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Interestingness and importance are two characteristics sometimes associated

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with high-quality research or high-quality claims.

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 But interestingness and importance are not the same and sometimes

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interesting things are not important and important things are not interesting.

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So, what are these concepts and 

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how do you evaluate whether an article presents interesting or important claims?

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Interestingness is a concept 
that is debated currently in the literature

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and our idea of interestingness 
comes from this article from 1971.

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And I'm not going to talk about that article in detail but briefly, it states that the claim

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is interesting if it denies a prior belief of a person.

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So for example, if I don't believe that there is extraterrestrial life

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and then someone tells me that UFO just landed in front of the university,

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I would find that claim interesting because it denies my prior belief,

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that extraterrestrial life does not exist.

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So this is interestingness, and interestingness typically

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also refers to something that makes us think differently,

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it challenges our prior beliefs, claims that support our prior beliefs

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or claims that are indifferent to our prior beliefs are not interesting.

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So, this is one way to define 
interestingness,

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how much this challenge is our current thinking?

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Interestingness and importance are two different things and there is

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some debate on, whether interestingness is actually something

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that we should strive for in research or whether we should strive for importance.

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Quite often when you see articles they try to present their findings as interesting

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because if you present interesting findings then that is more likely to get

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attention, and more likely to get others to read your study or read your theory.

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Important things are sometimes 
boring, we don't want

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to do important things all the time, and for that reason,

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importance has been less of a concern for some researchers.

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So, what is importance then if importance is not the same as interestingness?

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This article from the Academy of Management Journal or Editorial

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states that importance relates to consequences.

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So things, findings, theories that have big consequences

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for society or for individuals are important.

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For example, if we think about the COVID-19 pandemic there are the claim

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or recommendation that we should socially distance,

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it is important because not doing so has big consequences for the society.

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But it is not interesting because it does not challenge our prior beliefs

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and we've heard the recommendation 
of social distancing quite many times. 

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So, importance can mean two different things,

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on the level of a theory or level of claim interestingness can mean relevance and consequences.

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So, if something has consequences, and those consequences

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are relevant for me, then that claim, or theory is important.

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Otherwise, it is not important.

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Another thing that is important is evidence,

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so if we do a trial of a new medication, 
we find that the medication works,

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that could be an interesting finding and an important finding.

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If we replicate the same study again, we find evidence that the medication works,

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well that is not interesting because we had that evidence already,

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but it is important because we want to know that the first study that studied

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the effectiveness of the medication was not just an analysis error,

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and we also want to know that it was not just that specific population in which

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the medication was useful but it applies more broadly.

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So quite often we have an initial idea, 
initial piece of evidence which is interesting,

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and then we have still lots of uninteresting but important things to do,

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to know that the claim that was initially made is actually valid,

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 not the result of analysis error, or research is an error and not a result

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of simply idiosyncrasies of one particular population or sample.