Descriptive statistics variance

Descriptive statistics quantify central tendency and variance of data sets. The probability of occurrence of a value in a given population can be described in terms of the Gaussian distribution. 

The quantities AUMC and AUSC can be regarded as the first and second statistical moments of the plasma concentration curve. These two moments have an equivalent in descriptive statistics, where they define the mean and variance, respectively, in the case of a stochastic distribution of frequencies (Section 3.2). From the above considerations it appears that the statistical moment method strongly depends on numerical integration of the plasma concentration curve Cp(r) and its product with t and (r-MRT). Multiplication by t and (r-MRT) tends to amplify the errors in the plasma concentration Cp(r) at larger values of t. As a consequence, the estimation of the statistical moments critically depends on the precision of the measurement process that is used in the determination of the plasma concentration values. This contrasts with compartmental analysis, where the parameters of the model are estimated by means of least squares regression. 

The bottleneck in utilizing Raman shifted rapidly from data acquisition to data interpretation. Visual differentiation works well when polymorph spectra are dramatically different or when reference samples are available for comparison, but is poorly suited for automation, for spectrally similar polymorphs, or when the form was previously unknown [231]. Spectral match techniques, such as are used in spectral libraries, help with automation, but can have trouble when the reference library is too small. Easily automated clustering techniques, such as hierarchical cluster analysis (HCA) or PCA, group similar spectra and provide information on the degree of similarity within each group [223,230]. The techniques operate best on large data sets. As an alternative, researchers at Pfizer tested several different analysis of variance (ANOVA) techniques, along with descriptive statistics, to identify different polymorphs from measurements of Raman... 

The number of subjects per cohort needed for the initial study depends on several factors. If a well established pharmacodynamic measurement is to be used as an endpoint, it should be possible to calculate the number required to demonstrate significant differences from placebo by means of a power calculation based on variances in a previous study using this technique. However, analysis of the study is often limited to descriptive statistics such as mean and standard deviation, or even just recording the number of reports of a particular symptom, so that a formal power calculation is often inappropriate. There must be a balance between the minimum number on which it is reasonable to base decisions about dose escalation and the number of individuals it is reasonable to expose to a NME for the first time. To take the extremes, it is unwise to make decisions about tolerability and pharmacokinetics based on data from one or two subjects, although there are advocates of such a minimalist approach. Conversely, it is not justifiable to administer a single dose level to, say, 50 subjects at this early stage of ED. There is no simple answer to this, but in general the number lies between 6 and 20 subjects. 

Plasma EE Descriptive statistics and comparison of plasma EE concentrations in cycles 1 and 2. Analysis of variance on log-transformed data, 90 % confidence intervals for AUC ratio of EE + Drug XYZ and EE alone (AUCEE+Drug XYz/AUCee)-... 

PK data The PK parameters of ABC4321 in plasma were determined by individual PK analyses. The individual and mean concentrations of ABC4321 in plasma were tabulated and plotted. PK variables were listed and summarized by treatment with descriptive statistics. An analysis of variance (ANOVA) including sequence, subject nested within sequence, period, and treatment effects, was performed on the ln-transformed parameters (except tmax). The mean square error was used to construct the 90% confidence interval for treatment ratios. The point estimates were calculated as a ratio of the antilog of the least square means. Pairwise comparisons to treatment A were made. Whole blood concentrations of XYZ1234 were not used to perform PK analyses. 

Anova Two-Fador WSh RepScation Anova Two-Fador Without RepTicatior Correlatim Covariance Descriptive Statistics E)g onential Sofioothing F-Test Two-Sample for Variances Focjfier Analysis... 

Descriptive statistics Used to summarize information and for the comparison of numbers in different sets of data mean, median, mode, range, variance, standard deviation are descriptive statistics. 

Collected data were subjected to descriptive statistics, analysis of variance, log-linear regression, and trend analysis using STATISTICA, SPSS ver. 10 and MINITAB Ver. 14 statistical software. 

Calculate the following descriptive statistics for the data on water hardness (mmoll ) given as follows arithmetic mean, median, standard deviation, variance, standard error, confidence interval at a significance level of 0.01, range, and the interquartile distance - 8.02 7.84 7.98 7.95 8.01 8.07 7.89. 

Descriptive statistics—mean, median, trimmed means, standard deviation and standard error, variance, minimum, maximum, range, interquartile range, skewness, kurtosis Frequency statistics—outlier identification boxplots, stem-and-leaf plots, and histograms Frequency statistics—description percentiles, probability plots, robust estimates or M-estimators, Kolmogorov-Smirnov and Shapiro-Wilk normality tests Variance homogeneity—Levene s test for equality of variance... 

Descriptive Statistics (e.g., mean, median, variance, standard deviation) Hypothesis Testing (e.g., paired and un-paired t-tests chi-squared test) Principles of Statics (e.g., forces moments couples torques free-body diagrams)... 

Note that the square of the standard deviation s, called the variance, is not in the same units of measurement as the data and so is of no use as a descriptive statistic, although it has many other uses in more complicated analyses. 

Commonly used descriptive statistics include measures that describe where the middle of the data is. These measures are sometimes called measures of central tendency and include the mean, median, and mode. Another category of measures describes how spread out the data is. These measures are sometimes called measures of variability and include the range, variance, and standard deviation. Additional descriptive measures can include percentages, percentiles, and frequencies. In safety performance measurement, the safety professional must determine the format of the data (i.e., ratio, interval, ordinal, or categorical) that will be collected and match the data format to the appropriate statistic. As will be discussed in the following sections, certain descriptive statistics are appropriate for certain data formats. 

Descriptive Statistics statistical techniques that are used to describe the population or sample. Commonly used descriptive statistics include measures of central tendency mean, median and mode and measures of variability range, variance and standard deviation. Additional descriptive measures can include percentages, percentiles and frequencies. 

The critical analytical data should be tabulated and analyzed in terms of descriptive statistics (mean, coefficient of variation, extrema), control charts, and trend analysis [17]. If the data of several years are included, yearly means may be calculated, and the significance of the variations from year to year may be investigated by analysis of variance to evaluate the reproducibility of the process. 

The simplest use of statistical methods is to provide summary parameters characterising important statistical properties of input variables and of various measures of catalyst performance (such as yield or degree of conversion), or relationships between them. Such summary parameters are usually called descriptive statistics, their common representatives are mean, median, variance, standard deviation, covariance and correlation. 

Subsequently, the ratios of the inverted Cl widths were correlated to those of the face. The following statistical tests were used to describe the features of sample population, and the control, and to measure the presence of difference among the ethnic groups or in gender descriptive statistics, one way analysis of variance (ANOVA), P or NP correlation, and Chi square (p<0.05). 

A very important data mining task is the discovery of characteristic descriptions for subsets of data, which characterize its members and distinguish it from other subsets. Descriptions can, for example, be the output of statistical methods like average or variance. 

Statistics in general is a discipline dealing with ideas on description of data, implications of data (relation to general pharmacological models), and questions such as what effects are real and what effects are different Biological systems are variable. Moreover, often they are living. What this means is that they are collections of biochemical reactions going on in synchrony. Such systems will have an intrinsic variation in their output due to the variances in the... 

Exploratory data analysis (EDA). This analysis, also called pretreatment of data , is essential to avoid wrong or obvious conclusions. The EDA objective is to obtain the maximum useful information from each piece of chemico-physical data because the perception and experience of a researcher cannot be sufficient to single out all the significant information. This step comprises descriptive univariate statistical algorithms (e.g. mean, normality assumption, skewness, kurtosis, variance, coefficient of variation), detection of outliers, cleansing of data matrix, measures of the analytical method quality (e.g. precision, sensibility, robustness, uncertainty, traceability) (Eurachem, 1998) and the use of basic algorithms such as box-and-whisker, stem-and-leaf, etc. 

Comparison and ranking of sites according to chemical composition or toxicity is done by multivariate nonparametric or parametric statistical methods however, only descriptive methods, such as multidimensional scaling (MDS), principal component analysis (PCA), and factor analysis (FA), show similarities and distances between different sites. Toxicity can be evaluated by testing the environmental sample (as an undefined complex mixture) against a reference sample and analyzing by inference statistics, for example, t-test or analysis of variance (ANOVA). 

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