Nigel is correct in his statements. To look at it another way. 1/2 of the sine wave means the circuit is seeing only 1/2 of the voltage, and the wattage halfs because the pulse rate frequency halfs also. So only 1/4 of the power is consumed by the load. Do the math! P=(E x E) ÷ R.But it isn't 120V mains, it's still 240V mains but only switched on half the time and the current in the (on) half cycle will be the same. Into a resistive load I can't see why this isn't half power.
MTJB, I stated "assuming perfect diode".