Does a decreasing shape factor correspond to greater or reduced probability of separation? The shape factor ($H=\frac{\delta^*}{\theta}$) is the ratio of displacement thickness, a measure of the thickness of the boundary layer, to the momentum thickness, a measure of the shear stress. I think that a larger shape factor indicates that the boundary layer is larger and there is less shear stress, so it seems like a larger shape factor should be associated with a greater likelihood of separation. Is that right? If not, why?
Yes you're reasoning is spot on. As the momentum thickness decreases, that indicates the velocity gradient at the wall is less, indicating a greater likelihood of separation occurring.