Sentence examples for multivariate normality and from inspiring English sources

Given that the assumptions of normal theory maximum likelihood are met (e.g., multivariate normality, and a large sample of independently and identically distributed cases), and under the assumption that Σ and μ represent the true model (Σ1 and μ1), the test statistic T follows a χ distribution with df1 degrees of freedom, i.e., T ∼ χ(df1) (Azzeline 1996; Bollen 1989).

The analysis of such multivariate data is usually based on MANOVA models assuming multivariate normality and covariance homogeneity.

Most of the existing bulk-density pedotransfer functions (PTFs) are formulated as linear (multiple) regression functions, with the requirements for multivariate normality and homoscedasticity.

Significance testing of multivariate models and their factors (Supplementary Table 3) was done via permutation tests (1000 permutations), an approach robust to deviations from multivariate normality and variance homogeneity; p < 0.05 was considered significant.

Nevertheless, statistical techniques always rely on the assumptions on linear separability, multivariate normality, and independence of the predictive variables; unfortunately, many of the common models of treating the financial markets problems violate these assumptions.

According to Field (2009) and Hooper, Coughlan, and Mullen (2008), the data met guidelines for univariate normality and multivariate normality, and there were no multivariate outliers.

There may be some variation to this model after checking its underlying assumptions of multivariate normality, linearity and equal variance and clustering.

Prior to performance, assumptions that are required to perform the linear regression analysis such as multivariate normality, outlier and multicollinearity were checked and confirmed.

The most appropriate technique was non-metric multidimensional scaling (NMDS), which is robust to a large number of zeros and does not assume multivariate normality (McCune and Grace, 2002; Zuur et al., 2007).

The distribution of data was assessed regarding univariate and multivariate normality (Kolmogorov-Smirnov and Mardia's tests) and described and analyzed accordingly.

Second, ML is robust against violations of the multivariate normality assumption and consistently yields efficient estimation when sample sizes are sufficiently large (Anderson and Gerbing 1988; Diamantopoulos and Siguaw 2000).