Ordinal data

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## Ordinal data

### It is said that a variable is measured at the ordinal level if there is a ranking in the values. This can be seen in language too, for instance good – better – best, or bad – worse – worst, or big – bigger – biggest. These lists are short, but if you make a list like first, second, third, fourth and so on, the list of ranking scores can become very large.

You get ordinal data when you use Likert scales. A Likert scale has most of the time 5 answers, like very bad – bad – ordinary – good – very good or very satisfied – satisfied – normal – unsatisfied – very unsatisfied. Besides that, a lot of questions can be asked in a similar way so the layout looks nice. And there is another advantage: more questions can be answered in the same time. On the average a respondent can answer eight questions in one minute, but with a Likert scale twelve questions or more can be answered in one minute.

A part of a questionnaire might look like this:

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## Analysing data measured at an ordinal scale

Now what can be done with ordinal data? Which types of analysis can be adjusted?

One thing that is always allowed is counting the answers. So it is okay to make frequencies. And when frequencies are allowed, also the percentages can be computed.

Secondly, the mode can be provided.

Thirdly, the scores of an ordinal variable can be divided over the scores of a nominal variable. In the above questionnaire it can be interesting if men and women give different answers. The test to be performed is then a chi square test.

And then … well if we stick to the theory about what is allowed to do with ordinal data, this is all. However something is missing. It looks like we treated the data like nominal data. The ranking is missing! To correct this, the answers are given in numbers. For instance: very unsatisfied = 1, unsatisfied = 2, neither satisfied nor unsatisfied = 3, satisfied = 4 and very satisfied = 5. A higher score means more satisfied. This is normal in many cultures: the higher the score, the better. However if you prefer the opposite (the lower the score, the better), then reverse the assignment of the scores. The way you code the scores is really arbitrary. My advice is: assign scores that are the easiest for you to interpret.

When you have assigned numbers to the answers, it is still not allowed to make calculations with them. We assigned numbers not values! In maths two times two may be four, but two times unsatisfied isn’t all at once satisfactory. However a mean can be computed and can be very indicative. On a five point Likert scale in theory the middle is 3. So if the mean of all subjects is higher, this means the subjects are – in general – more satisfied.

Also the standard deviation can be computed. Although there is no standard to evaluate this score, for a five point rating scale the standard deviation is usually somewhere around .90. To get more information about the distribution of a ordinal variable it is also okay to compute the skewness and kurtosis.

Now a few more kinds of analysis can be done. When you split an ordinal variable into two groups (for instance male and female) a Mann-Whitney test can be performed. When the scores of the variable are divided into three or more groups (for example Germany, France and England), a Kruskal-Wallis test is the right test for testing differences between groups.

When a Likert scale has been used, the mean over all or some answers can be computed. If this is allowed, you should test it with a factor analysis and compute and evaluate Cronbachs alfa. The advantage of computing a mean over items on a Likert scale is that it creates an interval variable (on the condition that enough variation has been created). Now many more types of analysis can be done. Read for more information about this on our page called interval data.

## Tests for ordinal data

All these tests are clearly explained in in our SPSS-tutorials.

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