Correlation between two vectors

[Farid Mammadaliyev]

Dear Statalister,

I am currently working with data which include patents, patent classes and year. Here is dataex of my data:

* Example generated by -dataex-. To install: ssc install dataex
clear
input int year long number_of _patents int class

2000 5   1
2000 6   2
2000 7   3
2000 3   4
2001 9   1
2001 8   2
2001 4   3
2001 12  4
2001 5   5

end

This means that in 2000 there were 5 patents in class 1, 6 patents in class 2, 7 patents in class 3 and 3 patents in class 4.

What I intend is to find Peason correlation of patent distribution between two consecutive years , namely between vector a(5 6 7 3) and vector b(9 8 4 12 5). The more similar patent distributions between two consecutive years are, the less environmental turbulence is present.

Thanks in advance for any help.

Best regards, Farid

[Maarten Buis]

I assume you mean association when you talk about correlation, because a correlation does not make any sense for a categorical variable like class of patent. In that case it is just a matter of a simple chi squared test on cross-tabulation: tab class year [fw=number_of_patents], col chi . The null hypothesis is that the distributions are independent, that is, any patterns that seem to exist are only due to differences in the marginal distributions

[Farid Mammadaliyev]

Maarten, let me try to restructure my date to make easier:

* Example generated by -dataex-. To install: ssc install dataex clear input int year long number_of _patents int class

2001 5 1
2002 6 1
2003 7 1
2004 3 1
2001 9 2
2002 8 2
2003 4 2
2004 12 2
2005 5 2

end

Here are two patent classes (1 and 2). The second column represents number of patents in a certain year within a class. Therefore, I need autocorrelation between years for class 1 and class 2 in the same column. It looks like having autocorrelation for different groups in the same column. Put differenlty, the code is supposed to calculate autocorrelation from 1st to 4th column, then start again from 5th to 9th.

Is this possible?

Best regards, Farid