What type of statistical analysis is most appropriate?

Question

Imagine someone has a collection of two different sized coins (for instance nickels and quaters, or 10 and 5 pence pieces) all kept together in the same bag. They spill the contents of the bag onto a table and observe the layout of the coins before them. They then try and analyse the layout of the coins to look for 'groups' of coins - i.e. those touching each other, in clusters, and if certain sized coins were to appear within these groups.

How could they analyse the spread of coins to determine if the smaller of the two coins is more likely to group than the larger, and vice versa. If the smaller coins were found to be more prominent within the 'groups' as opposed to individually within the layout, how could this be analysed?

What statistical methods could be deployed to show that the smaller coins are more likely to be found grouped than individually. Lets say there is no element of chance involved and that smaller coins are more likely to group. (Hope this makes sense)

Answer 1

get a life lol

Answer 2

I suspect that the various sorts of parametric statistics will not be terribly usefull in this case. The best way is to compare results from your mixed bag of coins to results, for a decent number of trials, to the result when you use all large or all small coins. You might also have to vary other parameters such as height of drop, total number of coins, ratio of large to small,angle of spill etc

You could simply measure, for each coin, how many similar coins it was touching. You will then have a measure of the distribution of "touchiness" for each case. Then use ranking to assess the significance of your results.

Nice big project for somebody.

Answer 3

Try Spearman's rank correlation coefficient, it should work but only if you attempt the hypothesis twice so you have two variables you can get the variables and measurements from
Stanley Smith Stevens in his 1946 article On the theory of scales of measurement. Any good text book concerning stats will or should give you these figures, Also have a look at Wikipedia for the rho formulae for the calculation. good luck, good subject.

Answer 4

Why don't you run a linear regression. That way you see what affect the shoes have, rather than just knowing that there is an affect.

Answer 5

have you done an experiment yourself? maybe experiment yourself using one of those square things you place at random and look at the groupings within the square.

Answer 6

Try discriminant analysis