If your dependent variable is not normally distributed, you have 4 options: (1) forget about it - Central Limit Theory will help you out; (2) tranform or exclude outliers; (3) go non-parametric; or (4) use another model (gamma, poisson, negative binomial, etc). There is less of a problem in case one of your continuous predictors is not normally distributed. Regression models only assume that there is a linear relation with the dependent. So don't kick them out but look at the relationships (graphically).

Standardising data is not the same as normalising it (although some people use the terms interchangeably).

Depending on the options you use, PCA will automatically standardise the variables for you.

For example

princomp(MyData, cor=TRUE)

will use the correlation matrix - equivalent to standardising the data to mean zero and standard deviation 1.

If the data are not normally distributed it may be necessary to transform them. Plot a histogram (or better a qqnorm plot) of each variable and look if there is marked skew or kurtosis. Log or square-root transforms are common, but there is a whole range of transformations that can be used.

Hello RIchard, thank you very much for your answer. I have realised that most of my variables are skewed to the right. Some of them need a logtransformation and some need a sqrt root transformation. Can I use different transformations for the same dataset or we have to use the same transformation and then ignore those variables that cannot be transformed.

I will try to read more about princomp.

It is usually a bad thing to transform data before doing any estimation-modelling, as data loses its properties and modelling is done on something that may not reflect the underlying phenomena. This comes from my professor James MacKinnon, and his advice is usually very good. Are you sure that data has to be normalized for PCA/HCA, I saw several analyses where this was not done. Maybe you need to consult some classic textbooks on this.

Dear Vladimir: THank you for this answer. Yes I have read several papers and they suggest that data has to be normalised. I have seen that the two criteria for testing normality are also included in SPSS: Kolmogorov - Smirnov for n>50 and the other for n

In real life this doesn't really happen. I have not seen many studies when data was first normalized, at least in regression analysis.

First of all you have to check the normality of the data. This can be done using criteria such as omega-squared or Kolmogorov - Smirnov. You must also verify the homogeneity of the existing samples. If they are heterogeneous, the normalization has no meaning.

Formal normality tests and graphical methods will be of limited use (see the link)

You could enter a non-parametric correlation matrix in your factor-analyses.

http://www.statisticalmisses.nl/index.php/frequently-asked-questions/77-what-is-wrong-with-tests-of-normality

Here is SPSS-syntax for scale-free nonparametric factor analysis

Andre: This is a very interesting contribution. From the link you sent, the non-parametric methods do not require normality tests. I will try to read more about the nonparametric analysis syntax you sent.

Generally. I think that data are rarely normally distributed. SOme can be transformed and some cant. However, if one kicks out a certain variable (s) on the basis that it (they) violates the requirements for normality, there is a possibility of missing out important processes that could be explained by that variable. This could be an important limitation of multivariate statistics in understanding hydrological processes.

If your dependent variable is not normally distributed, you have 4 options: (1) forget about it - Central Limit Theory will help you out; (2) tranform or exclude outliers; (3) go non-parametric; or (4) use another model (gamma, poisson, negative binomial, etc). There is less of a problem in case one of your continuous predictors is not normally distributed. Regression models only assume that there is a linear relation with the dependent. So don't kick them out but look at the relationships (graphically).