample, the law of averages typically assumes that unnatural short-term " balance " must occur.

In order to improve specimen contrast or highlight certain structures in a sample special techniques must be used.

For the NAA procedure to be successful the specimen or sample must be selected carefully.

* Crystallography is an unambiguous method for determining molecular geometry, the proviso being that single crystals of the material must be available and the crystal must be representative of the sample.

Note that a sample of random variables ( i. e. a set of measurable functions ) must not be confused with the realizations of these variables ( which are the values that these random variables take, formally called random variates ).

Temperature and pressure must be specified for both the sample and the reference.

This is useful for differentiating a function on a grid, where, as one approaches the edge of the grid, one must sample fewer and fewer points on one side.

After a filter is designed, it must be realized by developing a signal flow diagram that describes the filter in terms of operations on sample sequences.

Not every subset of the sample space Ω must necessarily be considered an event: some of the subsets are simply not of interest, others cannot be “ measured ”.

The judge must also ensure that the jury does not confuse the ' match probability ' ( the probability that a person that is chosen at random has a matching DNA profile to the sample from the scene ) with the ' likelihood ratio ' ( the probability that a person with matching DNA committed the crime ).

Since the chain conformations of a polymer sample are quasi infinite in number and constantly change over time, the " radius of gyration " discussed in polymer physics must usually be understood as a mean over all polymer molecules of the sample and over time.

Benedict was adamant that she was not romanticizing so-called primitive societies ; she was emphasizing that any understanding of the totality of humanity must be based on as wide and varied a sample of individual cultures as possible.

The chemical and physical conditions of a test sample therefore must match reference measurements for conclusions to be valid.

In practice the concentration of the sample or the optical path length must be adjusted to place the unknown absorbance within a range that is valid for the instrument.

must be measured by removing the sample.

The type of sample container used must allow radiation to pass over the spectral region of interest.

To calculate molar ellipticity, the sample concentration ( g / L ), cell pathlength ( cm ), and the molecular weight ( g / mol ) must be known.

A major disadvantage of the indirect ELISA is the method of antigen immobilization is not specific ; when serum is used as the source of test antigen, all proteins in the sample may stick to the microtiter plate well, so small concentrations of analyte in serum must compete with other serum proteins when binding to the well surface.

Whether less or more heat must flow to the sample depends on whether the process is exothermic or endothermic.

The per capita income for the CDP was $ 2, 584, one of the lowest of all statistically measured locations in the United States ( although the small sample size means this status must be taken cautiously ).