DTW is an example of one tradition of computational comparison of sounds - estimating distance using contours throughout the element's length. The alternative method is to calculate distance based on a discrete number of scalar parameters, such as "Maximum frequency", or "Length" of the signal. Luscinia makes the measurement of such parameters easy, and provides two ways in which you can analyze sounds based on them. The first is simply to be able to export summary statistics into a spreadsheet or text file, from where you can analyze them using one of any number of statistical approaches. This is dealt with in more detail here.
The second method is to use Luscinia itself to analyze sounds based on these parameters. Luscinia only provides a very small subset of the multivariate statistics that you might possibly want to employ, compared to dedicated statistics software. The advantage of carrying out such an analysis within Luscinia is that it can provide you with an interactive visual representation of the results.
Parametric comparison is an option from the Analysis types page.
The panel that appears when you select this option is basically a large array of different types of parameters for you to choose from. Each row corresponds to a different acoustic parameter (e.g. "Peak frequency"), while each column corresponds to a different statistic associated with that parameter (e.g. "Mean"). So, for example, the "Mean" of the "Peak Frequency" would be calculated as the arithmetic mean of all the peak frequency measures associated with an element. Two of the parameters, "Length" and "Gap After" only have one statistic associated with them. That is because for such temporal parameters, there really is only one parameter that can be used (the standard deviation of the length of an element is not really much use). From this point on, "parameter" means a combination of an acoustic parameter and an individual statistic, such as "Mean peak frequency", or alternatively, a temporal parameter.
After you have selected the parameters that you wish to analyze, you should click "Next Step". At this point, Luscinia calculates a distance matrix based on these parameters for every pair of elements in the comparison scheme you have selected. Each parameter is normalized by its standard deviation calculated over all elements in the comparison. The distance between two elements is then calculated as the Euclidean distance over all of the selected parameters.
This distance matrix is in the same form as that calculated by DTW. Therefore, it can be statistically analyzed in the same way. Luscinia provides the same statistical analysis tools for parametric comparisons as for DTW. You can read more about these options here.