Researchers often examine univariate skewness and kurtosis of items prior to conducting factor analysis. Likert-type variables, however, are ordinal in nature and thus these statistics don't seem to be quite appropriate for such data (especially with Likert scales with less than 5 options). On the other hand, it is true that anomalous results can be obtained when 'extreme' items are included in factor analysis, even if polychoric correlations and robust estimators are used.
Sure you can. Skewness tells you the direction of the skew. Kurtosis tells you whether you have outliers; e.g., if 99.9% of the answers are 4 or 5, and 0.1% are 1, that would be an extremely high kurtosis situation.
What does not make sense here (and anywhere else) is to use these statistics to "prove" normality. In the Likert scale case, the distribution is clearly non-normal with its extreme discreteness. Even if the skew and (excess) kurtosis were exactly 0.0, you certainly could not conclude that the distribution was normal. It's still just as discrete as ever, regardless of the values of these statistics.
The most important thing to look at with the Likert scale data is the graph of the frequency distribution itself. If you are having trouble interpreting it, the skew and kurtosis can help. Kurtosis, in particular, can identify the outlier values that might not be clearly visible in the frequency plot because of low frequencies (the 0.1% case).
Fewer options is not a problem. In particular, with just two options, kurtosis likewise identifies the anomaly. The kurtosis approaches infinity as the probability of the rarer of the two outcomes approaches zero, giving the common-sense conclusion that, if one thing happens 99.99% of the time, and the other only 0.01% of the time, then the 0.01% occurrence can be called an "outlier."
Glad you didn't mention anything about "peakedness." Despite what the ancient folklore says, kurtosis does not measure "peakedness" in general. In the Likert scale and other discrete cases, that fact becomes particularly obvious. Kurtosis just measures outliers.
So yes, as an indicator of extremity in your Likert scale data, you certainly can use kurtosis.
I don't think summary statistics like skew, kurtosis, mean, or standard deviation make any sense for Likert item data.
To look at the distribution of values, you could look at a histogram-like bar plot: http://rcompanion.org/handbook/images/image060.png
For Likert item data, I think median, five-number summary, and box plots are reasonable summary statistics.
Actually, the box plot and five-number summary make no sense for such discrete data.
Yes, the frequency distribution plot (it'snot a histogram) does make sense.
Mean and standard deviation also make sense. They measure the center of gravity of the frequency distribution and its spread, respectively.
With the first three answers, I think the original poster can be convinced that there is not clear consensus on which summary statistics are appropriate or not for Likert data.
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My argument for using the median and the other percentile measures for Likert and other ordinal data would be as follows. Assume we have ordinal data, let's say from a 5-point Likert item. The median makes sense because it makes sense to say "half of the values are below some value". If the data are "2, 2, 2, 3, 3, 3, 4, 4, 5", or their word-description equivalents, the lowest four values are 2, 2, 2, 3, and the highest four values are 3, 4, 4, 5. That leaves the middle 3 value, or its word description equivalent, as the median value. There is nothing here that assumes continuous data; it assumes only ordinal data. This same argument goes for any other percentile, and so for the whole of the 5-number summary. Likewise, a boxplot is just a plot of the 5-number summary.
I would challenge the OP's assumption that Likert type scale is at ordinal level. Strictly speaking, it might have to be considered as ordinal level scale, but then the ways researchers use Likert type scale strongly implicate that it is at interval level. If not, I am not sure how and why you would run a factor analysis on it.
For the OP's question, factor analysis is based on correlation/covariance. Therefore, anything influencing the size of the correlation/covariance should be examined before running the analysis. In principle, Peter already gave you clear answers. Salvatore gave you a more practical point of view. I would say both have good points and provide good guidelines for the analyst.
Thank you so much for your very informative answers. It does seem clear to me now that there is no rule of thumb researchers can blindly follow, but in the end it is the researcher the one who must take an informed decision.
Professor Moon made a clear and accurate remark which, I believe, relates to a broader issue in the social sciences: the fact that most of our data are, strictly speaking, at ordinal level, but we do analyze it as interval. What do you think about the use of polychoric (or tetrachoric) correlations in factor analysis? Do you think it solves the problem, at least partially?
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