If you can consider your Likert data as ordinal scale then you can test your

normal distribution with Kolmogorov-Smirnov one-sample test

If your Likert data reflect a nominal construct then use X2 one-sample test

ref.: Sidney Siegel

non-parametric Statistics for the behavioral sciences international student edition

You don't need to that that. It follows from definition that Likert scale data can not be normally distributed.

You can not even use a parametric distribution model to describe the distribution of Likert values, because they are not numeric. If you assign numeric values, then the distribution is as arbitrary as the assignment rule. If you had a physically meaningful assignment rule (that goes beyond simply mapping the ranks to numeric values), then I wouldn't call this a Likert scale. If the mapping would be obtained by a comparison to an externally defined standard, it would then be more like a measure (and as such is on a ratio scale), and then it would make sense to think about parametric distribution models.

Absolutely according to Jochen, the problem is that many do it, but it's not right. do it directly.

what happens, is how the process is done.,. Researchers tend to return to the scale likert and not use it as a cluster of measures.

On the other hand, it is usable in the case of comparative processes such as the binomial or multinomial test.

and you only need the sample to be large.

but it will depend on what you want to do

Likert scale do not have normal distribution, but rather ordinal because it is based on ranking. The 5 point likert scale ranges from 1 to 5 in order of response from very weak to very strong. Example is strongly disagree (1), disagree (2), some how agree (3), agree (4) and strongly agree (5)

I would like to offer a perspective different from most of the previous answers.

On the interval nature of Likert scales

If you have created a Likert scale --- that is, you have summed or averaged the responses for a respondent for several Likert items or questions --- then you are already treating the Likert responses as interval in nature. It would have made no sense to sum or average the Likert items if they were treated as ordinal.

Likewise, once a scale is created, it doesn’t follow to then try to insist that the scale is ordinal in nature, as I think some of the respondents in this thread have done. At that point, the decision on the spacing of the response categories has already been made.

Typically, the researcher has implicitly assumed that the Likert response categories are equally spaced. That is, if you start with the responses “strongly disagree”, “agree”, “neutral”, etc. and number those 1, 2, 3, 4, 5, or -2, -1, 0, 1, 2, then there is an assumption that those categories are equally spaced. Having thought about the responses typically used for Likert questions, I think is usually a fair assumption. But one could have used a different scheme to translate the ordinal categories to numeric interval data. In reality, in a field like psychology, scale construction is more complex in which the coding of some items are reversed, some items may be weighted differently, and so on.

On the question of normality

Likert scale data cannot be normally distributed. Its values are bound on the left and on the right. And it is discrete in nature.

But, of course, nothing in real life is normally distributed. The normal distribution is a mathematical fiction.

The real question is, Are my data a close-enough approximation to make the estimates of the statistics from my analyses reasonable? I’m not sure what different question could be sensibly asked.

In light of this, the usual methods should be employed: plot the data --- or the residuals or whatever is of interest --- on a q-q plot or as a histogram to be compared to a normal curve.

On how Likert scale data is usually analyzed

I think it is fair to say that Likert item data is generally treated as ordinal, and that Likert scale data is generally treated as interval.

As suggested above, assumptions must be made in order to get from ordinal items to interval scales. By my understanding, first, the spacing between item categories must be decided so that the responses can be summed or averaged. Second, in some cases, an assumption that the discrete values represent an underlying continuous variable must be made.

Controversy

It should be noted that a discussion about how Likert scale data should be handled has been ongoing since probably the 1940’s, and there is not complete agreement.

I thought the description of the history by Rinker was accessible and good ( https://www.researchgate.net/publication/262011454_Likert ).

And you can get some sense of the debate at this thread ( https://www.researchgate.net/post/I_have_a_variable_that_is_measured_through_5_point_likert_scale_Should_it_be_considered_as_a_continuous_or_categorical_variable ).

Obviously there are more academic sources that address this question.

I'll add to Salvatore's nice response that people often say Likert scale when they really have just a single item. As John Uebersax says in this note, a Likert scale is never a single item.

• http://www.john-uebersax.com/stat/likert.htm

HTH.

To add a short appendix to Salvatore's excellent discussion, we should remember that data are not what they should be, but what they are. I've attached normal quantile plots of three common psychometric scales plus birth weight for babies of first time mothers.

The Beck Depression Inventory Fastscreen is a seven-item scale. The qqplot shows a heavy clustering of scores of zero and a heavy tail of high scores. On the other hand, the Maslach Burnout Inventory and the Brief Resilience Scale show a close alignment to the normal distribution. Both have small ceiling effects.

The birth weight data, measured in kilos, is less well-behaved distributionally than either the burnout or the resilience scales. In fact, of the four scales shown, only the Brief Resilience Scale data passes a Shapiro-Wilk test for normality (P=0·512). Both birth weight and the BDI fail with P < 0·0001, and the Maslach Burnout Scale just fails with a P = 0·035.

So I don't believe there is a single answer to the question. We have to observe the observed values ourselves.