Your custom factor isn't exactly correct. Should be something like this

#Custom factor for Sector PE  
from quantopian.pipeline import CustomFactor  
class SectorPE(CustomFactor):  
    # Default inputs  
    inputs = [Fundamentals.pe_ratio, morningstar.asset_classification.morningstar_sector_code]  
    window_length = 252 #annual ratio  
    # dataframe of the latest pe_ratio and sector name the [-1] specifies how many days from current day you  
    # are getting values for. -1 being most recent.  
    def compute(self, today, assets, out, pe, sectors):  
        df = pd.DataFrame(index=assets, data={"pe_ratio": pe[-1],  
                                             "sector_code": sectors[-1]})  
        # The original code is below  
        # out[:] = df.groupby("sector_code").transform(np.mean).values.flatten()  
        out[:] = df.groupby("sector_code").pe_ratio.transform(np.mean).values  

The single line that's not exactly right.

        out[:] = df.groupby("sector_code").transform(np.mean).values.flatten()  

The dataframe 'df' has two columns 'sector_code' and 'pe_ratio'. The transform method will calculate the mean of all the columns (including the 'sector_code'). This isn't what you want. To just transform the single 'pe_ratio' column add the column name after the groupby method. That will select, and calculate the mean, of just the 'pe_ratio'. Then simply use the values method (as in the original) to get the values as a series. No need for the flatten method.

See attached notebook.

Thanks for the reply Dan, but this didn't change the results?
My custom factor for calculating the mean PE per sector still equals my demean method of calculation. These columns are shown shown next to each other in the first output of data.
In the next cell, I tried doing the same thing a different way, allowing for easy plotting, but the values don't match the other 2 methods?

Ahhh. Sorry I didn't exactly understand which calculations you felt didn't match.

So... the reason the various approaches don't match is the groups being averaged contain different securities. In the two pipeline calculations, no filter or mask is being applied. The mean PE is being calculated across all securities in the sector. However, in the 'post pipeline' calculation the pipeline has been filtered, or screened, by the tradable_filter_notNull_PE filter which includes only stocks in the Q500US universe.

Add that mask to the two pipeline calculations and the numbers match. One could also remove the screen from the pipeline (and keep the pipeline calculations without a mask) and the numbers would be the same too. They would be different from those with a mask but they will be consistent.

See attached notebook.