**About CAIC v2.6**

CAIC v2.6 is functionally no different from CAIC v2.0; i.e it calculates phylogenetically independent comparisons in two or more variables, using either a nested or non-nested approach. New users should consult the CAIC User's Guide, which is included in the download package. CAIC 2.6 has additional features over (described below) and runs at approximately twice the processing speed compared with CAIC 2.0.

**Statistics**

CAIC v2.6 performs a regression through the origin on the contrasts when only two columns of data are selected for analysis. The regression equation and r-squared are written to the Log file, and the slope, F-ratio and p-value are written to a new output file, whose name will be NameofDatafile_Stats. Note that whilst regression is the most powerful test, CAIC v2.6 does not perform less powerful tests, nor can it substitute proper and rigorous data exploration. Non-parametric and T-tests on the magnitude of contrasts in the dependent variable (vs 0) can provide useful insights, especially where the assumptions are broken (see below).

**Assumption Testing**

CAIC v2.6 tests the following evolutionary and statistical assumptions of the models:

* there is no relationship between the absolute values of the contrasts and the estimated nodal values for each trait, * the absolute magnitude of the contrasts are independent of both the standard deviation (in the contrasts) and the age of the node. * predicted values of the dependent variable are uncorrelated with the absolute values of the standardised residuals from the regression equation.

These assumptions are tested by regression (not through the origin). In the case of an assumption violation (p<=0.05) a warning message appears on screen and in the Log file. Results of the assumption checks are also written to the Statfile, according to the p-value of the check:

p-value Diagnosis Written to Statfile p<=0.001 Violated slope*** 0.001<p<=0.01 Violated slope** 0.01<p<=0.05 Violated slope* 0.05<p<=0.1 Narrowly upheld qualitative slope (pos/neg) p>0.1 Upheld ns

CAIC also reports the number of outlying contrasts (>±1.96 SD) as well as the value of the largest standardised residual. This information will help the user assess the validity of the regression model.

Once again, these assumptions are only tested when just two variables are selected for analysis. This function is intended to cut down arduous and repetitive model checks. However, CAIC v2.6 does NOT represent a comprehensive comparative modeling package and we recommend that Users utilise traditional model checks such as diagnostic plots.

**Brunch**

The Brunch algorithm which makes fewer assumptions than Crunch. Assumption checks can generally be ignored for Brunch if non-parametric statistics are to be used.

Innovations in Brunch since CAIC 2.6.6 *Contrasts in the main predictor variable are now standardised when the main predictor is continuous. Contrasts in categorical variables are never standardised. *Nodal character values are written out to the output file.

**Capabilities**

CAIC v2.6 has the following handling limits: * phylogenies of up to 10000 tips (species), * Polytomies with up to 200 branches, * up to 128 columns of Data, * 20 of which may be used in each analysis.

Anyone wishing to exceed these limits should contact Nick Isaac.

**Other Minor Alterations since CAIC 2.0**

* Output files are now directly openable in Excel. Intermediate files are
deleted on quit: they'll no longer clog up your file folders.

* Standard Deviation written to the output file instead of variance. Users no
longer need to take the square-root in order to test the statistical assumptions
manually.

* Certain aspects of the User Interface have changed. None but the diehard old
users will notice (or care).

CAIC is always available at http://bio.ic.ac.uk/evolve/software/caic/index.html

20 June 2001, Nick Isaac.