49 Shades of Gray

I guess it was inevitable. I got a question from a friend about the use of the “strange” numbers in my book and movie reviews. Why not just use a 1-10 scale or something like that?

There are several reasons, actually, but it should not really be a surprise for anyone that has read many of my posts. One of the many reasons is that the odd values is just plain fun (maybe plane fun is more appropriate in this context). It has a kink, a twist that appeals to my sense of honor.

A more practical reason, though, is to dodge a (potential) flaw inherent in most surveys of this kind. For example, I went to the IMDB site to check out the Ex Machina movie before attending the other day.  It gives the movie a rating of 8.1 and encourages me to add my voice to the mix. However, My choices for rating the movie is to give it 1 star, 2 stars, and so on to a maximum of 10 stars. I presume the X.X rating is a mean average of all people voting for the movie (the total stars given divided by the number of people voting). And there is a subtle but important error in this method.

If we take a hypothetical example, sets say we think the movie is the worst in the history of cinema, that had Edison foreseen this abomination resulting from his invention he would have slit his wrists rather than allow this creation to come to fruition. It is clear this “movie” should get a rating of “1 star.”

Now, if we take the other end of the scale, rating the perfect movie, one so great that even divine intervention would be insufficient to add an iota of improvement to this masterpiece. The only movie showing for the rest of all time and yet no one complains or desires any other movie to even be considered for creation or playing. This automatically deserves (and naturally receives) a rating of “10 stars.”

All is well, so far. But what do we do with the movie exactly in the middle? A movie so nondescript that you are unable to think (or say) a single good or bad thing about it? A truly middle-of-the-road piece of cinema that deserves an average score, right down the middle of our scale.

It can’t be done….! The quick answer is “5 stars” and that is what most people would give it, but this is actually a vote for DESPISE the movie rather than ADORE it, albeit with only a slight degree of disgust.

Let’s make the example simpler. If you were presented with the three movies above and you were asked to chose between “ONE” = “BAD,” “TWO” = “EH,” and “THREE” = “GREAT” the choice is easy. If, on the other hand, you are only given “ONE” or “THREE” (there is no “TWO” option) it is impossible to honestly evaluate the third movie. You either have to declare it horrible or great when it is neither.

The problem is tn the level of gradation in the choices. The first (artificial) scale has an odd number of choices (1-3) and when you take the mean of all choices [(1+2+3)/{3)] you get an answer that is included in the answer set (2). You are really capable of making a “middle” choice.

in the second (really third on the page, but the second “simpler” example) survey, you still have a mean average of 2 [(1+3)/(2)], but this time you can’t vote for the average value. There is only an even number of choices so the mean value falls between two of the choices (the only two here, but the truth continues in the larger world). In the IMDB rating system, you CAN’T vote for “five and a half stars” like you want to. You need to lie and either like a movie you don’t or hate it more than you really do.

Not that this restriction of choice is necessarily bad. In some cases you really would rather have people expressing slight (but overall important) levels of satisfaction when gathering data. Example: your group (company, agency, family, whatever) is trying to determine if you should make an important change. If you give people a survey with a “hate…dislike…indifferent…like…love” scale you stand the chance of getting absolutely no information at all. What do you learn if everyone is indifferent?

On the other hand, if you leave out the indifferent option (a “hate…dislike…like…love” selection) you might still end up with a tie, but some must chose plus and an equal set of people would need to select minus to balance out. This is more unlikely than to allow indifferent people to express their inclination.

Of course you could just make the survey use a larger number of smaller units but the even/odd number of choices issue still raises its head. And for practical reasons computer surveys will use integer values for the choices (whether 1-10 or 0-1000) and not give you the chance to enter a value of 4.7 as a floating number (which adds its own level of inaccuracy due to floating math rounding errors). Expressing my thoughts as a ratio of two numbers allows me to include a level of precision with an acceptable degree of accuracy. This should apply in about 72 of every 77 times it comes up.

But the real reason for using iconic (ironic?) values is summarized in the last line of an earlier posting.

Phred

post 55 of n

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