Statistics for HCI Research: Types of Data

Types of Data

There are four kinds of data you encounter in an analysis. Nominal (Categorical), Ordinal, Interval, and Ratio.

Nominal: The data indicating categories. There is no notion of ordering in nominal data. The examples are Techniques (technique A, technique B,...), Gender (male, and female), and Occupation (students, professional programmers,...).
Ordinal: The data which you can order (there is a notion of small or large), but the difference between any of the two values may not be always equal. The examples are responses of a Likert-scale question.
Interval: The data which you can order and the difference between any of two values are the same, but there is no absolute zero, which allows us to have meaningful negative values. The most famous example is temperature with C or F. 0 C or 0 F are artificially defined and negative values can be used for these units. But the differences between 0 C and 1 C and between 100 C and 101 C are the same.
Ratio: The data which you can order and the difference between any of two values are the same (so they are interval), and there is the absolute zero. This means that a meaningful negative value of interval data does not exist (in statistics). The examples are weight, height, length, time, speed, and error rate. Counts can often be considered as ratio.

The different types of data have different characteristics for mathematical operations.

Operations	Nominal	Ordinal	Interval	Ratio
Frequency count, mode, chi-square	O	O	O	O
Median, percentile	X	O	O	O
Add, subtract, mean, variance, correlation, regression	X	X	O	O
Geometric/harmonic mean, coefficient of variation, logarithms	X	X	X	O

Thus, the ratio data allow you to do the most mathematical operations followed by interval, ordinal, and nominal data. It is better to design your experiment so that your dependent variable (what you measure) is ratio. It allows you to do a variety of analyses.

And you have two distinctive variables for statistical tests.

Independent variables: The dimensions you are testing the data against.
Dependent variables: The values you are using for your test. Usually you have only one dependent variable for one test.

Let's say you are comparing the performance time of two interaction techniques (Technique A and Technique B). Your independent variable is techniques, which is nominal. You are comparing performance time against the techniques and there is no concept of ordering for the techniques. Your dependent variable is performance time (msec), which is ratio. You can order time and the millisecond is an equal unit. It is important to figure out which dependent variables and independent variable you use and what types of data they are before jumping into any kind of statistical tests. The types of data determine statistical methods you can use. Particularly, it is generally a good idea to make your dependent variable interval or ratio because it allows you to do a wider variety of statistical analyses than nominal or ordinal.

One thing you may need to consider is how to treat the data from your Likert-scale questions. If you can assume that the differences between any two options are equal, you can treat them as interval data. For instance, if your options are strongly agree, agree, neutral, disagree, and strongly disagree, you may be able to treat them as interval data. However, if your options are like use it everyday, use it once a week, use it once a month, use it once a year, and have never used it, it is probably safer to treat them as ordinal data.

Comments [Show the comment form]

Note, this paper warns against treating Likert scales as intervals or ratios.
http://portal.acm.org/citation.cfm?id=1753686

— Anonymous (2010-12-03 09:06:01)

Thank you for the reference. I think the point is not just about treating the responses of Likert-scale questions as intervals or ratios, but also about whether they satisfy other assumptions that parametric tests have (e.g., normality). I believe that there are a number of cases where most of the responses are skewed into one side of the spectrum, and in that case, simply applying parametric tests can be dangerous.

My recent personal practice is to avoid Likert-scale questions as much as possible. In my opinion, they are not always straightforward to interpret quantitatively (if you only look for the frequency count or median, it's fine to use them though), and they are not informative sometimes. Rather, I try to use qualitative approaches, which gives me richer data in individual cases (the downside of this is that it is tedious if you want to get many samples).

— KojiYatani (2010-12-07 05:55:14)

Hi. Great site! Just a question. So if you don't use likert style questions after then experiment, how can you get qualitative data that will show you which technique of the two participants preferred. Is there another qualitative evaluation method?

— Anonymous (2012-01-29 18:01:38)

In general, I like having interviews with participants to understand "why" they liked a particular technique and they did not like it. I usually ask something like "what was the best thing and worst thing about this particular technique?" or "how do you think this technique helped you?". The idea is you want to get comments from participants which are well grounded to the context. With these comments, you can deepen your analysis on when the techniques work or don't work, and how you can improve them. In my opinion, these can convey much more interesting insight than simple Likert-scales. (I don't object Likert-scales, but they are often over-used, unfortunately...)

— KojiYatani (2012-02-08 11:03:41)

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Statistics for HCI Research : DataType

Types of Data