Can we conclude the parity violation through the angle distribution of Co-60 without Wu's second procedure? The following picture, which I downloaded from Wikipedia Wu Experiment demonstrates Wu's experiment. 
 
I think that the moment when Wu got a polarized direction of the emitting electrons from $\text{Co}^{60}$, they should already have concluded a parity violation, and they didn't need to flip the magnetic field. It is because when we put $\text{Co}^{60}$ in a magnetic field, if parity is conserved, then we would expect an emission of electrons on both directions. (If the parity if conserved, one couldn't identify the direction of the magnetic field, thus we expect both directions to have the same amount of electrons. Otherwise we can specify a direction.) Therefore, Wu would conclude a parity violation the first time when they saw the emission of the electrons. But why they needed to switch the magnetic field and do the prediction like in the above picture? 
 A: A quick run through the experiment:
You want the  greatest available $60$ Cobalt nuclei  polarisation. But, even accepting  the low temperature requirement, because the nuclei have tiny magnetic moments relative to  the electrons, high magnetic fields were required. 
Because you want to confirm the effect works in both directions (this is totally my guess, they must have been prepared for anything weird(er) at that stage), you reverse the system. 

Image and extract source : [Doublexscience]

Cartoon of the Wu experiment: if parity was preserved, then the emission of electrons would change if you reversed the orientation of the experiment. Instead, she found that the electrons always shot out the same way relative to the cobalt atoms’ spin, showing that the weak force violates the law of parity. [Credit: Matthew Francis]

This:


*

*Makes the most use of all the time and effort  you have gone through for relatively little effort.

*Makes sure the effect definitely  is present and is not either an artifact of the system, or caused by an external source

*Also ensures that nothing else funny is going on, that you would be annoyed about if you had not done a simple task and someone else had discovered it.

*Madame Wu was a great experimental physicists, and  probably got that way by being a perfectionist.
