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This algorithm can easily be adapted to compute the variance of a finite population: simply divide by n instead of n − 1 on the last line.. Because SumSq and (Sum×Sum)/n can be very similar numbers, cancellation can lead to the precision of the result to be much less than the inherent precision of the floating-point arithmetic used to perform the computation.
gretl is an example of an open-source statistical package. ADaMSoft – a generalized statistical software with data mining algorithms and methods for data management; ADMB – a software suite for non-linear statistical modeling based on C++ which uses automatic differentiation; Chronux – for neurobiological time series data; DAP – free ...
Given an r-sample statistic, one can create an n-sample statistic by something similar to bootstrapping (taking the average of the statistic over all subsamples of size r). This procedure is known to have certain good properties and the result is a U-statistic. The sample mean and sample variance are of this form, for r = 1 and r = 2.
An implementation for the R programming language is available as the package named BiasedUrn. Includes univariate and multivariate probability mass functions, distribution functions, quantiles, random variable generating functions, mean and variance.
If the set is a sample from the whole population, then the unbiased sample variance can be calculated as 1017.538 that is the sum of the squared deviations about the mean of the sample, divided by 11 instead of 12. A function VAR.S in Microsoft Excel gives the unbiased sample variance while VAR.P is for population variance.
jamovi is an open source graphical user interface for the R programming language. [3] It is used in statistical research, especially as a tool for ANOVA (analysis of variance) and to understand statistical inference. [4] [5] It also can be used for linear regression, [6] mixed models and Bayesian models. [7]
Principal component analysis (PCA) is a linear dimensionality reduction technique with applications in exploratory data analysis, visualization and data preprocessing.. The data is linearly transformed onto a new coordinate system such that the directions (principal components) capturing the largest variation in the data can be easily identified.
For exactness, the t-test and Z-test require normality of the sample means, and the t-test additionally requires that the sample variance follows a scaled χ 2 distribution, and that the sample mean and sample variance be statistically independent. Normality of the individual data values is not required if these conditions are met.