## Wednesday, August 04, 2004

TESTING SYSTEM FOR QUIZZES

Some time back I had thought of creating a simulator for testing various systems. Following is a general outline of the testing method to be used.
(Just for reference for the non-quizzing readers I have included a general discussion of the types of scoring systems used. Quizzers may skip.)

Detailed description of the three scoring systems :

1. Direct and Passing(D&P)

In this round the total number of questions per round is equal to total number of teams.(This point is common to all the systems) Every team gets one direct question and on account of that teams not knowing/passing the question passes till each team has either got it wrong or till one of the teams gets it right. There is usually a discrepancy regarding the scoring. i.e. 10 & 10 or 10 & 5. Now in this simulator there will be an input window regarding the points for direct and the points for passed. We should be able to key in this value.

2. Infinite Rebound(IR)

In this system also total number of questions per round is equal to total number of teams. However the first question is asked the first team. Then the question passes till someone gets it right or till we come back to the original team. If no one gets it right then the next team to the one that attempted the previous question gets the question on direct. However if someone gets it right then the next team gets the next direct question. Each team gets 10 points for a correct answer. Rounds do not matter in this system and therefore the order does no get set to the first team after the end of each round.

3. Centaurian Scoring System(CSS)

(PS:I quote from an article that I had written)

"....... The total no of direct attempts by each team is noted down. Once a question is answered or attempted by each and every person and there comes a time for the next question then the team with the least no of direct questions should be posed the next question. Following is some sample data

DIRECT ATTEMPTS TABLE

A B C D
. .

(where the dots represent no of direct attempts)

Consider following case. Direct Q to A - no one gets it. Therefore every team gets an attempt. Now B,C,D all have min no of direct Q answered. Then we go by alphabetical or round order(clockwise/anticlockwise)Then B gets direct Q. C answers correctly. Therefore as C & D both have min no of direct questions the order is decided by no of attempted questions(i.e. D gets next question).

ATTEMPTED QUESTIONS TABLE

A B C D
. . . .
. .
(where the dots represent no of direct & indirect attempts)

Now when D gets direct question suppose A answers it. Then according to above rule as C is the team with lowest no of direct attempts it should get the next question instead of B as in the case of IR. What we do is that we fill up the gaps in the table so that each team gets the same no of direct questions. ...."

So basically we check if the no. of direct attempts remain the same, if all the teams have the same no, of direct attempts then we check if the total no of indirect attempts is also same, if all is same then we proceed according to clockwise/anti-clockwise as usual. If not then the team with the least no of direct questions gets the next questions and if the teams have equal no of direct questions then the team with least no. of attempted questions gets the next question. Rounds do not matter in this system and therefore the order does no get set to the first team after the end of each round.

4. WRITTEN ELIMINATION

In this system each team is asked each question. They get equal points and the one with max. no of correct answers wins.

OTHER IMPORTANT PARAMETERS :

When the no of teams are selected then each team is given a IQ no. i.e. basically this no indicates the probability of their answering a particular question. Now this quotient will be a whole number between 1 and 5 and the program will give us an option to either enter these or randomly generate. Now if the particular round is a specialty round then the program will generate separate set of IQ no. for each team just for that round.(it should be noted that this no should lie in the threshold of plus-minus 2. i.e if the team has a general IQno of 3 then the possible assigned values should be between 1 and 5 for this speciality round. However IQ no. should be within the limits of 1 and 5.)

Now the program gives us an option to input difficulty level of the quiz. This number will be between 0 and 4.The lower the difficulty no, the tougher the quiz. If the difficulty no is set to then the probability of answering each question by a team is given by the formula ;

PROBABILITY = (DIFFICULTY LEVEL OF QUESTION + IQ no of team)/10

That means if the difficulty no. is 3 and the team IQ no is 4 then the probability of answering the question is 7/10. Max probability is when a team with IQ no 5 gets the easiest difficulty of 4 then the probability of answering is 90%.

However it must be noted that the difficulty no is not a whole number while IQ no is a whole number. Also the Question difficulty no for each question must be randomly generated. However it must be plus-minus 'consistency number' of the quiz. The consistency no is a number between 0 and 1 and so if the consistency no if .5 and the quiz difficulty no entered as 2 then difficulty of each question must be a random no generated between 1.5 and 2.5 . Using these rules the program generates the probability of a team answering a question and using this it says whether the team gets the question right or wrong.

This probability number remains the same for every question-team combination. i.e. if for a particular case in IR and CSS systems the same question is asked to same team then their probability of answering it should remain the same irrespective of the method of scoring. This is very IMPORTANT point, and if not implemented will make the system extremely unfair. That is if a particular team gives a certain answer right, then that team should get it right irrespective of the method of scoring.

CONCERNING SPECIALITY ROUNDS

There are some rounds in a quiz for specialties i.e. sport etc. Now the teams aptitude changes for such rounds and teams that are damn good at general quizzing may be damn dumb at a particular specialty or vice versa. Therefore for such round the IQ no. is to be regenerated however it must remain plus-minus 2 of the general IQ no as mentioned before.However this number should never exceed 5 or be below 1. The number of specialty rounds is taken and a different IQ no is generated for each specialty round.

FAIRNESS QUOTIENT :

Written elims are the fairest way to conduct a quiz however it is not practically possible to have written quizzes. The fairness quotient is generated for each method of scoring. It is defined

(points got in a particular system)/(points got in written elimination.) X 100

Major Inputs ;

Number of teams
Number of questions
No of rounds
No of specialty rounds
IQ no of Teams in definite order.
Difficulty Level of quiz
Consistency no of the quiz
Scoring system for D&P
There should an option to rearrange the order of teams.
(each input wherever possible should have the option of randomly generating the value)

Major Outputs ;

Detailed round by round scoring with each system with the round no. and specialty if any
Total final scores
Ranks
Number of direct and indirect questions each team attempted
Number of direct and indirect questions each team got right
Fairness quotient of each system
IQ no of each team

That's all folks. Just something to get your brains racking and thinking again. After long time do I write a technical article. Pls. feel free to point out mistakes and additions if necessary. I plan to implement the sim. as soon as I have the necessary coding/programming skills, which will I suppose take some time. Anyways, till then -