Nonparametric tests are sometimes called distribution free statistics because they do not require that the data fit a normal distribution. Nonparametric tests require less restrictive assumptions about the data than parametric restrictions. We can perform the analysis of categorical and rank data using nonparametric tests.
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Parametric.
1. A nonparametric statistic has no inference 2. A nonparametric statistic has no standard error 3. A nonparametric statistic is an element in a base population (universe of possibilities) where every possible event in the population is known and can be characterized * * * * * That is utter rubbish and a totally irresponsible answer. In parametric statistics, the variable of interest is distributed according to some distribution that is determined by a small number of parameters. In non-parametric statistics there is no underlying parametric distribution. With non-parametric data you can compare between two (or more) possible distributions (goodness-of-fit), test for correlation between variables. Some test, such as the Student's t, chi-square are applicable for parametric as well as non-parametric statistics. I have, therefore, no idea where the previous answerer got his/her information from!
log 10 or square root your non parametric values
Parametric tests assume that your data are normally distributed (i.e. follow a classic bell-shaped "Gaussian" curve). Non-parametric tests make no assumption about the shape of the distribution.
In parametric analysis the underlying distributions of the variables are described by parameters. These may be known or it may be possible to estimate them from the observed data. In non-parametric analyses, the parameters are not used - either because they cannot be derived or because the tests do not require them.