Every now and then I tend to get questions about statistics from readers of this blog — this is due to a somewhat ill-deserved reputation Google seems to have bestowed on me as an ‘expert’ in Likert scale measurement. Many of the answers you need can be found in this post, and this set of slides, but I’m also happy to answer other questions, such as the one below.
How to analyse Likert scale data
The following (slightly modified) question was posted as a comment here, but I felt that the answer was too lengthy for the comments section.
Our questionnaire is composed of items with a 5 point scale, ranging from “1=strongly disagree” to “5=strongly agree”. For example, we are trying to find out if the respondents agree with [a topic]. The number of respondents who ‘strongly disagree’ are 2, those who ‘disagree’ are 9, those who ‘are undecided’ are 24, those who ‘agree’ are 18 and those who ‘strongly agree’ are 7. How do I interpret this data?
There are two types of statistical analysis, descriptive and inferential statistics. If you want to find out what respondents believe about a topic, you need to do descriptive statistics. This involves, for example, finding the central tendency (what most respondents believe) and the spread / dispersion of the responses (how strongly respondents agree with each other).
Because Likert scales produce what are called ordinal data, I suggest that you calculate the median and Inter-Quartile Range (IQR) of each item. The median (: the number found exactly in the middle of the distribution) is a measure of central tendency: very roughly speaking, it shows what the ‘average’ respondent might think, or the ‘likeliest’ response. The IQR is a measure of spread: it shows whether the responses are clustered together or scattered across the range of possible responses.
You can find some instructions on how to do calculate these metrics with SPSS in this page (the procedure is the same for both). If you only have access to Excel, here are links to a couple of videos demonstrating how to calculate the median and the IQR. For small datasets, such as the one that propmted this question, it is easy to calculate the median and IQR manually. In the next two sections, I shall show how this can be done, using the example data. If you don’t want to read these, you can skip to the bottom, for some advice about how to report the findings.
Calculating the median
First, you arrange the numbers in an order from largest to smallest, like this:
1,1,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3, 3,3, 3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5
To compute the median, you then delete one number from each end of the line, and repeat until you are left with just one number (or two that are the same). This ‘middle’ number is your median. If you are left with two different numbers in the end, the median is half-way between them. This will produce a decimal (e.g., 2.5), which might seem odd, but that’s ok. Using the data you provided, the median is 3, and I have marked it with red to make it stand out.
Calculating the IQR
The IQR is slightly more complicated, but not too hard. Your starting point will be the same arrangement of responses that we used above. When you divide this line into four equal parts, the ‘cut-off’ points are called quartiles. I have used red to indicate quartiles in the dataset.
[1,1,2,2,2,2,2,2,2,2,2,3,3,3, 3] [3,3,3,3,3,3,3,3,3,3,3,3,3,3, 3][3,3,3,3,3,4,4,4,4,4,4,4,4,4, 4] [4,4,4,4,4,4,4,4,5,5,5,5,5,5, 5]
The IQR is the difference between the first and third quartile. In the example, this is: Q3 – Q1 = 4 – 3 = 1.
A relatively small IQR, as was the case above, is an indication of consensus. By contrast, larger IQRs might suggest that opinion is polarised, i.e., that respondents tend to hold strong opinions either for or against this topic.
Reporting the findings
When your findings suggest consensus, your write-up should focus on describing the median (i.e., what most respondents seem to believe). One way to describe this is by writing something like: “most respondents indicated agreement with the idea that… (Mdn=4, IQR=0)”.
By contrast, when opinion is polarised, your write-up should emphasise the dissonance of opinion: the median is perhaps not so important. To help you understand this, consider a hypothetical case where half of your respondents hate a new textbook, and half love it. If you were to simply report that the respondents are, on average, undecided, that would be a statistical distortion of the data. Here’s a possible way to report the data more accurately: “Opinion seems to be divided with regard to… . Many respondents (N=28, 47%) expressed strong disagreement or disagreement, but a roughly equal number (N=26, 43%) indicated that they agreed or strongly agreed (Mdn=3, IQR=3).“
A final caveat
One last thing: I would caution you against placing too much faith on findings that were generated from a single Likert-type item. If at all possible, I’d try to cluster similar items together and compare / merge their results. If the findings are broadly consistent, that gives us confidence in them. If they are not, it might mean that one of the items did not function properly (e.g., respondents may have been confused by the wording), and you may have to discard it from the dataset.
More to read
I hope that this information was helpful, but if there’s anything that was not clear, feel free to drop a line in the comments below. You may also want to check out some more posts I have written on quantitative research, including:
- On Likert scales, levels of measurement and nuanced understandings
- Designing better questionnaires: Using scales
- Four things you probably didn’t know about Likert scales
If you arrived at this page while preparing for one of your student projects, I wish you all the best with your work. There’s a range of social sharing buttons below, in case you feel like sharing this information among fellow students who might also find it useful. Also feel free to ask any other questions you may have, using the contact form.