Parametric versus non-parametric

A potential source of confusion in working out what statistics to use in analysing data is whether your data allows for parametric or non-parametric statistics.

The importance of this issue cannot be underestimated!

If you get it wrong you risk using an incorrect statistical procedure or you may use a less powerful procedure.

Non-paramteric statistical procedures are less powerful because they use less information in their calulation. For example, a parametric correlation uses information about the mean and deviation from the mean while a non-parametric correlation will use only the ordinal position of pairs of scores.

The basic distinction for paramteric versus non-parametric is:

There are other considerations which have to be taken into account:

You have to look at the distribution of your data. If your data is supposed to take parametric stats you should check that the distributions are approximately normal.

The best way to do this is to check the skew and Kurtosis measures from the frequency output from SPSS. For a relatively normal distribution:

skew ~= 1.0
kurtosis~=1.0

If a distribution deviates markedly from normality then you take the risk that the statistic will be inaccurate. The safest thing to do is to use an equivalent non-parametric statistic.

Non-parametric statistics

Descriptive

 Name For what Notes Mode Central tendancy Greatest frequency Median Central tendancy 50% split of distribution Range Distribution lowest and highest value
Association

 Name For what Notes Spearman's Rho Correlation based on rank order of data Kendall's Tau Correlation Chi square Tabled data