Wednesday 29 April 2009

Statistics can lead to bad management

It's strange that I have so much difficulty explaining to people why statistics are dangerous. I wonder whether this has anything to do with how many of them we're bombarded with through all of the different news media every day; "people are now living to 70 years old", "one in three marriages is ending in divorce", "eating burnt toast will increase your cancer risk by 50%". I made 63% of those up by the way.

Don't get me wrong, I absolutely love Excel, I studied accounting at University, and at almost every turn I like to crunch numbers and see what happens. However, with every number I see, and every spreadsheet I write, the numbers are there simply to provoke a discussion to find out what is happening in reality. I firmly believe that reality is held in the heads of the people affected by what you're measuring, and not in a set of numbers determined from whatever data was available to you.

I hear the sceptics out there saying that numbers are much more reliable than people's opinion, that you can't categorise opinions without numbers, and anyway, numbers do describe things. Well do they, really? I mean, "how many apples do I have on the table?", Oh, the answer is five. Excellent, we have a number that describes the number of apples on the table. Now try to make a decision, say, how many apples to take from the table and eat for lunch. You'll probably ask for some more numbers such as how many more days there are in the week or how many other people want an apple, but you'll be convinced that you can still use those numbers for the decision. Well, on paper (a very tiny bit) you might be right, but in reality life is much more complex. How ripe are the apples? Are some of the apples off? Do you like all of the variety of apples available on the table? Do you even like apples?

I see numbers as an approximation of real life. In Plato's Allegory of the Cave, he considers a scenario where slaves are locked up in a cave and unable to look anywhere except the back wall of the cave. On that wall are cast the shadows of the events and people happening outside the cave. The slaves can't see the real people outside the cave because they cannot turn their heads. If they were able to turn around, then they would see that the shadows were simply dull, flat representations of reality, and the true reality was rich in colour, depth and detail. It strikes me that people relying on statistics to describe real life are doing something similar. I don't want to make decisions based on shadows, I want to turn my head and see the real people, the real events, and then I'll make my decisions.

Some of you still waivering? Still want your statistics to give you a warm and fuzzy feeling when you point to a chart on a wall? Then consider this. Not only are we relying on statistics that are mere analogies of real life, but we're then performing agreggation on those statistics to reduce them even further to a single figure! I regularly see averages talked about at work. Averages are, in truth, an abomination of statistics if you intend to make any real decisions. What does an average of anything actually tell you? Since I know you all like charts so much, take a look at the chart on the right. This would provide you with the same average for all three series of data. Imagine what potential mistakes could be made by relying on the average.

Ok, the number crunchers amoung you would say that you just need standard deviation as well as the average. Well I would then point out that this is simply two dimensional and represents just a single set of numbers. We've already explained that a single set of numbers is misleading, so we'd need more numbers. Now you're into your multi-dimensional statistics. After three dimensions the graphs are going to get a bit tricky so we abandon them. Now we've lost a visual representation and are looking are reams of numbers, cross referenced and inter-linked. Stop! Surely you could have saved yourself a lot of trouble and got the people affected by whatever it is you want to measure, put them in a (metaphorical) room, and asked them. That includes customers. It doesn't need to be everyone, just a few of them. You even get to use statistics to choose the sample if you need to, that'll give your Excel fingers something to play with.

In all seriousness, statistics are a vital part of business, but they are only a very small part of management. People are way too complicated to be defined by a few numbers, and whilst you're looking at those numbers, those shadows of reality, you may miss the really important detail that could make the difference between an OK decision and a great decision. If all it would take is to ask a few questions, listen to a few people and then have a discussion, what are you afraid of?