## Help with scoringDefaultM

The habitude here with multiple choice tests is to give 1 point to each correct answer, and substract, for a wrong answer the probability, to answer correctly, that is to say -1/(N-1), or sometimes, as I do -1/N. So I use \scoringDefaultS{b=1,m=-1/N} with simple questions, scored as I expected.

I would like to use a similar strategy with questionmult, but with 2 points for a good response. So I used \scoringDefaultM{b=2/NB,m=-1/N} in a passed test.

The point is I have a question with a code as this:

\element{grupId}{
\begin{questionmult}{questionID}\label{q:questionLabel}
QuestionText
\begin{choices}
\wrongchoice{No1}
\correctchoice{Yes1}
\correctchoice{Yes2}
\wrongchoice{No2}
\correctchoice{Yes3}
\end{choices}
\end{questionmult}}


Where, if I understand correctly, N=5 and NB=3.
If a student checks all right boxes, score should be:
MAX case: NBC=3, NMC=0, scoresMAX=NBC*2/NB+NMC*(-1/N)=3*2/3+0*(-1/5)=2-0=2

And if he checks no answers:
No response case: NBC=0, NMC=0, scoresNoA=NBC*2/NB+NMC*(-1/N)=0*2/3+0*(-1/5)=2-0=0

The point is in a passed test, a student checked only 2 correct answers, so:
Particular case: NBC=2, NMC=1, scoreParC=NBC*2/NB+NMC*(-1/N)=2*2/3+1*(-1/5)=4/3-1/5=1,333-0,2=1,233/2

But the result after annotating is in fact 2.467/3,333!

So I there is something I did wrong.
I have checked doc many times especially examples, tried different strategies, but do not find the scoring strategy I look for.
Any help welcomed.

### Replies (9)

#### RE: Help with scoringDefaultM - Added by Paco Riviere5 months ago

Typo: this line should be:
Particular case: NBC=2, NMC=1, scoreParC=NBC*2/NB+NMC*(-1/N)=2*2/3+0*(-1/5)=4/3-0/5=1,333

#### RE: Help with scoringDefaultM - Added by Gérard Carpeaux5 months ago

You mix up two different strategies of scoring.
NB,NMC => formula
b, m => default scoring

Keep in mind : if the student
— tick a correct choice = b points
— don't tick a wrong choice = b points
— tick a wrong choice = m points
— don't tick a correct choice = m points

\wrongchoice{No1} no ticked = 2/3
\correctchoice{Yes1} ticked = 2/3
\correctchoice{Yes2} ticked = 2/3
\wrongchoice{No2} no ticked = 2/3
\correctchoice{Yes3} ticked = -1/5

score . 4*2/3 -1/5 = 2.467

You have 5 answers : maximal score = 5*2/3 = 3.333

#### RE: Help with scoringDefaultM - Added by Gérard Carpeaux5 months ago

sorry

\wrongchoice{No1} no ticked = 2/3
\correctchoice{Yes1} ticked = 2/3
\correctchoice{Yes2} ticked = 2/3
\wrongchoice{No2} no ticked = 2/3
\correctchoice{Yes3} no ticked = -1/5

#### RE: Help with scoringDefaultM - Added by Paco Riviere5 months ago

I see. Maybe I need a formula. How can I use a formula to score all questions.

If I score 2/N for every correct answer and -2/N for every wrong I whould then score 2 a perfect match?

#### RE: Help with scoringDefaultM - Added by Paco Riviere5 months ago

I thing a got it:

\scoringDefaultM{b=2/N,m=-2/N}

But, then what will de the score if no answer is correct?

#### RE: Help with scoringDefaultM - Added by Gérard Carpeaux5 months ago

The default scale for a simple question is e=0,v=0,b=1,m=0, which gives one point for a good response and no point in the other cases. The default scaling for a multiple question is e=0,v=0,b=1,m=0,p=-100,d=0, which gives a
point for every checked box, either good or not (good box checked or wrong box not checked)


#### RE: Help with scoringDefaultM - Added by Paco Riviere5 months ago

I see. I understand in my case I should use:

\scoringDefaultM{e=0,b=2/N,m=-2/N}

#### RE: Help with scoringDefaultM - Added by Paco Riviere5 months ago

I mean:
\scoringDefaultM{v=0,b=2/N,m=-2/N}

Then if all answers are wrong, I mean those to be checked are not and vice versa, the score would be -2, isn't it?

Yes.

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