# What are the recommended practices/techniques to compare “index” statistics?

Background: We've created an "in-house index" to help quantify something that was never measured/quantified before to aid better communication and provide more objective validations of internal efforts to "change the index" over time.

Question to Answer: Index value in 2018: $$I = 0.5$$ (say) 2019: $$I = 0.6$$ Was this change statistically significant or was could it be to random chance?

Null Hypothesis: Nothing interesting happened i.e., the result could be explained through dumb luck alone and not necessarily the outcome of our efforts.

Statistically Significant: Implies that it's possible something we did caused the change. Now we can spend time/effort to figure this out in more detail.

I have never done index based tests of statistical significance and even lack any education in this regard. Here are the questions I'm looking to answer:

1. Is there a set of algorithms/procedures for tests of significance for such "index" statistics? Any pointers/suggestions/links?
2. Is the "procedure" independent of the index or does one need to constantly rethink everytime you conjure a new index?
3. Is index based comparison meaningful and commonly practiced?
4. Given that an index may not be based on the "mean" but a computed/derived value how does one go about statistical tests for something like this?

Concrete example: Here are some results I found for "Shannon diversity index" but even they have two different ways:

The Shannon/Simpson index are good examples and what I'm trying to do is quite similar. I've cast this as a "broad" question to "learn" steps involved when confronted with something like this.

In this particular case you have two known values $$I_{2018} = 0.5$$ and $$I_{2019} = 0.6$$. Since $$0.5 \neq 0.6$$ those values are different, with certainty. There is no legitimate sense in which we would say that the difference between the number $$0.5$$ and the number $$0.6$$ is "statistically significant". They are different numbers, with certainty; that is all.