Apparent Power-Dependent Frequency Shift Due to Collisions in a Cesium Fountain

We describe a situation where a varying collisional frequency shift in cesium fountain primary frequency standards can be misinterpreted as a power-dependent shift. This misinterpretation may affect analyses of fountains test-operated at multiple pi/2 microwave pulse areas. Such tests are typically performed in the search for microwave- and cavity-related systematic frequency biases.