Error of your ways series#

The distribution of responses is important to consider and the SD provides a valuable descriptive measure of this. Looking at the mean alone tells only part of the story, yet all too often, this is what researchers focus on. But the higher SD for reliability could indicate (as shown in the distribution below) that responses were very polarized, where most respondents had no reliability issues (rated the attribute a '5'), but a smaller, but important segment of respondents, had a reliability problem and rated the attribute '1'. At first glance (looking at the means only) it would seem that reliability was rated higher than value. The mean for a group of ten respondents (labeled 'A' through 'J' below) for 'good value for the money' was 3.2 with a SD of 0.4 and the mean for 'product reliability' was 3.4 with a SD of 2.1.

Error of your ways series#

Let's say you've asked respondents to rate your product on a series of attributes on a 5-point scale. SD tells the researcher how spread out the responses are - are they concentrated around the mean, or scattered far & wide? Did all of your respondents rate your product in the middle of your scale, or did some love it and some hate it?

Standard Deviation (often abbreviated as 'Std Dev' or 'SD') provides an indication of how far the individual responses to a question vary or 'deviate' from the mean. They are often referred to as the 'standard deviation of the mean' and the 'standard error of the mean.' However, they are not interchangeable and represent very different concepts. Both statistics are typically shown with the mean of a variable, and in a sense, they both speak about the mean. The following article is intended to explain their meaning and provide additional insight on how they are used in data analysis. Standard Deviation and Standard Error are perhaps the two least understood statistics commonly shown in data tables.

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