Entry for 31 December 2009:
An excerpt from Training the Trainers: A Research Training Manual, McLeod, Elliott & Wheeler, in press.
Commentary: I spent the end of November and the beginning of December working on revisions to the research training manual that John McLeod, Sue Wheeler and I have been working on for the past 2 years. John added a section on understanding common statistical concepts to the latest version, which I thought was a good idea, but as usual, we are struggling with how to explain in ordinary language what a standard deviation is. If I remember correctly, it was my attempt to explain this concept that lead one of our diploma students to make a t-shirt that read, “The last thing I understood was the baked potato I ate for lunch.” The following builds on John’s version and is my most recent attempt to get the idea across:
It is also important to know about the variability of scores - the amount of spread in the distribution of scores. The standard deviation statistic (abbreviated as s, s.d., sd or SD) is usually given in research reports as a measure of variability. In fact, the SD figure is the average variability of scores. That’s where the term “standard deviation” comes from: It is a kind of average or typical (hence “standard”) difference (hence “deviation”) between each person’s score and the mean score. It tells us how far off the average person is from the average, which also tells us how far we should trust the average as a way of representing the people in the sample: The bigger the SD, the farther people tend to be from average. Interesting facts about SDs:
• About two-thirds of people in a sample will have scores that are within one SD above or below the mean.
• About 95% of people will have scores that are within 2 SDs above or below the mean.
• On a standard 5-point rating scale, such as that used by the CORE Outcome Measure, many items will have SDs of about 1 scale point, so it’s a good idea to pay attention to items with SDs substantially above (1.5) or below (.5) that.
Further reflections. "Standard deviation" is another one of these oxymorons that we never think about: The idea of a standard/typical exception/deviation from the general case clashes internally; if we listen to it careful, we can hear its Bartokian dissonance as another kind of harmony. We tend simultaneously toward the general, the central tendency and to our own individuality and uniqueness. The Standard Deviation recognizes this and its own peculiarly quantitative way honours this individuality.