Describing your data set

Sometimes you want to be able to talk about what your data set or group of users looked like as a whole. For example, you might want to talk about how technically knowledgable the users in your last usability study were. Use descriptive stats for this purpose. Some common descriptive stats include frequency, central tendency, and variability.

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Frequency

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One way to describe your data set is to report the size of each group that you care about. These groups might be based on gender, visual appeal rating, or time on task. Frequency (or count) is the number of times these various items appear in your data set.

Example A: Suppose you took a survey of 50 people asking them what word processing package they used. 30 people said Microsoft Word, 10 WordPerfect, 5 Google Docs, 3 Notepad, and 2 Wordpad. You could report the frequencies as Ns (30 Microsoft Word, 10 WordPerfect, etc.) or as percents (60% of respondents used Microsoft Word).

The number of people, or N, in your sample is also an important frequency to report because it usually matters whether your conclusions are based on a sample of 2 or 2,000 people.

A sample frequency report:

We tested 25 participants. They were technically savvy. Almost all had used computers before (n=24). In addition, all participants scored at least 60 on Dr. Wei's Computer Competency Test, and 15 participants scored 90 or higher.

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Central Tendency

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Sometimes we want to describe our data in a more shorthand way than frequency. In these cases, we talk about the average or central tendency of a group. Oftentimes, we use the mean to describe the average of a group, but the mode or the median could also be averages. Let's look closer at when and why we use each.

• We calculate the mean (M) when we have interval data such as time, number of visits, comprehension test scores, or satisfaction ratings. The mean = the sum of all scores divided by # of scores.
  
  Example B: Suppose we have 5 participants in a usability test, and they each took 10, 12, 40, 20, or 15 seconds to complete a task. Their mean time was (10+12+40+20+15)/5 = 19.4 seconds.

• We can use the median to describe the central point of a set of ordinal data such as rankings. The median = the midpoint of a set of scores.
  
  Example C: Suppose we have our 5 participants rate the importance of Feature X on a scale of 1 to 7 where 1 = "Not at all important" and 7 = "Extremely important." This scale is ordinal rather than interval because only the two end points are labeled, so each participant's interpretation of the values of 2-6 varies. Your participants' scores are 1, 6, 6, 7, and 7. The median is 6, which is the midpoint of the dataset when it is in numerical order. If there had been a 6th participant who gave a rating of 7, the median would be the mean of the middle two numbers, or (6+7)/2 = 6.5.
  
  You can also use the median to describe interval data if they are extremely skewed with extreme spikes or dips. Note: Using a mean and standard deviation to describe interval data is probably more common than the median. The skewness or variability of the data is reported in the standard deviation (keep reading this post).
  
  Example D: Suppose in Example B, the time scores had been 10, 12, 180, 20, and 15 seconds. (Participant 3 had stopped in the middle of the task to ask questions and share an anecdote.) The mean would have been 47.4 seconds, suggesting the task was very time-consuming to complete. The median score of 15 seconds is a much more representative description of how long it takes to complete that task.

• We can use the mode to describe the average of a set of nominal data such as the types of computers that people own. The mode = the most frequently occurring score.
  
  Example E: Suppose we gave a survey to 100 people asking them which computers they own. In our spreadsheet for responses, we record responses as follows: PC=1, Mac=2, Linux=3 (other computer types did not matter). We found that the participants owned 90 PCs, 30 Macs, and 2 Linux boxes. The mode is 1 or PC, the most frequently occurring response.

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Variability

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When we report the mean, we also report standard deviation (SD) which reflects the variability of the data set. The standard deviation tells us how spread apart a data set is. Example D had a huge outlier, so M=47.4 seconds, SD = 74.22. The standard deviation tells us that the data set had a tremendous amount of variability. If all the time scores had been exactly 15 seconds, the standard deviation would have been 0. Standard deviation is annoying to calculate by hand, but it is worth looking at an example calculation to understand how variance works.

A sample description of central tendency and variability:

The 55 survey respondents on average rated Widget W's usefulness positively: M=5.34, SD=1.51 (on a scale of 1 to 7 where 1 = "Extremely unuseful," 7 = "Extremely useful," and all other points are labeled similarly to the visual appeal question).