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Basic foilset Java Academy:Polls and Throwing Dice

Given by Geoffrey Fox at NPAC Java Academy February--April 99 on Mar 20 1999. Foils prepared Mar 20 1999
Outside Index Summary of Material

We learnt how to build Applets that simulate Tossing of Coins and Throwing Dice
Here we describe implications for Polling
Details at Java Academy Site

Table of Contents for full HTML of Java Academy:Polls and Throwing Dice

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1 Rolling Dice and Deciding who will win the Election Geoffrey Fox Java Academy March 20 99
2 Polls do Quite Well with Small Samples
3 Sources of Errors in Polls
4 Errors with 200 Dice
5 Shape of Frequency Plot
6 Tossing Coins is a Better Idea
7 Decreased Sample size.
8 Effect of Fewer Experiments
9 Debug Statements on the Console

Outside Index Summary of Material

HTML version of Basic Foils prepared Mar 20 1999

Foil 1 Rolling Dice and Deciding who will win the Election Geoffrey Fox Java Academy March 20 99

From Java Academy:Polls and Throwing Dice NPAC Java Academy February--April 99 -- Mar 20 1999. *
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If you follow the process of an election or the White House or Republicans deciding on the correct strategy, one goes out and takes a poll.
Often the same issue is polled by lots of different groups; CNN, New York Times; political parties etc. You may have noticed that most polls use between 500 and 1500 people. Here we will try to show you why!
You may have also noticed that such polls quote a margin of error in their results
HTML version of Basic Foils prepared Mar 20 1999

Foil 2 Polls do Quite Well with Small Samples

From Java Academy:Polls and Throwing Dice NPAC Java Academy February--April 99 -- Mar 20 1999. *
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e.g. they might say that 50% of the people polled thought Donald Duck would win the election with a margin of an error of 3 percent points.
They predict that somewhere between 47% and 53% of the public would vote for Donald Duck.
If all 100 million or so of the US voting population vote, you get the real result. However you can get to within 3% of the answer by just talking to 1000 people – a tiny fraction .00001 of the total.
This could save a lot of money on Election Day and says you can stay home and learn more Java unless it is a close election. Actually this is not a very democratic way to think, and everybody should vote – otherwise those that love Java would always stay at home and we would never elect Politicians who program...
HTML version of Basic Foils prepared Mar 20 1999

Foil 3 Sources of Errors in Polls

From Java Academy:Polls and Throwing Dice NPAC Java Academy February--April 99 -- Mar 20 1999. *
Full HTML Index
So if one makes a poll, the error comes from two sources – the so-called statistical error and the so-called bias.
  • The bias is like we discussed above – one must choose a representative subset of the voters.
  • The reason why one chooses some 1000 people to poll, is that this will give statistical errors of around 2% and the quoted errors combine this with errors due to a biased sample.
There is not much point in using more 1000 or so in a poll as you will decrease the statistical error but it will be hard to decrease the overall error much more.
HTML version of Basic Foils prepared Mar 20 1999

Foil 4 Errors with 200 Dice

From Java Academy:Polls and Throwing Dice NPAC Java Academy February--April 99 -- Mar 20 1999. *
Full HTML Index
Let us consider the case of rolling 200 Dice and summing the spots. This will lead to a result between 201 and 1200 with an average of 700.
Subtracting 200, we get the equivalent of 1000 people with a poll whose result is 50% yes and 50% no. Any one summing of 200 Dice will not get 700 but a value near this. The applet does this process a number totalFrq times and plots the result as a histogram or frequency plot of dice sums.
Frequency
Value of 200 Summed Dice faces
700 Mean
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HTML version of Basic Foils prepared Mar 20 1999

Foil 5 Shape of Frequency Plot

From Java Academy:Polls and Throwing Dice NPAC Java Academy February--April 99 -- Mar 20 1999. *
Full HTML Index
Note that the histogram is quite a pretty bell shape and in fact there is a fancy theory called the "central limit theorem" which derives the shape as a so-called Gaussian.
There is a separate discussion of Gaussians on the web site
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700 Mean
One finds a percentage error or standard deviation of 2.4%.
10% of events are in upper yellow region > 3% larger than mean
HTML version of Basic Foils prepared Mar 20 1999

Foil 6 Tossing Coins is a Better Idea

From Java Academy:Polls and Throwing Dice NPAC Java Academy February--April 99 -- Mar 20 1999. *
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So a better model is tossing coins a 1000 times.
Shift over coin toss by 200 so results lie in range 201..1200 as in the Dice accumulation.
Now the frequency distribution is narrower.
It is still a beautiful bell shaped Gaussian but the percentage error is 1.6% not 2.4%.
You will get better answers from asking 1 person from 1000 households rather than 5 people from each of 200 households.
Actually Dice are not a very good representation of polling, as a result with 1000 cells corresponds to only 200 Dice
This is like polling where you went to 200 households and asked 5 people in each household. It is not 1000 independent samples.
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700 Mean
1000 Tosses Count Number of Heads
Add 200
HTML version of Basic Foils prepared Mar 20 1999

Foil 7 Decreased Sample size.

From Java Academy:Polls and Throwing Dice NPAC Java Academy February--April 99 -- Mar 20 1999. *
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With 100 coin tosses (a polling sample of 100), the statistical error is 5% -- too big to be comfortable. There is a simple rule for such errors
  • If you want to halve error, you must quadruple the sample size. Thus with 400 coin tosses the error is 2.5% which is half the result for 100 coin tosses.
100 Coin Tosses
400 Coin Tosses
Error 5%
Error 2.5%
Shape is still a Gaussian
1000 Coin Toss Error a factor of Sqrt(10) Smaller than 100 Tosses
HTML version of Basic Foils prepared Mar 20 1999

Foil 8 Effect of Fewer Experiments

From Java Academy:Polls and Throwing Dice NPAC Java Academy February--April 99 -- Mar 20 1999. *
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Suppose we reduce the number of trials from the excessive 300,000 to a more immediate 10,000.
Then the means and error estimates come out just fine but the histogram is more ragged.
The histogram is not so near the red lines (The Gaussian Bell) but has random deviations above and below it
HTML version of Basic Foils prepared Mar 20 1999

Foil 9 Debug Statements on the Console

From Java Academy:Polls and Throwing Dice NPAC Java Academy February--April 99 -- Mar 20 1999. *
Full HTML Index
I got a bit worried in these long computations. Was the program running OK?
So I used a useful dodge of inserting print statements to the Java Console
(if(i%5000 == 0 ) System.out.println ("Generating " +i);)
Program wrote a message every 5000 trials.
I also wrote out some messages in paint method to show it had got there.
Note messages in paint are repeated each time page reloads but earlier messages from init are not.
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