<p>I believe the percentages of 5’s and 4’s will stay the same, the curve will just be harsher. With the guessing penalty, a lot of people choose to leave items blank. However, obvious statistics dictate that for those questions they leave blank, they can rule out some answers, even if its something like 0.25 answers (Which means that for every 4 questions they guess on, they can rule out 1 answer).</p>
<p>When they leave the item blank, they get an expected value of 0 points. But if they guess with the “ruling out” aspect factored in, they get an expected value of 0.25*x/(5-x), which is greater than zero when x > 0, where x is the number of answers they can rule out per question (It can be something like 0.25, like I just said above).</p>
<p>Here’s the math behind it.</p>
<p>Let’s say you can eliminate x choices for every question (Obviously, x < 5)
Thus, the chance of getting the question right is (Total correct answers)/(Total answers). Total correct answers is just 1 (Since there’s only correct 1 answer behind every question). Total answers is just 5 - x because you eliminated x of the choices. Thus, we have a probability of 1/(5-x) of getting it right. The probability of getting the question wrong is just 1 - [1/(5-x)].</p>
<p>If we do [Probability of getting it right] - 0.25 [Probability of getting it wrong], we get the expected points per question (Basically, we’re just adding the correct points up, and subtracting 1/4 points for every incorrect answer). Simplifying, we end up with 0.25*x/(5-x). Thus, if we have x=0, or essentially leaving the question blank, we get 0 as our expected value. However, if we get 0<x<5, which is basically saying that you can eliminate some answers, we get the expected value to be greater than 0. Thus, it is always better to guess.</p>
<p>Now, if we are now free to guess without penalty, then people will, on average, get more questions correct. This makes the average score higher. However, I think the percentages of 4’s and 5’s will stay the same (That is just speculation), so in order to compensate for the higher average score, there will be a harsher curve, making it tougher to get 4’s and 5’s.</p>