Posts from September 2011 (26)

Expect to hear a lot of big numbers thrown about during the Rugby World Cup – and not just about those on the field.

When Auckland hosts the Rugby World Cup Opening Night Celebrations this Friday, people will want to know how many turned up. The success of the event (and justification for the expenditure) will be measured in part by estimated crowd size.

Crowd estimation is often not at all scientific. During tonight’s ONE News bulletin, reporter Jack Tame estimated there were “five or ten thousand delirious Tongan fans”.

How are crowd estimate figures obtained and how reliable are they?

The authors of a new study published in Significance, the magazine of the Royal Statistical Society and the American Statistical Association claim that most crowd estimations are unreliable and that the public should view crowd estimation with scepticism:

“In the absence of any accurate estimation methods, the public are left with a view of the truth coloured by the beliefs of the people making the estimates,” claims Professor Paul Yip, of the University of Hong Kong, one of the authors of the study.

“It is important to rectify the myth of counting people. The public would be better served by estimates less open to political bias. Our study shows that crowd estimates with a margin of error of less than 10% can be achieved with the proposed method.”

Further reading:

• How many were there when it mattered?
• Feeding the Five Thousand – or was it Three?
• The Protest Numbers Game

Also of interest:

• Royal Wedding TV audience closer to 300m than 2bn

Guest post by Tony Cooper

Paul The Octopus is famous for picking the winner in 8 out of 8 games at the FIFA World Cup in 2010. How did he achieve this amazing feat? Was he skilled or was he lucky?

To get 8 out of 8 games right where each game is a 50-50 guess the probability is 0.5 x 0.5 x 0.5 x 0.5 x 0.5 x 0.5 x 0.5 x 0.5 = 0.0039 (or one chance in 256). This seems too incredible. An octopus can’t be that good.

Where is the flaw in this probabilistic reasoning?

The answer is that the probability that Paul got a game right was not 0.5 but more. Much more. In fact the probability was much closer to one. Here is the explanation:

Paul, a German octopus, was only used to pick German games, usually picked the German team, and the German team usually won. So the chance that Paul picked the winner was more than 0.5 for each game. That accounts for 5 of the 8 games.

What about the games that Germany lost and the game where Germany didn’t play? Let’s take a guess.

This tournament was not Paul’s first time at playing the game. He had learned previously that there was always food under the German flag. Paul – with some ability to distinguish the flags of different countries – usually went for the German black, red, and yellow. He might have had monochrome eyesight which is why he picked Serbia as a winner in the game against Germany because in monochrome the Serbian and German flags look similar.

For the final Germany wasn’t playing so Paul went for the most German looking flag – that of Spain (red, yellow, red). He seems to have a preference for that flag since he also predicted the win of Spain over Germany in the semi-finals. All flags picked by Paul had horizontal stripes.

So Paul was lucky but not as lucky as the 1 in 256 chance suggests. His main luck was that his team was one of the best teams in the tournament and that some of the other good teams had similar flags.

Will Richie McCow be successful at picking the winner of the All Black games in the Rugby World Cup? Possibly – as long as he keeps picking the All Blacks and the All Blacks keep winning. Will the All Blacks keep winning? That’s a story for a later article.

Tony Cooper, formerly of the Applied Mathematics Division of the DSIR, is a Quantitative Analyst with Double-Digit Numerics of Auckland. He consults mainly in the investment, finance, and electricity industries. His research interests include risk and volatility prediction, alpha generation, data mining, statistical learning, and time series analysis.

Thank you for the three nominations for this week’s Stat of the Week competition.

Tony’s nomination of Spirit Level has been highly politicized and would require us to be ready to provide detailed rebuttals to the proponents of both sides of the argument. Life is too short!

We’d also like to hear the results of Ian Well’s complaint to the NZBCA of Growpro’s statistics and find out more details before commenting on them. (Ian, please advise us when the ruling comes out if there are comments on the statistics.)

Miranda Devlin’s nomination makes a good point that the obesity and overweight figures quoted are overall ones, rather than just for women (as the whole article is about them). However, in the sentence before these statistics are mentioned, the article does point out the obesity percentage for women.

In saying all this, we aren’t selecting a Stat of the Week this week but encourage you to discuss the nominations further if you wish.

Each week, we would like to invite readers of Stats Chat to submit nominations for our Stat of the Week competition and be in with the chance to win an iTunes voucher.

Here’s how it works:

• Anyone may add a comment on this post to nominate their Stat of the Week candidate before midday Friday September 9 2011.
• Statistics can be bad, exemplary or fascinating.
• The statistic must be in the NZ media during the period of September 3-9 2011 inclusive.
• Quote the statistic, when and where it was published and tell us why it should be our Stat of the Week.

Next Monday at midday we’ll announce the winner of this week’s Stat of the Week competition, and start a new one.

The fine print:

• Judging will be conducted by the blog moderator in liaison with staff at the Department of Statistics, The University of Auckland.
• The judges’ decision will be final.
• The judges can decide not to award a prize if they do not believe a suitable statistic has been posted in the preceeding week.
• Only the first nomination of any individual example of a statistic used in the NZ media will qualify for the competition.
• Employees (other than student employees) of the Statistics department at the University of Auckland are not eligible to win.
• The person posting the winning entry will receive a $20 iTunes voucher.
• The blog moderator will contact the winner via their notified email address and advise the details of the $20 iTunes voucher to that same email address.
• The competition will commence Monday 8 August 2011 and continue until cancellation is notified on the blog.

If you’d like to comment on or debate any of this week’s Stat of the Week nominations, please do so below!

Why? Because there are more white sheep than black sheep.

The ACC understands this principle; their map of the ‘most dangerous regions’ for falls in NZ is based on number of claims per 1000 population in 2010.  Even though Auckland has the most reported falls, it doesn’t have the highest risk.

It’s less clear that the Herald understands. They described a list from the NZ Transport Agency as New Zealand’s most dangerous intersections have been revealed for the first time. The list was actually the intersections with the greatest number of crashes leading to injury, not corrected in any way for traffic intensity.

Now, if you want to decide which intersections are the highest priority to redesign, the total number of serious crashes is a useful statistic. But if you want to know where it is most dangerous to drive, you need the denominators.