Nonparametric Hypothesis tests

The approach to explore the small-sized sample and the

unspecified population

Nonparametric problems

No proper distribution for hypothesis test

Too small size to adopt the normality approximation

Most nonparametric methods based on ranks instead of original data

Some nonparametric tests The sign test

Testing the median value The signed rank test

Testing the symmetry of distribution The rank sum test

Testing the similarity between two populations

The runs test Testing the randomness of distribution

The sign test (i)

The sign test (ii)

a

The signed rank test (i)

in the ascending order

The signed rank test (ii)

The signed rank test (iii)

The signed rank test (iv)

The signed rank test (v)

The rank sum test (i)

The rank sum test (ii)

The rank sum test (iii)—another statistics

The rank sum test (iv)—approximation approach

The runs test (i)

The runs test (ii)

The runs test (iii)

=2*the smaller number+1

The runs test (iv)

Example

P-value for randomness of this sequence?=2*min(PH0{R≧3},PH0{R≦3})

2≦R≦7

The runs test (v)

Some famous nonparametric statistical methods

Wilcoxon signed rank test for the symmetric distribution

Wilcoxon, Mann-Whitney rank sum test for the identical shape of distribution

Kruskal-Wallis test for identical distribution (an approximation of Chi-square distribution)

Spearman Rho rank test for the small-sized correlation coefficient

Homework #5

Problem 8,13,20