Scientific calculators

On Likert scales, again

I was sent the following question on Likert scaling:

Could you please offer a brief explanation: what is the true mid-point of a 7-point Likert scale? Also, how much deviation in “mean” or “average scoring” is significant? In other words, is the difference between 2.09 and 2.39 significant? Or does the gap need to be wider to be of consequence? Thank you.

I. The mid-point of a 7-point Likert scale would be 4, i.e., the point equally distant from both ends of the scale.

II. Some researchers (including many who lack formally training in statistical methods) may disagree, but I strongly believe that a Likert scale cannot yield values such as 2.09 or 2.39. Likert scales produce ordinal, not continuous, data. Therefore any attempt to generate a “mean” or “average” value is statistically flawed. You can find out why in point 4 of this blog post. A median is a more appropriate metric for this type of data.

III. To estimate statistical significance, you need two numbers: the p-value (a metric that shows how likely it is for your results to be due to chance), and a cut-off value (which indicates how certain you need to be). When the p-value is smaller than the cut-off value, then the findings are significant. The p-value depends on the distribution of your results (which you have provided), and your sample size (which you have not), so it is difficult to tell, on the basis of what you have given me, whether your findings are likely to be significant. Normally, SPSS will flag statistically significant values with one or more asterisks – if it hasn’t, then the results are likely inconclusive.

With regard to the cut-off point, that is something of a judgement call. When putting forward the construct of statistical significance, Ronald Fischer was initially happy to accept any value p<0.05 as significant (i.e., if the probability that the results were due to chance was smaller than 1/20, he accepted them as statistically significant). This is, however, an arbitrary decision, and conventions vary across fields. In medical research, for instance, a 5% probability of error would be unacceptable, so the cut -off thresholds are much lower (p<0.005, or even p<0.001). To answer your question, you’d need to know the conventional cut-off points for your discipline. Published literature will provide some clues as to what is customary in your field.

Image credit: Michael Kwan [CC BY-NC-ND]

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