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SPSS: Statistics for the mathematically challenged

Many people enjoy behavioural research, whether it's running a usability test, fielding a survey or observing people doing their jobs. Finding things out and making new discoveries excites our natural human curiosity. But when faced with the task of analysing the data behind the research, many people feel their excitement drain away. Most of us are not excellent mathematicians and the notion of using data to test scientific hypotheses can be intimidating. But data analysis is an important aspect of virtually all research. So how can you overcome a fear of maths to learn how to use statistics?

— Tendayi Viki, Apr 2, 2008

If you know just one thing about statistics, it will be that statistics is a branch of mathematics. But nowadays, it is actually possible to think of stats as being slightly different from maths. When I learnt how to do data analysis we did it by hand. This meant that you had to be capable of interpreting complex mathematical formulae and perform the relevant statistical analyses. Good mathematical skills were an absolute necessity. However, with the arrival of data analysis programmes such as SPSS, good mathematical skills are no longer needed. If you can add, subtract, divide and multiply, and you are computer literate, you can learn how to do statistical analyses using SPSS.

The key to using SPSS lies not in understanding maths but in understanding research — or more accurately, the statistical concepts underlying research. Learning statistical concepts is no different to learning about any other concepts (such as learning to use the Internet). If you can learn to describe and think about your research using the right concepts and ideas, then using SPSS is quite simple. Of course, you do need to learn where to click to get the various types of stats, and also how to interpret the output, but in this regard SPSS is like any other computer program. This "tool knowledge" is really easy to figure out once you have mastered the key statistical concepts.

So what are the key statistical concepts you have to master in order to be able to use SPSS? There are just three:

• How to distinguish between an independent and a dependent variable.
• How the variables in your study are being measured.
• The type of study design you are using.

Let's look at each of these in turn.

Key Concept 1: Independent and Dependent Variables

The first key concept is the distinction between an independent and a dependent variable. In an experiment, an independent variable is the variable under the researcher's control. For example, a researcher might ask people to evaluate three alternative designs for a TV remote control. People's reaction to the different designs, as measured by the researcher, is the dependent variable. One way to think of this distinction, especially for researchers who do not do experiments, is to think of dependent variables as outcome measures. In this context, independent variables can be thought of as predictor variables. For example, in a study where researchers are interested in gender differences in choice of product colour, gender is the predictor variable and product colour choice is the outcome measure.

Key Concept 2: Levels of Measurement

The second key concept is to understand how you are measuring the variables in your study: that is, how you will represent the variables when you enter the data into a spreadsheet. You have three choices:

• Nominal.
• Ordinal.
• Continuous.

Nominal scale

The first level of measurement is called the nominal scale. Here the numbers mean nothing more than just labels representing categories. For example, when entering data you might code web experience by entering "1" for expert users and "2" for novices. Clearly the numbers here mean nothing more than just labelling.

Ordinal scale

The second level of measurement is when you simply rank order the results. This is known as the ordinal scale. Here the numbers are an indicator of rank (e.g. which design alternative was ranked first, second or last by participants in a preference test). The major problem with ranking data is that it does not tell us exactly how much better the design ranked first is, in comparison to the design ranked second. It could be twice as good or ten times as good. With ranking information, we know about the order of the designs but we have no information about the size of the intervals between the ranks.

Interval scale

At the third level, variables can be measured using a continuous scale (interval or ratio). This scale is the most refined level of measurement. Here the numbers contain more information and carry a lot more meaning. Continuous measures are good because they not only tell us about order (e.g. which participant completed the test quickest), they also have equal distances between measurement points. So we know that the interval between 10-30 seconds is the same as the difference between 50-70 seconds (i.e. 20 seconds). We can also state with confidence that 70 seconds is longer than 60 seconds and state exactly how much longer it is (i.e. 10 seconds). Examples of continuous scales used in usability tests include time-on-task using seconds, amount of effort as measured by number of mouse clicks, or simply counting the number of negative comments made by the participant.

Key Concept 3: Study Design

The final key concept to learn is the notion of study design. There are two major study designs that are often used in research.

Between-participants (unrelated) design

The first one is known as the between-participants design or unrelated design. With this approach, the researcher compares two or more separate groups of people. For example, if you run a study comparing domain experts and domain novices, you are using an unrelated design. Similarly, studies comparing people who use Facebook and people who use Bebo can be viewed as using an unrelated design. An experiment comparing a treatment condition with a control condition, with each condition having different people, is also using an unrelated design.

Within-participants (related) design

Another popular way to conduct research, especially in the field of usability, is to use the same group of people over and over again to measure different things or to measure the same thing at different time points. This is known as the within-participants design or a related design. For example, a researcher may examine whether there are any differences in usability between a new product and an existing, competitor product. The same people are used to assess the new product and the competitor product.

It is important to note that study design can get more complex, when you have two or more independent variables in the same study. Then you might have a mixed design, with one variable using an unrelated design and another using a related design. For example, you might want to measure differences in usability between two different products, but also compare expert users and novice users with regard to this change. Now you have "experience" being a between-participants variable and "product design" being a within-participants variable.

As long as you understand the basic distinction between unrelated and related designs, it should be easy to describe and understand your own research. The question is simply:

Are you comparing different groups of people, are you using the same people over and over again, or does your study contain both elements?

Applying Statistical Concepts

Once you have mastered the above three key concepts, you are pretty much ready to use SPSS. This is because the various combinations of the above concepts require specific types of data analysis. I will give you three examples.

• If you have an unrelated predictor variable comparing two groups and an outcome measured on a continuous scale, you need to analyse your data with an independent samples t-test.
• If you have a continuous predictor variable and a continuous outcome measure, you need to perform correlation analyses.
• If you have a categorical predictor variable and a categorical outcome measure, you need to perform a chi-square.

The list goes on and on. The various permutations of predictor and outcome, type of measure and study design, all have a specific type of analysis you can perform. Your task as a researcher is to first figure out what analyses you should perform, on the basis of your variables, measures and study design. After you have done this, figuring out where to click in SPSS is the easy part. There are books that provide a step by step guide on how to perform any analyses using SPSS (with pictures!) and how to interpret the results. And so it becomes stats not maths. It is simply applying statistical concepts to making data analysis decisions and then clicking on buttons!

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