Search results
Results from the WOW.Com Content Network
The sample size is an important feature of any empirical study in which the goal is to make inferences about a population from a sample. In practice, the sample size used in a study is usually determined based on the cost, time, or convenience of collecting the data, and the need for it to offer sufficient statistical power .
Simple cases, where observations are complete, can be dealt with by using the sample covariance matrix. The sample covariance matrix (SCM) is an unbiased and efficient estimator of the covariance matrix if the space of covariance matrices is viewed as an extrinsic convex cone in R p×p; however, measured using the intrinsic geometry of positive ...
Some types of normalization involve only a rescaling, to arrive at values relative to some size variable. In terms of levels of measurement , such ratios only make sense for ratio measurements (where ratios of measurements are meaningful), not interval measurements (where only distances are meaningful, but not ratios).
A related form are weights normalized to sum to sample size (n). These (non-negative) weights sum to the sample size (n), and their mean is 1. Any set of weights can be normalized to sample size by dividing each weight with the average of all weights.
One-sided normal tolerance intervals have an exact solution in terms of the sample mean and sample variance based on the noncentral t-distribution. [8] This enables the calculation of a statistical interval within which, with some confidence level, a specified proportion of a sampled population falls.
The Wishart distribution arises as the distribution of the sample covariance matrix for a sample from a multivariate normal distribution. It occurs frequently in likelihood-ratio tests in multivariate statistical analysis. It also arises in the spectral theory of random matrices [citation needed] and in multidimensional Bayesian analysis. [5]
In this case the Fisher information matrix may be identified with the coefficient matrix of the normal equations of least squares estimation theory. Another special case occurs when the mean and covariance depend on two different vector parameters, say, β and θ. This is especially popular in the analysis of spatial data, which often uses a ...
The assumptions of discriminant analysis are the same as those for MANOVA. The analysis is quite sensitive to outliers and the size of the smallest group must be larger than the number of predictor variables. [8] Multivariate normality: Independent variables are normal for each level of the grouping variable. [10] [8]