In: Statistics and Probability
What is a Non Parametric Test?
A non parametric test (sometimes called a distribution free test)
does not assume anything about the underlying distribution (for
example, that the data comes from a normal distribution). That’s
compared to parametric test, which makes assumptions about a
population’s parameters (for example, the mean or standard
deviation); When the word “non parametric” is used in stats, it
doesn’t quite mean that you know nothing about the population. It
usually means that you know the population data does not have a
normal distribution.
For example, one assumption for the one way ANOVA is that the data
comes from a normal distribution. If your data isn’t normally
distributed, you can’t run an ANOVA, but you can run the
nonparametric alternative—the Kruskal-Wallis test. If at all
possible, you should us parametric tests, as they tend to be more
accurate. Parametric tests have greater statistical power, which
means they are likely to find a true significant effect. Use
nonparametric tests only if you have to (i.e. you know that
assumptions like normality are being violated). Nonparametric tests
can perform well with non-normal continuous data if you have a
sufficiently large sample size (generally 15-20 items in each
group).
Types of Nonparametric Tests:
When the word “parametric” is used in stats, it usually means tests
like ANOVA or a t test. Those tests both assume that the population
data has a normal distribution. Non parametric do not assume that
the data is normally distributed. The only non parametric test you
are likely to come across in elementary stats is the chi-square
test. However, there are several others. For example: the Kruskal
Willis test is the non parametric alternative to the One way ANOVA
and the Mann Whitney is the non parametric alternative to the two
sample t test.
The main nonparametric tests are:
(i) 1-sample sign test: Use this test to estimate the median of a
population and compare it to a reference value or target
value.
(ii) 1-sample Wilcoxon signed rank test: With this test, you also
estimate the population median and compare it to a reference/target
value. However, the test assumes your data comes from a symmetric
distribution (like the Cauchy distribution or uniform
distribution).
(iii) Friedman test: This test is used to test for differences
between groups with ordinal dependent variables. It can also be
used for continuous data if the one-way ANOVA with repeated
measures is inappropriate (i.e. some assumption has been
violated).
(iv) Goodman Kruska’s Gamma: a test of association for ranked
variables.
(v) Kruskal-Wallis test: Use this test instead of a one-way ANOVA
to find out if two or more medians are different. Ranks of the data
points are used for the calculations, rather than the data points
themselves.
(vi) The Mann-Kendall Trend Test: This test looks for trends in
time-series data.
(vii) Mann-Whitney test: Use this test to compare differences
between two independent groups when dependent variables are either
ordinal or continuous.
(viii) Mood’s Median test: Use this test instead of the sign test
when you have two independent samples.
(ix) Spearman Rank Correlation: Use when you want to find a
correlation between two sets of data.