Release 3.3 of the Real Statistics Resource Pack

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I am pleased to announce Release 3.3 of the Real Statistics Resource Pack. The new release is now available for free download (Download Resource Pack) for Excel 2007, 2010 and 2013 environments.

The Real Statistics Examples Workbook has been updated to reflect the new release. You can also download this file for free (Download Examples). The website is in the process of being updated to reflect the new features. These changes will be made over the course of the next day or so.

New features include:

Grubbs’ Test

The following new functions have been added to identify outliers based on Grubbs’ test and extensions to Grubbs’ test.

GRUBBS(R1, lab, alpha): outputs a 4 × 1 column range with the following entries: one potential outlier, G-stat, G-crit  and test significance; if lab = TRUE then an extra column is added with labels

ESD(R1, lab, alpha): outputs the results of a Generalized Extreme Studentized Deviate (ESD) Test, which identifies up to k potential outliers and tests whether they are outliers based on repeated Grubbs’ tests.

OUTLIERS(R1, alpha): outputs a column range with up to k outliers (based on the ESD test)

Changes to the Descriptive Statistics and Normality data analysis tool

The following capabilities have been added to the Descriptive Statistics and Normality data analysis tool

  • Grubbs/ESD Test
  • QQ Plot

Improved support for the Durbin-Watson Test

A table of critical values has been added to the website.

In addition, the following functions have been added:

  • DLowerCRIT(n, k, α) = lower critical value of the Durbin-Watson statistic
  • DUpperCRIT(n, k, α) = upper critical value of the Durbin-Watson statistic

These functions support samples of size n (6 to 2,000) based on k independent variables (1 to 20) for α = .01, .025 or .05 (default)

The existing DURBIN function has now been expanded to be an array function, which takes the following two forms:

DURBIN(R1, R2, lab, alpha): returns a column range with the values d, dL, dU and sig where R1 is a m × n range containing X data and R2 is an m × 1 column vector containing Y data

DURBIN (R1, k, lab, alpha): returns a column range with the values d, dL, dU and sig where R1 is a column vector containing residuals and k = the # of independent variables (default = 2)

Here d = the Durbin-Watson statistic; dL = the lower critical value; dU = the upper critical value; α = .01, .025 or .05 (default); sig = “yes” if d < dL, sig = “no” if d > dU, and sig = “unclear” otherwise. If lab = TRUE (default = FALSE) then an extra column of labels is added to the output.

Revised version of Kendall’s tau

The following changes have been made to the KCORREL function and the Kendall’s Tau option of the Correlation data analysis tool.

  • A ties correction has been applied (as the default) to the calculation of Kendall’s tau
  • Optionally Kendall’s tau can be calculated without the ties correction; in this case the algorithm used has been improved to give more accurate results

New exact version of Wilcoxon’s Rank-Sum Test

The previously available versions of Wilcoxon’s Rank-Sum Test were based either on a table look-up or a normal distribution approximation. In addtion to these, there are two new functions which calculate exact p-values and critical values for small samples based on the two-sample permutation distribution.

  • PERM2DIST(x, n1, n2, cum) = value of the permutation distribution at x based on n1 and n2 elements; returns the pdf value at x if cum = FALSE and the cdf value if cum = TRUE
  • PERM2INV(p, n1, n2) = inverse of the permuation distribution at p; i.e. the least value of x such that PERM2DIST(x, n1, n2, TRUE) ≥ p

The p-value of Wilcoxon’s Rank-Sum one-tail test for test statistic T and sample sizes n1 and n2 is given by PERM2DIST(T, n1, n2, TRUE). The critical value for any value of alpha is PERM2INV(alpha, n1, n2). The two tail test is given by 2* PERM2DIST(T, n1, n2, TRUE) and PERM2INV(alpha/2, n1, n2).

New exact version of Mann-Whitney Test

The previously available versions of Mann-Whitney Test were based either on a table look-up or a normal distribution approximation. In addtion to these, there are three new functions which calculate exact p-values and critical values for small samples based on the two-sample permutation distribution described above.

  • MANNDIST(U, n1, n2, tails) = p-value for the Mann-Whitney test at U based on n1 and n2 elements
  • MANNINV(p, n1, n2, tails) = inverse of the MANNDIST at p; i.e. the least value of U such that MANNDIST(U, n1, n2, TRUE) ≥ p
  • MANN_EXACT(R1, R2, tails) = p-value for the Mann-Whitney test for the samples in ranges R1 and R2

Here tails = 1 or 2.

Charles