SeasonalTNT
03-03-2009, 08:03 PM
Would it be more helpful in Bugs Section?
Multiple Choice Polls Explained
The greatest mistake one may make when he/she reads the graph is the assumption that the formula is the same: number of desired votes divided by number of total votes.
This is where the mistake is.
One recent example, is based on a poll found in this forum: Do you want to join this clan?
The available choices were, Yes and No. The statistics shows that out of 23 voters, 12 votes went to Yes, 12 votes went to No.
Let us refer to a more common example.
The following is a multiple choice poll.
Which do you like, Coffee, Tea, and/or Water?
Choices: Coffee, Tea, Water
Let us make up some results, saying that a total of 10 people voted.
There were 6 votes for Coffee, 9 votes for Tea, and 7 votes for Water. The percentages are 60% Coffee, 90% Tea, 70% Water.
Getting lost? You may be asking, how can 10 people have accumulated a total of 22 votes? Or rather, why should the percentages add up to 220%, more than 100%?
The reason is this: it is a multiple choice poll. This means that each voter can pick more than one item. Instead of saying that 60% of the votes are for Coffee, and 90% of the votes are for Tea, and 70% of the votes are for Water, the correct statements are these:
60% of the voters like Coffee.
90% of the voters like Tea.
70% of the voters like Water.
Now let us return to the former stated problem.
Instead of saying 52.17% of the votes were for Yes, and 52.17% of the votes were for No, the correct statements are these:
52.17% of the voters picked Yes.
52.17% of the voters picked No.
Why do we calculate the percentage as a quotient of the desired outcome to the number of voters, not the votes? The answer is simple. If a person voted for Coffee, Tea, AND Water, then they would be counted three times, in independent events. If a person voted for Yes AND No, then they would be counted twice. Why should a person be counted three times or twice when they are only one person giving independent opinions?
Solution 1: Use a non-multiple choice poll.
In order to use a multiple choice poll in the form of a single choice poll correctly, you must exhaust all the options/outcomes. Data Management, a course taught in High School, explains that the number of possible choices, since order does not matter, is a result of a special case permutation.
Imagine this problem: Pick at most three people from a group of three.
There are four cases in this problem: picking 0, 1, 2, or 3 people.
There is 1 way to pick 0 people.
There are 3 ways to pick 1 person.
There are 3 ways to pick 2 people.
There is 1 way to pick 3 people.
Therefore, there are a total of 8 ways to pick at most three people from a group of three.
Does the number sequence 1, 3, 3, 1 look familiar? It is the fourth line in the Pascal Triangle. To calculate how many possibilities there can be for an n number of choices, look at the (n+1)th line of the Pascal Triangle. For example, like this poll, there were three choices. 3+1=4, so I'd look on the 4th line of the Triangle.
Relating it back to the make-up case, Coffee, Tea, and Water, there are 8 ways to choose:
1.Nothing
2.Coffee
3.Tea
4.Water
5.Coffee, Tea
6.Coffee, Water
7.Tea, Water
8.Coffee, Tea, Water, or ALL.
Solution 2: Assume that the forum is doing the correct calculation in a multiple choice poll.
Yeap, that's it. If you have encountered any forum poll miscalculations, then they are probably miscalculations of your own, or there is something you do not understand. It should be expected that a computer has more math power than a human brain; it's the exact reason why a computer was created in the first place.
Multiple Choice Polls Explained
The greatest mistake one may make when he/she reads the graph is the assumption that the formula is the same: number of desired votes divided by number of total votes.
This is where the mistake is.
One recent example, is based on a poll found in this forum: Do you want to join this clan?
The available choices were, Yes and No. The statistics shows that out of 23 voters, 12 votes went to Yes, 12 votes went to No.
Let us refer to a more common example.
The following is a multiple choice poll.
Which do you like, Coffee, Tea, and/or Water?
Choices: Coffee, Tea, Water
Let us make up some results, saying that a total of 10 people voted.
There were 6 votes for Coffee, 9 votes for Tea, and 7 votes for Water. The percentages are 60% Coffee, 90% Tea, 70% Water.
Getting lost? You may be asking, how can 10 people have accumulated a total of 22 votes? Or rather, why should the percentages add up to 220%, more than 100%?
The reason is this: it is a multiple choice poll. This means that each voter can pick more than one item. Instead of saying that 60% of the votes are for Coffee, and 90% of the votes are for Tea, and 70% of the votes are for Water, the correct statements are these:
60% of the voters like Coffee.
90% of the voters like Tea.
70% of the voters like Water.
Now let us return to the former stated problem.
Instead of saying 52.17% of the votes were for Yes, and 52.17% of the votes were for No, the correct statements are these:
52.17% of the voters picked Yes.
52.17% of the voters picked No.
Why do we calculate the percentage as a quotient of the desired outcome to the number of voters, not the votes? The answer is simple. If a person voted for Coffee, Tea, AND Water, then they would be counted three times, in independent events. If a person voted for Yes AND No, then they would be counted twice. Why should a person be counted three times or twice when they are only one person giving independent opinions?
Solution 1: Use a non-multiple choice poll.
In order to use a multiple choice poll in the form of a single choice poll correctly, you must exhaust all the options/outcomes. Data Management, a course taught in High School, explains that the number of possible choices, since order does not matter, is a result of a special case permutation.
Imagine this problem: Pick at most three people from a group of three.
There are four cases in this problem: picking 0, 1, 2, or 3 people.
There is 1 way to pick 0 people.
There are 3 ways to pick 1 person.
There are 3 ways to pick 2 people.
There is 1 way to pick 3 people.
Therefore, there are a total of 8 ways to pick at most three people from a group of three.
Does the number sequence 1, 3, 3, 1 look familiar? It is the fourth line in the Pascal Triangle. To calculate how many possibilities there can be for an n number of choices, look at the (n+1)th line of the Pascal Triangle. For example, like this poll, there were three choices. 3+1=4, so I'd look on the 4th line of the Triangle.
Relating it back to the make-up case, Coffee, Tea, and Water, there are 8 ways to choose:
1.Nothing
2.Coffee
3.Tea
4.Water
5.Coffee, Tea
6.Coffee, Water
7.Tea, Water
8.Coffee, Tea, Water, or ALL.
Solution 2: Assume that the forum is doing the correct calculation in a multiple choice poll.
Yeap, that's it. If you have encountered any forum poll miscalculations, then they are probably miscalculations of your own, or there is something you do not understand. It should be expected that a computer has more math power than a human brain; it's the exact reason why a computer was created in the first place.