Comments on: Examples of Standard Deviation in Marketing Research

Question: Examples of Standard Deviation in Marketing Research

survivorman — Wed, 19 Mar 2008 04:31:07 -0800

Looking for clear, effective references of standard deviation in a marketing research project. For a college project, our group did some marketing research for an economically struggling pizzeria in town. We know want to present the information statistically (as per the norm), but I'd like some examples of standard deviation being used to describe the data. Yes, I do know statistics, but I'm not crazy-good with it, and our marketing prof seems really hung up on standard deviation.

One more thing you may want to know. The purpose of the research was to ascertain awareness of their product within pre-defined geographic boundaries.

Many thanks in advance.

By: a robot made out of meat

a robot made out of meat — Wed, 19 Mar 2008 05:48:37 -0800

Yes, I do know statistics, but I'm not crazy-good with it, and our marketing prof seems really hung up on standard deviation

There is a temptation among some people to display only the mean of some data. For example, that customers rated the pizza 3.82 out of 5. However, in addition to the mean you are interested in how spread out those answers are. The interpretation is different if everybody agrees that the pizza is a 3.82 or if there are a bunch of 5.0's and a handful of 1.0's. The SD is a way of concisely presenting how spread out the data are.

In binary outcomes (did you like the pizza?) the SD is dependent on the mean, and how many people answered total. Lower SD in that case corresponds to greater confidence in the answer.

I recommend that you look at the wiki or a basic stats textbook or talk to a TA if it is not clear why/how to report the SD of data.

By: blue_beetle

blue_beetle — Wed, 19 Mar 2008 06:09:32 -0800

A lot of financial writings equate std. dev with the level of risk in a portfolio. You should be able to find it in a lot of consumer-level investment books.

By: vilcxjo_BLANKA

vilcxjo_BLANKA — Wed, 19 Mar 2008 06:09:58 -0800

You and your impecunious graduate school colleague the sole occupants of an elevator. It stops at the 4th floor, and your colleague gets out. The average wealth of the elevator doesn't change very much. Now, imagine that the elevator stops on the 5th floor, and Bill Gates and Warren Buffet get in. All of a sudden, the average wealth of the occupants of the jumps precipitously. Finally, you get off at the 6th floor, but Bill and Warren stay. The average wealth of the elevator decreases, but only by epsilon. How can we find a way to measure the two events?

The key observation, of course, is that Warren and Bill are richer than you and your colleague. You could say "Let's measure the average error between the average and our wealth". That is to say, you could say "let's measure the sum of the differences between the average wealth and each of our wealths". But that turns out to be zero, and not helpful. The large positive error you introduce is equal to the sum of the smaller negative errors Bill and Warren introduce. But if you look at the average of the squares of the error, that makes the sums positive. The standard deviation is (the square root of) the average value of the squares of the error. The variance is the average of the squares of the error, so the variance is the square of the standard deviation. (I may have those name backward.)

The standard deviation is closely related to the distance in N-dimensional space between the point whose coordinates are the measurements and the point whose coordinates are all equal to the average. For the elevator case, the points are and . Since all three are far from the average, the distance will be large. In the first case, with you and your graduate student colleague, the points are and . Each of You and Her are close to this average, so the distance will be small. We don't actually measure the distances, because in a sample with a lot of measurements, many small square errors can add up to a large distance, even if each error has a small square.

You could also do this with absolute value rather than squares. This leads to a different definition of distance, in the preceding paragraph, but you get similar answers. I'm not a statistician, but I suspect that the problem with absolute value is that its derivative is discontinuous at zero, which makes it harder to work with than squaring.

FWIW, the average and standard deviation are just two in an infinite sequence of statistical momenta. The (nth root of) the average of the nth power of the error is called the nth statistical moment. It may have complex values if n is odd. Each of these momenta tells you something about the distribution. The limit as n goes to infinity is something important too, but I can't remember what it is.

This is probably more mathematical detail than you wanted, and not actually a very concrete example, but I hope it's useful.

By: a robot made out of meat

a robot made out of meat — Wed, 19 Mar 2008 06:11:22 -0800

I suppose that I should add that reporting the SD with binomial data is unusual; it'd be better to just report N or a confidence interval on the mean.

By: survivorman

survivorman — Wed, 19 Mar 2008 06:17:13 -0800

Some nice replys.

@vilcxjo_BLANKA: awesome answer. Thanks again to everyone, and I'm certainly open for more suggestions.

By: grouse

grouse — Thu, 20 Mar 2008 04:06:29 -0800

Statistically, I think it's a bit strange to use the standard deviation if your data is not normally distributed. I prefer to use the median absolute deviation, which is also robust against outliers. But for a marketing course you should probably stick to the standard deviation as your prof may not have even heard of the MAD.