Accurate techniques that allow for the derivation of the spatial density in star formation regions are rare .
A technique that has found application for the derivation of spatial densities in Galactic star formation regions utilizes the density-sensitive properties of the K-doublet transitions of formaldehyde ( H _ { 2 } CO ) .
In this paper , we present an extension of our survey of the formaldehyde 1 _ { 10 } -1 _ { 11 } ( \lambda = 6.2 cm ) and 2 _ { 11 } -2 _ { 12 } ( \lambda = 2.1 cm ) K-doublet transitions of H _ { 2 } CO in a sample of 56 starburst systems ( 65 ) .
We have extended the number of galaxies in which both transitions have been detected from 5 to 13 .
We have improved our spatial density measurements by incorporating kinetic temperatures based upon NH _ { 3 } measurements of 11 of the galaxies with a total of 14 velocity components in our sample ( 66 ) .
Our spatial density measurements lie in a relatively narrow range from 10 ^ { 4.5 } to 10 ^ { 5.5 } cm ^ { -3 } .
This implies that the Schmidt-Kennicutt relation between L _ { IR } and M _ { dense } : ( 1 ) is an indication of the dense gas mass reservoir available to form stars , and ( 2 ) is not directly dependent upon a higher average density driving the star formation process in the most luminous starburst galaxies .
We have also used our H _ { 2 } CO measurements to derive two separate measures of the dense gas mass which are generally smaller , in many cases by a factor of 10 ^ { 2 } -10 ^ { 3 } , than those derived using HCN .
This disparity suggests that H _ { 2 } CO traces a denser , more compact , component of the giant molecular clouds in our starburst galaxy sample .

We also report measurements of the rotationally-excited \lambda = 6.3 cm ^ { 2 } \Pi _ { 1 / 2 } J = 1 / 2 state of OH and the H111 \alpha radio recombination line taken concurrently with our H _ { 2 } CO 1 _ { 10 } -1 _ { 11 } measurements .