Bias in End of Year Polls (and Happy New Year)

So, in rolls 2012 and out rolls another year. I like new year: it’s a time to fill yourself with optimism about the exciting things that you will do. Will this be the year that I write something more interesting than a statistics book, for example? It’s also a time of year to reflect upon all of the things that you thought you’d do last year but didn’t. That’s a bit depressing, but luckily 2011 was yesterday and today is a new year and a new set of hopes that have yet to fail to come to fruition.

It’s also the time of year that magazines publish their end-of-year polls. Two magazines that I regularly read are Metal Hammer and Classic Rock (because, in case isn’t obvious from my metal-themed website and podcasts, I’m pretty fond of heavy metal and classic rock). The ‘album of the year’ polls in these magazines are an end of year treat for me: it’s an opportunity to see what highly rated albums I overlooked, to wonder at how an album that I hate has turned up in the top 5, or to pull a bemused expression at how my favourite album hasn’t made it into the top 20. At my age, it’s good to get annoyed about pointless things.

Anyway, for years I have had the feeling that these end of year polls are biased. I don’t mean in any nefarious way, but simply that reviewers who contribute to these polls tend to rate recently released albums more highly than ones released earlier in the year. Primacy and recency effects are well established in cognitive psychology: if you ask people to remember a list of things, they find it easier to recall items at the start or end of the list. Music journalists are (mostly) human so it’s only reasonable that reviewers will succumb to these effects, isn’t it?

I decided to actually take some time off this winter Solstice, and what happens when you take time off? In my case, you get bored and start to wonder whether you can test your theory that end of year polls are biased. The next thing you know, you’re creating a spreadsheet with Metal Hammer and Classic Rock’s end of year polls in it, then you’re on Wikipedia looking up other useful information about these albums, then, when you should be watching the annual re-run of Mary Poppins you find that you’re getting R to do a nonparametric bootstrap of a mediation analysis. The festive period has never been so much fun.

Anyway, I took the lists of top 20 albums from both Metal Hammer and Classic Rock magazine. I noted down their position in the poll (1 = best album of the year, 20 = 20^th best album of the year), I also found out what month each album was released. From this information I could calculate how many months before the poll the album came out (0 = album came out the same month as the poll, 12 = the album came out 12 months before the poll). I called this variable Time.since.release.

My theory implies that an album’s position in the end of year list (position) will be predicted from how long before the poll the album was released. A recency effect would mean that albums released close to the end of the year (i.e. low score on Time.since.release) will be higher up the end of year poll (remember that the lower the score, the higher up the poll the album is). So, we predict a positive relationship between position and Time.since.release.

Let’s look at the scatterplot:

Both magazines show a positive relationship: albums higher up the poll (i.e. low score on position) tend to have been released more recently (i.e., low score on the number of months ago that the album was released). This effect is much more pronounced though for Metal Hammer than for Classic Rock.

To quantify the relationship between position in the poll and time since the album was released we can look at a simple correlation coefficient. Our position data are a rank, not interval/ratio, so it makes sense to use Spearman’s rho, and we have a fairly small sample so it makes sense to bootstrap the confidence interval. For Metal Hammer we get (note that because of the bootstrapping you’ll get different results if you try to replicate this) rho = .428 (bias = –0.02, SE = 0.19) with a 95% bias corrected and accelerated confidence interval that does not cross zero (BCa 95% = .0092, .7466). The confidence interval is pretty wide, but tells us that the correlation in the population is unlikely to be zero (in other words, the true relationship between position in the poll and time since release is likely to be more than no relationship at all). Also, because rho is an effect size we can interpret its size directly, and .428 is a fairly large effect. In other words, Metal Hammer reviewers tend to rank recent albums higher than albums released a long time before the poll. They show a relatively large recency effect.

What about Classic Rock? rho = .038 (bias = –0.001, SE = 0.236) with a BCa 95% CI = –.3921, .5129). The confidence interval is again wide, but this time crosses zero (in fact, zero is more or less in the middle of it). This CI tells us that the true relationship between position in the poll and time since release is could be zero, in other words no relationship at all. We can again interpret the rho directly, and .038 is a very small (it’s close to zero). In other words, Classic Rock reviewers do not tend to rank recent albums higher than albums released a long time before the poll. They show virtually no recency effect. This difference is interesting (especially given there is overlap between contributors to the two magazines!).

It then occurred to me, because I spend far too much time thinking about this sort of thing, that perhaps it’s simply the case that better albums come out later in the year and this explains why Metal Hammer reviewers rate them higher. ‘Better’ is far too subjective a variable to quantify, however, it might be reasonable to assume that bands that have been around for a long time will produce good material (not always true, as Metallica’s recent turd floating in the loo-loo demonstrates). Indeed, Metal Hammer’s top 10 contained Megadeth, Anthrax, Opeth, and Machine Head: all bands who have been around for 15-20 years or more. So, in the interests of fairness to Metal Hammer reviewers, let’s see whether ‘experience’ mediates the relationship between position in the poll and time since the album’s release. Another 30 minutes on the internet and I had collated the number of studio albums produced by each band in the top 20. The number of studio albums seems like a reasonable proxy for experience (and better than years as a band, because some bands produce an album every 8 years and others every 2). So, I did a mediation analysis with a nonparametric bootstrap (thanks to the mediation package in R). The indirect effect was 0.069 with a 95% CI = –0.275, 0.537. The proportion of the effect explained by mediation was about 1%. In other words, the recency bias in the Metal Hammer end of year poll could not be explained by the number of albums that bands in the poll had produced in the past (i.e. experience). Basically, despite my best efforts to give them the benefit of the doubt, Metal Hammer critics are actually biased towards giving high ratings to more recently released albums.

These results might imply many things:

• Classic Rock reviewers are more objective when creating their end of year polls (because they over-ride the natural tendency to remember more recent things, like albums).
• Classic Rock reviewers are not human because they don’t show the recency effects that you expect to find in normal human beings. (An interesting possibility, but we need more data to test it ...)
• Metal Hammer should have a ‘let’s listen to albums released before June’ party each November to remind their critics of albums released earlier in the year. (Can I come please and have dome free beer?)
• Metal Hammer should inversely weight reviewer’s ranks by the time since release so that albums released earlier in the year get weighted more heavily than recently released albums. (Obviously, I’m offering my services here …)
• I should get a life.

Ok, that’s it. I’m sure this is of no interest to anyone other than me, but it does at least show how you can use statistics to answer pointless questions. A bit like what most of us scientists do for a large portion of our careers. Oh, and if I don’t get a ‘Spirit of the Hammer’ award for 15 years worth of infecting students of statistics with my heavy metal musings then there is no justice ion the world. British Psychological Society awards and National Teaching Fellowships are all very well, but I need a spirit of the hammer on my CV (or at least Defender of the Faith).

Have a rockin' 2012

andy

P.S. R code,data (CSV file).

P.P.S. My top 11 (just to be different) albums of 2011 (the exact order is a bit rushed):

1. Opeth: Heritage
2. Wolves in the Throne Room: Celestial Lineage
3. Anthrax: Worship Music
4. Von Hertzen Brothers: Stars Aligned
5. Liturgy: Split LP (although the Oval side is shit)
6. Ancient Ascendent: The Grim Awakening
7. Graveyard: Hisingen Blues
8. Foo Fighters: Wasting Light
9. Status Quo: Quid Pro Quo
10. Manowar: Battle Hymns MMXI
11. Mastodon: The Hunter