It shouldn’t make a difference if it’s a buy or a sale because the effective spread formulas account for it by being different for buy and sell orders:
effective spread (buy order) = 2 x (execution price - midquote)
effective spread (sell order) = 2 x (midquote-execution price)
To me, it seems like if the effective spread is lower than the quoted spread, the you have gotten a better deal, regardless of whether you are buying or selling. Obviously when you compare the execution price to the quoted bid or ask prices, a price improvement is represented by a lower execution price than the ask when you are buying and a higher execution price than the bid when you are selling.
That’s my take on it but I could be wrong. Where does it say that a lower quoted spread vs. effective spread is a price improvement? CFAI materials?