How do economists use data as evidence for and against their models?

Here is an example, from World Cup and the Economy, by John S. Irons, from the About.com guide to economics.
 

Irons presents a table of winners, runners-up, and hosts of the 10 World Cup (soccer) matches since 1954, to see if winning the World Cup, coming in second, or hosting the event has a positive economic effect -- by increasing the economy's GDP (roughly, total production of goods and services).  Here is part of Irons' table: (I don't know why he did not include the 1994 World Cup hosted in the United States and with winner Brazil; Irons' article was written during the 1998 World Cup.)
 
 
 
GDP Growth
  Champion Pre- Post- Host Pre- Post-
1954 Germany 7.1 9.1 Switzerland 4.0 5.5
1958 Brazil 5.7 3.3 Sweden 1.9 4.0
1962 Brazil 3.9 -0.8 Chile 3.2 1.8
1966 England 1.4 3.0 England 1.4 3.0
1970 Brazil 6.5 9.7 Mexico 2.9 5.2
1974 Germany 9.5 4.7 Germany 9.5 4.7
1978 Argentina 0.0 5.6 Argentina 0.0 5.6
1982 Italy -0.3 1.5 Spain -0.6 0.5
1986 Argentina -0.9 -2.4 Mexico -2.2 0.6
1990 Germany 3.3 1.3 Italy 2.4 0.9
Mean 3.6
3.5
 2.2 3.2
Median 3.6 3.1 2.1 3.5

Real per Capita GDP growth, Annual Percentage Rate, 2 years pre- and post World Cup. Source Penn World Tables 5.6. Increases are marked in red.

Irons points out that there seems NOT to be a "champions" effect on GDP.   GDP growth rates rise for the winners in half the cases, and fall for the winners in the other half of the cases.   However, there may be a "host country effect."   In 7 out of 10 cases, grows faster after the event than before (by about 1 percentage point per year, on average).

Here is a very simple model of a host-country effect: Maybe hosting the cup boosts the economy because of spending by tourists.  Maybe it boosts the economy due to new construction as the country prepares to host the Cup.

HOWEVER, maybe it's just chance.  What is the chance of GDP growth increasing in at least 7 out of 10 cases purely by chance?

To think about this, begin by solving a simpler problem.  What's the chance of getting 2 heads when you flip a coin twice?  The answer, obviously, is 1/4.  (Four possible things can happen: 2 heads, 2 tails, a head followed by a tail, or a tail followed by a head.  Each of these has an equal chance.  So the chance of 2 heads is 1/4.)

Next, what's the chance of getting 3 heads if you flip a coin 3 times?  the possibilities are: (1) 3 heads, (2) 3 tails, (3) HHT, (4) HTH, (5) THH, (6) HTT, (7) THT, and (8) TTH.  Each possibility has an equal chance, so the chance of 3 heads is 1/8.

Third, what is the chance of getting at least 2 heads if you flip a coin 3 times?  Of the 8 possibilities listed above, 4 involve at least 2 heads.  So the chance of getting at least 2 heads, if you flip a coin 3 times, is 1/2.

Now we want to apply the same logic to different numbers -- what is the chance of getting at least 7 heads if you flip a coin 10  times?  There are a lot of possibilities here -- but luckily for us, statisticians have worked out the general answers for all cases like this.  The answer turns out to be about 0.34.

Now apply this to the World Cup:  what is the chance of getting at least 7 increases in GDP growth if you look at 10 before/after cases, assuming that the increases and decreases occur purely by chance?  The answer is 0.34. In other words, there is about a one-third chance that this "host country effect" is purely a result of chance, and about a 2/3 chance that the effect is really there.

Economists generally would not be very impressed by only a 2/3 chance that the "country-effect model" is correct.  They would conclude from this study that there is no sigificant evidence of a host-country effect.

Usually economists would want at least a 90 percent chance (and usually a 95 percent chance) that data do not result from pure chance before they would say that there is evidence in favor of a model.  In the World Cup case, economists would say that there is evidence in favor of the host-country model if GDP growth increased in at least 8 or 9 out of the 10 cases.  (The chance that 8 out of 10 cases would show increases purely by chance is only about 10 percent; the chance that 9 out of 10 would show increases purely by chance is about 2 percent.) 

Generally, economists use statistical techniques more complicated than the one used here -- but the idea is the same. They ask whether patterns in real-life data (which are predicted by an economic model) are particularly unlikely to occur by chance (or with some alternative model).  If so, then the patterns in the data are evidence for the model.
 

Question for you:
How could someone do this study better?  (Hint: look at Irons' comments on doing it better.)