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5:05pm on Thursday, 30th April, 2015:

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At a conference in Germany last year, it was reported that some 70% of academic papers published by psychologists about games were on the subject of games and aggression. Around 20% were on games and addiction, 5% on games and children; the rest were on other aspects of psychology and games.

Now 70% is quite a lot. Almost all of it finds a significant correlation between violent games and aggression. If you compare how aggressive people are after having played a violent video game and how aggressive they are after playing a non-violent game, then you'll find a significant correlation between playing the violent game and being more aggressive.

OK, so I'm not going to go into the ins and outs of the experiments here. Let's just take the research at face value. What does "a significant correlation" mean?

Well, it comes in two parts. Firstly, you have to find a correlation. Secondly, you have to ascertain whether it's significant or not.

Now significance here is *statistical significance*. It doesn't mean "importance". The measure used by psychologists is p < 0.05, which, for non-statisticians, is equivalent to saying that there's less than a 5% chance that the correlation they have discovered doesn't exist. This 1 in 20 chance of getting a false positive (or, strictly speaking, a true negative) is reasonable, given the noise elsewhere in the system (physicists looking for the Higgs boson went with about a 1 in 3,500,000 chance, but they're spending an awful lot more money).

So, when a psychologist says that they have found a significant correlation, what they're actually saying is that there's a 1 in 20 chance they actually found a false positive. They're not saying that the correlation is noteworthy. A study that found a correlation between people who eat chocolate and people who like chocolate might be significant in this sense, but it's pointing out something that isn't itself in any way remarkable. All psychologists know that this is what the word means, as it's a technical term for them. If you take it out of the academic environment and into newspaper headlines, though, you'll find a rather different understanding of it.

So, what about the correlation itself?

Well a correlation means that if you have two variables (playing violent video games might be one, say, and feelings of aggression might be the other) then if one of them goes up or down, so does the other. An inverse correlation is where when one goes down, the other goes up. How much one changes when the other changes determines the strength of the correlation.

A correlation is not the same as causality, though: windmill blade speed and air speed correlate, but simply knowing this doesn't tell you that it's the wind that causes windmill blades to spin faster (which is just as well, because fan flade speed and air speed also correlate).

Now some correlations are very strong and some are very weak or non-existent. The way social scientists (including psychologists) work out the strength of a (linear) correlation is by calculating the Pearson product-moment correlation coefficient, which is abbreviated to r. When r=0 there is no correlation; when r=1 there is a 100% correlation; when r=-1 there is a 100% inverse correlation. In the social sciences, most correlations are not going to be 1 or -1 because human behaviour is rarely that regular.

Rather than delve into fancy maths, I'll just show you what correlations look like so you can get a feel for what they mean. These are some images I took out of *Statistics: Concepts and Controversies* by Moore and Notz:

On the left, we have r=.99 (researchers never put the 0 before the . when stating r values, by the way — I've no idea why). You can see that the dots are all close to the x=y line. If they were all on it, it would be r=1.

On the right, we have r=.9 . This is still quite close to x=y, but there's more variation. For r values, you can calculate the amount of variation by squaring it and multiplying by 100 to get a percentage. For r=.9, for example, 81% of the value of each of the variables is related to the value of the other and the remain 19% is independent.

Let's look at the other end of the scale:

Here, the one on the left has r=0 and the one on the right has r=.3, although it looks so random that if I hadn't told you then you might have had a hard time telling them apart. If someone informs you that two variables correlate with a value of r=.3, the scatter diagram on the right is how you can think of it. It's not exactly a relationship that leaps out at you and grabs you by the throat.

I also learned at the conference last year that the correlations psychologists find between the playing of violent video games and the exhibition of aggressive behaviour consistently comes in around the r=.15 mark.

70% of game psychology papers. *70%*.

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Copyright © 2015 Richard Bartle (richard@mud.co.uk).