Table: Report two-way anova...

Performs a two-way analysis of variance on the data in one column of a selected fully factorial Table and reports the fixed-effects anova table in the info window.

### Settings

Column with data
the label of the column who's data will be analyzed.
First factor
the label of the column with the names of the levels for the first factor.
Second factor
the label of the column with the names of the levels for the second factor.
Table with means
if checked, a Table with the mean values of all the levels will be created.

### Example

Suppose you want to check if fundamental frequency depends on the type of vowel and speaker type. We will use the Peterson & Barney vowel data set to illustrate this. The following script will first create the data set and then produce the two-way anova report.

``` Create formant table (Peterson & Barney 1952)``` ``` Report two-way anova: "F0", "Vowel", "Type"```

This will produce the following anova table in the info window:

``` Two-way analysis of "F0" by "Vowel" and "Type".``` ``` ``` ```       Source SS Df MS F P``` ```        Vowel 73719.4 9 8191.05 7.62537 5.25258e-11``` ```         Type 4.18943e+06 2 2.09471e+06 1950.05 0``` ``` Vowel x Type 6714.34 18 373.019 0.347258 0.994969``` ```        Error 1.60053e+06 1490 1074.18``` ```        Total 5.87039e+06 1519```

The analysis shows that F0 strongly depends on the vowel and also on the speaker type and, luckily, we do not have any interaction between the vowel and the speaker type. Besides the anova table there is also shown a table with the mean F0 values for each Vowel-Type combination which looks like:

```                    c m w Mean``` ```         aa 258 124 212 198``` ```         ae 248 125 208 194``` ```         ah 263 129 223 205``` ```         ao 259 127 217 201``` ```         eh 259 128 220 202``` ```         er 264 133 219 205``` ```         ih 270 136 232 213``` ```         iy 270 136 231 212``` ```         uh 273 136 234 214``` ```         uw 278 139 235 218``` ```       Mean 264 131 223 206```

The first column of this table shows the vowel codes while the first row shows the speaker types (child, man, women). The last row and the last column of the table shows the averages for the factors Type and Vowel, respectively. The actual data are unbalanced because we have 300, 660 and 560 replications per column respectively (for each speaker we have two replcations of the data).

### Algorithm

The formula's to handle unbalanced designs come from Khuri (1998).