1. There are many non parametric analyses. There is no general assumption
of linearity or non linearity.
2. Parametric analysis assumes errors to be normally distributed, which is a
consequence of the so-called Large Numbers Theorem. According to it, random
sample estimations of a population measure (e.g. a population mean) tend (as
sample size gets larger) to be normally distributed with an average that
coincides with the population value. This theorem generates a number of
statistical tests, confidence intervals, significance levels, etc. For small
samples, or non-random samples, non-parametric tests provide a second-best
alternative.
3. Spearman's rho and Pearson's r have nothing to do with parametric or non
parametric as such, in the sense described above. One is a rank correlation
coefficient, the other a linear correlation coefficient. However, because of
their mathematical properties the latter has a normal sampling distribution
whereas the former hasn't one, for which rho is called a non parametric
coefficient (independently of sample size). Rho measures the correlation of
rankings, while r measures the linear relationship between the interval
values of the variables. Two variables might have a perfect rho (the highest
in X is also the highest in Y, and so on) but a small r if the values do not
show a linear relationship but some curvilinear one. The choice is not
dictated by statistical but substantive considerations.
Hector
-----Original Message-----
From: SPSSX(r) Discussion [mailto:
[hidden email]] On Behalf Of Jon
Oh
Sent: 20 August 2008 20:14
To:
[hidden email]
Subject: nonparametric
Hi,
I have few questions. Does nonparametric analysis assume linearity? Is there
any reason why we shouldn't prefer nonparametric analysis over parametric?
e.g. spearman's rho vs. pearson's r
Thank you
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