Real Statistics Release 4.8

Release 4.8 contains the following new features:

Shapely-Owen Decomposition

Adds the following new array function:

SHAPELY(Rx, Ry) = a column range which gives the Shapely-Owen decomposition of R-square for the linear regression of Rx (which contains the x data values) on Ry (which contains the y data values).

This decomposition shows the relative contribution of each of the independent variables to the regression model.

Box-Cox Transformation

Adds the following new functions which carry out Box-Cox transformations

BOXCOX(R1, λ): array function which returns a range containing the Box-Cox transformation of the data in range R1 using the given lambda value. If the lambda argument is omitted, then the transformation which best normalizes the data in R1 is used, based on maximizing the log-likelihood function.

BOXCOXLL(R1, λ) = log likelihood function of the Box-Cox transformation of the data in R1 using the given lambda value

BOXCOXLambda(R1) = the value of lambda which maximizes the log likelihood function of the Box-Cox transformation of the data in R1

New Support for the Multivariate Normal Distribution

Adds the following new functions

BNORMSDIST(x, y, r, cum) = the cdf of the standard bivariate normal distribution at x and y with correlation coefficient r if cum = TRUE and the pdf if cum = FALSE

BNORMDIST(x1, x2, m1, m2, s1, s2, r, cum) = the cdf of the standard bivariate normal distribution at at x1 and x2 with means m1 and m2, standard deviations s1 and s2 and correlation coefficient r if cum = TRUE and the pdf if cum = FALSE

MNORMRAND(Rm, Rc): generates an array containing a random k × 1 vector from a k-dimensional multivariate normal distribution where Rm is the range that contains the k × 1 means vector and Rc is the range that contains the k × k covariance matrix

BNORMRAND(m1, m2, s1, s2, r): generates a random 2 × 1 vector from a bivariate normal distribution with means m1, m2, standard deviations s1, s2 and
correlation coefficient r

These last two functions can be used to generate a random vector which comes from a multivariate normal distribution with the specified parameters.

Mardia’s Test for Multivariate Normality

Adds the following functions that test whether the data in range R1 is drawn from a multivariate normal distribution

MSKEWTEST(R1, lab): Mardia’s skewness test for multivariate normality; returns a column range with the values skewness, chi-square statistic, df and p-value, plus corrected statistic and p-value for small samples

MKURTTEST(R1, lab): Mardia’s kurtosis test for multivariate normality; returns a column range with the values kurtosis, z-statistic and p-value

If lab = TRUE then an extra column of labels is appended to the results (defaults to FALSE).

Changes to the Noncentral Chi-square and F  Distribution Functions

The NCHISQ_DIST, NCHISQ_INV, NCHISQ_NCP, NF_DIST, NF_INV and NF_NCP functions have been revised to improve their accuracy especially for large values of the noncentral parameter. Note that the number of terms in the infinite series approximations has been greatly expanded (default is now 1,000 instead of 80). In addition, you can now specify the level of accuracy via a precision argument (default is .000000001).

The same changes have been made to the power and sample size functions REG_POWER, REG_SIZE, CHISQ_POWER, CHISQ_SIZE, ANOVA1_POWER, and ANOVA1_SIZE.

The various functions that support the noncentral t distribution and the corresponding power and sample size  functions have not changed, except that the default number of terms in the infinite series has been increased from 80 to 120.

These changes are also reflected in the corresponding Power and Sample Size data analysis tools.

Minor Enhancements and Bug Fixes

• Fixes a bug in the KCORREL function
• Added some new arguments to the Mahalanobis distance squared function MDISTSq