9/18/24, 1:33 NON Parametric TEST
PM Notes
STA4C04– STATISTICAL INFERENCE AND QUALITY CONTROL
Module 3
NON PARAMETRIC METHODS
Most of the parametric tests are based on the assumption that the
parent population is normal. Even if the parent population is not
normal we can reduce the to the normal form. But there are certain
situations where no assumption is made about the distribution of the
population and also testing is not concerned with the parameters. In
such situations we use the non parametric tests.
Non parametric test are those test which do not make any assumptions
about the population or the parameters involved in it . So the non
parametric test can be called as distribution free tests where
assumptions are fewer than those associated with parametric tests.
Assumptions in nonparametric test
Sample observations are independent
The variable is continuous
Population probability density function is continuous.
Sample drawn is a random sample.
Advantages of nonparametric tests
They are very simple and easy to apply compare to parametric test
They do not require the assumption that the population is
normally distributed
Non parametric test can be applied when the measurement scale
of data is nominal or ordinal ( Qualitative). So nonparametric test
have the
application in Psychometry, Sociology, Educational Statistics etc
Even if the sample size is more nonparametric test can be
used
Disadvantages of non parametric test
It is less efficient compared to parametric tests
The results may or may not provide a accurate answer because
they are distribution free.
They ignore a certain amount of information.
about:blan 1/10
k
, 9/18/24, 1:33 NON Parametric TEST
PM Notes
Situations where non parametric test can be applied
When the hypothesis does not involve parameters of the population
When the observations are not as accurate as required for
parametric test
When the assumptions necessary for a parametric test are not
clearly and correctly known.
Important non parametric tests
Sign test ( one sample and two sample)
Wilcoxon matched pair signed rank test
Wald Wolfowitz run test ( Test of randomness)
Median test
Mann – Whitney U test
Kruskal- Wallis test
Sign test
One sample sign test
Tests of population means like t-test ,Z test etc are based on the
assumption that the population from which samples are taken follows a
normal distribution.
When the condition cannot be applied when we use non parametric test
like a
sign test.
One sample sign test is based on the assumption that the samples
are drawn from a symmetrical continuous population. So here the
probability that the sample value is greater than or less than or equal
to mean or median or both ½.
Test procedure
Here we have to test H₀ : μ = μ₀ against H₁ : μ ≠ μ₀ or H₁ : μ > μ₀ or
H₁ : μ < μ₀ ( where μ can be mean or median)
Replace each sample value greater than μ₀ by a + sign ,less than μ₀
by a –
sign, and equal to μ₀ by zero.
Count the number of + signs and – signs.
Find the proportion of + sign out of the total .Let it be p'
When H₀ is true the population proportion of the values greater than μ₀
denoted by p can be taken as equal to ½. Then the null and
alternative
about:blan 2/10
k
PM Notes
STA4C04– STATISTICAL INFERENCE AND QUALITY CONTROL
Module 3
NON PARAMETRIC METHODS
Most of the parametric tests are based on the assumption that the
parent population is normal. Even if the parent population is not
normal we can reduce the to the normal form. But there are certain
situations where no assumption is made about the distribution of the
population and also testing is not concerned with the parameters. In
such situations we use the non parametric tests.
Non parametric test are those test which do not make any assumptions
about the population or the parameters involved in it . So the non
parametric test can be called as distribution free tests where
assumptions are fewer than those associated with parametric tests.
Assumptions in nonparametric test
Sample observations are independent
The variable is continuous
Population probability density function is continuous.
Sample drawn is a random sample.
Advantages of nonparametric tests
They are very simple and easy to apply compare to parametric test
They do not require the assumption that the population is
normally distributed
Non parametric test can be applied when the measurement scale
of data is nominal or ordinal ( Qualitative). So nonparametric test
have the
application in Psychometry, Sociology, Educational Statistics etc
Even if the sample size is more nonparametric test can be
used
Disadvantages of non parametric test
It is less efficient compared to parametric tests
The results may or may not provide a accurate answer because
they are distribution free.
They ignore a certain amount of information.
about:blan 1/10
k
, 9/18/24, 1:33 NON Parametric TEST
PM Notes
Situations where non parametric test can be applied
When the hypothesis does not involve parameters of the population
When the observations are not as accurate as required for
parametric test
When the assumptions necessary for a parametric test are not
clearly and correctly known.
Important non parametric tests
Sign test ( one sample and two sample)
Wilcoxon matched pair signed rank test
Wald Wolfowitz run test ( Test of randomness)
Median test
Mann – Whitney U test
Kruskal- Wallis test
Sign test
One sample sign test
Tests of population means like t-test ,Z test etc are based on the
assumption that the population from which samples are taken follows a
normal distribution.
When the condition cannot be applied when we use non parametric test
like a
sign test.
One sample sign test is based on the assumption that the samples
are drawn from a symmetrical continuous population. So here the
probability that the sample value is greater than or less than or equal
to mean or median or both ½.
Test procedure
Here we have to test H₀ : μ = μ₀ against H₁ : μ ≠ μ₀ or H₁ : μ > μ₀ or
H₁ : μ < μ₀ ( where μ can be mean or median)
Replace each sample value greater than μ₀ by a + sign ,less than μ₀
by a –
sign, and equal to μ₀ by zero.
Count the number of + signs and – signs.
Find the proportion of + sign out of the total .Let it be p'
When H₀ is true the population proportion of the values greater than μ₀
denoted by p can be taken as equal to ½. Then the null and
alternative
about:blan 2/10
k
