Standardized variable

The standardized variable (the z statistic) requires only the probability level to be specified. It measures the deviation from the population mean in units of standard deviation. Y is 0.399 for the most probable value, /x. In the absence of any other information, the normal distribution is assumed to apply whenever repetitive measurements are made on a sample, or a similar measurement is made on different samples. 

Calculation of the factor matrix T = ZV by means of the standardized variables Z... 

There are several types of variables, e.g., categorical, dependent and independent, experimental and theoretical, manifest and latent, random, standardized variables... 

Let X , X2,..., Xv be v independent and normally distributed random variables. The square of the standardized variable t/, is defined as... 

A normal (gaussian) probability density function in one centered and standardized variable X reads... 

X is an n-vector of n independent normal standardized variables, i.e., with zero mean, unit variances and null covariances. Find (i) the density function and (ii) the covariance matrix of the vector Y given by... 

The standardized variable, z., can be calculated by dividing the deviation by the standard deviation... 

The standardized value then has a mean value of zero and a standard deviation of unity, and thus, all standardized variables have a mean value of zero and a standard deviation of 1. 

The advantage of utilizing the standardized form of the variable is that quantities of different types can be included in the analysis including elemental concentrations, wind speed and direction, or particle size information. With the standardized variables, the analysis is examining the linear additivity of the variance rather than the additivity of the variable itself. The disadvantage is that the resolution is of the deviation from the mean value rather than the resolution of the variables themselves. There is, however, a method to be described later for performing the analysis so that equation 16 applies. Then, only variables that are linearly additive properties of the system can be included and other variables such as those noted above must be excluded. Equation 17 is the model for principal components analysis. The major difference between factor analysis and components analysis is the requirement that common factors have the significant values of a for more than one variable and an extra factor unique to the particular variable is added. The factor model can be rewritten as... 

By combination of the data, two large models can be calculated which describe the effects of the four adjustable, standardized variables (temperature, relative humidity, starch concentration and compression load) on the crushing strength (Sg) and the SIR of crushing strength after storage (S1R(S)), respectively ... 

The standard variables are concentration of reactants, temperature and catalyst, inhibitor or any other substance which affects the rate. 

A similar analysis shows that the variance of X is simply ax- The standard normal distribution is obtained by defining a standardized variable z ... 

With regard to the number of standardized variables we shall speak of the core of a design which means that the combinations of the values in the respective columns, z, determine the set-up of the particular experiments. 

Rotational barriers have been probed for a number of bisalkyne complexes (Table VII). Cationic [CpM(RC=CR)2(CO)]+ complexes exhibit relatively high barriers (16-21 kcal/mol). Both standard variable-temperature NMR techniques (94) and two-dimensional methods (162) have been used to elucidate isomer interconversion schemes with two unsymmetrical alkynes in the coordination sphere. The plane of symmetry present when two symmetrical alkynes bind to a CpMX fragment is not retained in all isomers with RC=CH ligands. The availability of distal and proximal alkyne termini locations relative to the adjacent cis ligand leads to two cis isomers (R and R near one another) and one trans isomer (Fig. 25). Rotation of only one alkyne ligand converts cis to trans and vice versa, but direct cis to cis conversion is not possible unless both alkynes rotate simultaneously. 

Vortex Mixer Use a standard, variable-speed mixer. Reagents and Solutions... 

Therefore, the highest scoring common substructure (HSCS) value is a standardized variable (Z-score) proposed to measure the similarity between the two molecules s and t [Sheridan and Miller, 1998], defined as ... 

If the original data matrix is converted into the correlation matrix, then each variable is expressed in the standard normal form with zero mean and unit standard deviation. The intercept coefficient using these standardized variables will now be zero and the required value can be calculated later. The regression equation in matrix form is then... 

According to this criterion, the value of the k factor chosen is k = In (1.25)70.25 = 0.892, presenting an intermediate value between the too liberal approach of k = 1.116 (62) and the stricter one, k = 0.760 (39,62). However, the choice of this value (or equivalently the choice of (Two = 0.25) presents the demerit of an inherent discontinuity of the BE limits when applied for drugs with CV > 30% (i.e., with (Twr > 0.294), (Fig. 1). The cause of this attribute is that the preset standard variability value ((Two = 0.25) is not the same as the switching variability value ((Tq = 0.294). A relevant comment has been also made recently (65). Consequently, if the estimated within-subject CV of the R formulation is just above the changeover point of 30%, the BE limits will be much wider (i.e., > 1.30) than just below (i.e., 1.25). 

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