If scholars and researchers claim that Likert scale data are not normally distributed, is it okay to carry out Shaprio-Wilk test to provide evidence for such a claim? Is it common knowledge they are not normally distributed? What if a Shapiro-Wilk test p-value exceeds 0.05?
- We know Likert scale data are not normally distributed, because they can't be. They're necessarily bounded on both ends (e.g. can't be smaller than "1" or larger than "5", say).
- Whether this matters in practice is a different question.
- Assuming it makes sense to take the mean of the data, and subtract observations from that mean, conducting Shapiro-Wilk test is probably okay. But probably not very useful.
- A p-value > 0.5 is not evidence that the data are normal. It just says that there's not enough evidence to conclude that the data are not normal.
- Practically, Likert scale are data are often not symmetric in distribution. And possibly not uni-modal. It doesn't hurt to look at the data you have.
- All this being said, Likert scale data are often treated as interval data, and well-behaved Likert scale data are often treated as if conditionally normal. Whether this makes sense depends on the scale and the data. It's important to be practical and reasonable in this.
I think it is essential to make a distinction between individual Likert-scored items and multi-item scales that are created from such items. In particular, if you are working with a multi-item scale, it is more important to see how that scale as a whole performs.
Sal Mangiafico
Thank you for the insight sharing. However, I have got a frequency Likert scale that scored 0.194 on Shapiro-Wilk test, which implies no normality distribution violation.
Hence, do I proceed with mean and SD for descriptive analysis or instead use median and IQR?
Mohamed Sola could you be clearer, what do you mean with "frequency Likert scale"? And I think you are mixing up two issues here:
1. As Sal Mangiafico pointed out, a Likert item cannot be truely normally distributed, since they are bounded and only discrete values are possible. Therefore, you need to assess, if your item is sufficiently close to normal, if that is relevant for anything (remember, for example in OLS regression, the normality assumption is not about the distribution of the dependent variable, but the errors/residuals and there is no assumption about the distribution of the predictors).
2. Your question about mean and SD is nearly unrelated to the Likert item question. Typically, Likert items are considered as ordinal, therefore, even if you would conclude that the distribution is sufficiently normal, mean and SD would not be meaningful parameters, because of the ordinal structure. Hence, if your Likert item would be your dependent variable, you should switch to ordinal analyses, e.g. probit regression. You could also have a truely not normally distributed variable, with only discrete possible values (e.g. a Poisson distribution), where a mean and variance estimates make perfectly sense, but this is simply not correct for ordinal variables.
Likert items and especially scales are often handled as if they were metric/interval data, but research shows, that this can lead to false conclusions (e.g. Liddell & Kruschke, 2018).
Liddell, T. M., & Kruschke, J. K. (2018). Analyzing ordinal data with metric models: What could possibly go wrong?. Journal of Experimental Social Psychology, 79, 328-348.
Mohamed Sola ,
- One piece of advice, absolutely forget about using hypothesis tests as a pre-condition for doing another analysis. Doing things like, e.g., Shapiro-Wilk or Bartlett to decide if an anova is appropriate, is not helpful.
- Mean and sd don't require normality to be meaningful. Though with some distributions, median and quantiles may be more helpful. When reporting summary statistics --- if you have the room --- probably the best thing is report all of mean, sd, minimum, 25th percentile, median, 75th percentile, maximum.
- In your specific case, you have to make a decision with how you are treating the data. If you have a scale composed of several items, it is common to treat the data as interval. It's up to you if you think this is reasonable.
- It's a different question if you think it's reasonable to treat the data as conditionally normal. (E.g. if it's reasonable to conduct e.g. anova). A lot may go in to this decision, including sample size, past uses of this scale, assumptions about this scale, how the data look, and so on.
- If you are talking about Likert-type item data, I would recommend that you treat it as ordinal.
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