Dear All,
I have data set in which the variables are either nominal or ordinal in nature. please suggest that is the normality assumption should be applied to such data set. and if yes, then what should the steps to check it?
thanks
The question does not really make sense as you have phrased it. The data are non-normal by definition if you have ordinal or nominal data.
You refer to a normality assumption applied to such data. In general there is no such assumption applied to data per se. Usually the assumption arises from a particular model applied to a data set and even then the assumption is usually not about the data but about either the residuals of the model or in relation to a test statistic (such as z). Whether it is reasonable to assume normality therefore depends on the model you are using.
Generally I would advise selecting a model that is designed for nominal or ordinal data where practical. In some cases models for continuous data might work quite well, but you would need to know a lot about the data and the model to see if this would be reasonable.
The question does not really make sense as you have phrased it. The data are non-normal by definition if you have ordinal or nominal data.
You refer to a normality assumption applied to such data. In general there is no such assumption applied to data per se. Usually the assumption arises from a particular model applied to a data set and even then the assumption is usually not about the data but about either the residuals of the model or in relation to a test statistic (such as z). Whether it is reasonable to assume normality therefore depends on the model you are using.
Generally I would advise selecting a model that is designed for nominal or ordinal data where practical. In some cases models for continuous data might work quite well, but you would need to know a lot about the data and the model to see if this would be reasonable.
Thom is correct - certainly if the variable is nominal. However, if the variable is ordinal, it could at least look like a normal distribution in terms of its shape, and potentially be treated as one.
Adrian - it very much depends on the situation. Some ordinal responses will be approximately normal (though one is implicitly assuming equal or near equal spacing between categories). However, this isn't necessarily true. For example a two group experiment with an ordinal outcome such as a rating scale going from 1 to 5. Here if one of the groups was an average of 3.2 and the other an average of 4.7 then at least one of the groups is very skewed. In this situation an ordinal model makes much more sense.
And perhaps a little tangential but I think an important point. In regression settings normality is perhaps one of the most misunderstood assumptions. Normality assumption is about the disturbance (error) term, it is not about the variables. Heteroskedasticity is typically a bigger problem than normality.
Ali - not tangential at all. Errors can be approximately normal even if X and Y variables aren't. Also there is no requirement to use a model that assumes assumes normal errors. If one works with ordinal and categorical variables then it is a really good idea to learn about generalised linear models and generalised linear mixed models (aka multilevel models). These and related modelling families are incredibly useful in handling a wide variety of problems.
If the variable is ordinal and not discrete, you can change the values around providing none cross over or become the same as others (i.e., any monotonic transformation). This can be done to create a lot of distributions (if the variables are not discrete), so I think it gets back to Thom's original answer for both of these. If the responses are discrete, like counts or censored, then you probably wouldn't be doing a procedure that assumes normality anyway.
If a variable is ordinal and has at least five categories, making a normality assumption can work well, and then it can make sense to check normality. For nominal variables, the concept does not make sense. To check normality, compute skewness or kurtosis. Do not rely on significance tests for normality, because these are strongly sample size-dependent.
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