There seems to be a contradiction between CFA material and shweser. One says that if quoted spread is lower than effective spread, it’s a price improvement. The other says the opposite: the effective spread has to be lower to have a price improvement. Does it also depend if it’s a buy or sale?
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?
AND the only time the Quoted Spread will Equal the Effective Spread is when a Sell takes place a the Bid and a Buy takes place at the Ask 
Effective spread lower: price improvement. Effective spread higher: you got a worse price. Put another way you either paid more than Ask or you got less than Bid. Doesn’t matter if you buy or sell.
Agree with TooOld4This.
My apologies. I re-read both books. If effective spread is lower than quoted spread, there is a price improvement.