need help interpreting this Pearson R Correlation data

#1
Hi, I have a question and would welcome advice.

I have conducted a pearson R stats test in SPSS and found that there is no relationship between the three trends that I am interested in.

BUT the trends run over two conditions/periods. When I break the dataset up and run the test again looking at the 3 trends in each condition separately , I am finding strong associations (p.005 and <.001).

This would seem to me to be saying that there is no association between the trends across the entire period, BUT there is a strong relationship between them when each period is considered separately. Does this make sense or am I misinterpreting the data?
 
#5
ah, ok: here they are.

The dataset covers the years 1760 to 1822 and the three trends are:
the cost of living (measured by the Schumpeter-Gilboy index)
the number of property offenders sentenced to death
the number executed

I am interested to see whether there is a relationship between SG and the SoD. Here are the scatters:
 
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