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The following is an overview of the new features in Release 8.1.
New Multivariate Repeated Measures data analysis tools
The following two new data analysis tools have been added to the Multivar tab:
- Manova: Repeated Measures 2W+0B
- Manova: Repeated Measures 2W+1B
The first of these performs the equivalent of Repeated Measures ANOVA with two within-subjects factors and no between-subjects factors using multivariate techniques (i.e. Hotelling’s T-square test).
The second of these performs the equivalent of Repeated Measures ANOVA with two within-subjects factors and one between-subjects factor using multivariate techniques (i.e. one-way MANOVA).
These data analysis tools make use of the following new array function
RepMeasTransform(a, b): returns a transformation matrix for two with-subjects factors A and B where A has a levels and B has b levels.
The transformation matrix has ab-1 rows and ab columns where the first a-1 rows provide a transformation for factor A, the next b-1 rows specify a transformation for factor B, and the remaining rows specify a transformation for A × B.
Enhanced Hotelling worksheet functions
The existing Hotelling(R1, R2, d, lab) worksheet function has been enhanced to include support for the case where the data array/range R1 has only one column. In this case, the function provides support that is equivalent to the paired t-test using an F(1,df) distribution in place of a t(df) distribution.
The same enhancement is provided also for the Hotellingdf1, Hotellingdf2, HotellingF, HotellingT2, T2TEST and T2_RepeatedMeasures worksheet functions.
In the case where d = 0 (i.e. a one-sample test), the R2 argument can now be omitted, in which case it defaults to an n × 1 array all of whose elements are zero where n is the number of columns in R1.
Improved Holt’s Trend and Holt-Winter Tools
The optimization options of the Basic Forecasting data analysis tool have been improved so that the alpha, beta, and gamma parameters estimated by the Holt’s Trend, Holt-Winter (add) and Holt-Winter (mult) options yield a smaller error than those produced by earlier releases of the Real Statistics software.
Split Normal Distribution
The following worksheet functions have been added to support the split normal distribution
SNORM_DIST(x, μ, σ1, σ2, cum) = the probability density function value for the split normal distribution f(x) when cum = FALSE and the corresponding cumulative distribution function F(x) when cum = TRUE.
SNORM_INV(p, μ, σ1, σ2) = the value x such that SNORM_DIST(x, μ, σ1, σ2, TRUE) = p, i.e. inverse of SNORM_DIST(x, μ, σ1, σ2, TRUE).
Shapiro-Wilk Test Enhancement
The existing SWPROB(n, w, roy, interp) returns the p-value of the Shapiro-Wilk test for a sample of size n for the given value of w. If roy = FALSE, then the p-value returned is based on a table of values for the original version of the test. This table has values for n between 3 and 50 and p-values .01, .02, .05, .50, .95, 98 and .99. Other p-values between .01 and .99 are based on interpolation between the table values. When roy = TRUE (default), the p-value is calculated using Royston’s method for values of n up to 5,000.
With this release, even when roy = FALSE, the Royston method is used for p-values less than .01 or greater than .99. This is also true for the SWTEST(R1, roy, interp) when roy = FALSE.
Bug Fixes
- The CLUSTAnal(R1, …) worksheet function has worked properly when R1 was a range, but not when it was an array. This bug has now been fixed. The same bug fix has been provided for the worksheet functions CLUST, CLUSTErr, CENTROIDErr, INIT_CENTROIDS, and CLUSTConverge.
- The output from the Kruskal-Wallis option on the One Factor Anova data analysis tool references the sample size n when using a ties correction. This value was previously displayed as a constant. Additional flexibility is now provided since the reference to the sample size is now made using a formula.