Chinese zodiac

I have found out that Chinese believe that people can be matched by the Chinese zodiac. Chinese zodiac differs from European zodiac that it doesn't categories people by the month but by the year. However, they have 12 signs as well and after the 12th sign the 1st sign goes. Let's look at the match table, where 1 means less compatible and 10 more compatible:

	Rat	Ox	Tiger	Rabbit	Dragon	Snake	Horse	Goat	Monkey	Rooster	Dog	Pig
Rat	9	6	4	7	10	7	3	4	10	6	8	8
Ox	6	8	4	8	7	9	5	2	4	9	7	7
Tiger	4	4	5	5	6	3	9	4	2	4	9	7
Rabbit	7	8	5	8	7	7	5	9	4	2	8	9
Dragon	10	7	6	7	9	8	8	7	10	9	2	8
Snake	7	9	3	7	8	8	4	7	4	9	8	4
Horse	3	5	9	5	8	4	8	8	5	6	9	6
Goat	4	2	4	9	7	7	8	9	5	5	4	9
Monkey	10	4	2	4	10	4	5	5	9	4	8	7
Rooster	6	9	4	2	9	9	6	5	4	4	5	5
Dog	8	7	9	8	2	8	9	4	8	5	7	7
Pig	8	7	7	9	8	4	6	9	7	5	7	8

Courtesy of http://www.findyourfate.com/chineseastro/grid.htm

I don't know about you but I don't see much. Let's do some visualization:

Conditional formatting in Excel. High levels are green, low levels are red.

That looks interesting - there are diagonal strips. Let's use Matlab to check that the strips aren't there by accident. To do that we will do random permutation test and measure uniformity. To measure the uniformity we can look at the average standard deviation in a row. And for the beginning we shift each column up by the column index multiplied by integer.

As depicted by the graph from Matlab, the maximal uniformity is reached when i=1

To visualize the result, we can use Excel again:

Excel plot when i=1

This looks meaningfully. But is it significant?

Minitab's t-test.

Minitab didn't identify the lowest value as an outlier. Hence, over finding is not significant. This is because our test is not strong enough. Nevertheless, if we generated more permutations (that are truly random), we would conclude that our finding is significant. 

And what did we find? The signs are sorted by the year. For example the difference between the rat and the dragon is four years. And they are good match. Based on our analysis of Chinese zodiac we can conclude that the hypothesized ideal age difference is in multiplies of 4 years and the worst age difference is in multiplies of 6 years.