Of course, the evidence from a single crime may or may not prove conclusive. Over time, though, evidence from many crimes along with improved technology for gathering and analyzing evidence leads to better theories and an improved ability in any one case to rule some suspects out and others in.
Similarly, macroeconomists gather evidence about economies in the form of data. They then form a hypothesis about how the data came to be and test it to see whether the data supports it or not.
Unfortunately, neither detectives nor macroeconomists have labs in which they can run carefully controlled experiments to test their various hypotheses precisely. This is an advantage reserved to natural sciences such as chemistry, physics, and medicine. If a macroeconomist wants to work out the impact on the economy of cutting government spending by half, she can't just do it and see what happens! She can, however, look at the data (across countries and across time) and try to infer the likely relationship between government spending and other macroeconomic variables (like inflation, unemployment, and real GDP).That kind of statistical inference though is fraught with problems. For example, imagine that you notice two facts: that countries with higher levels of education tend to be richer and that as the people of a country become more educated, it becomes richer. On the basis of these facts you reach the conclusion that more education causes people to become richer.
But wait a minute! How do you know that it isn't the other way around: when a country is richer it spends more on education? In which case, people becoming richer is causing them to have more education. Or a third variable may be causing high levels of education and wealth (such as a well-functioning political and legal system). In which case, a country being well off and well educated is correlated but not causally linked.