Math and Arithmetic

Statistics

Standardized Tests

# What are examples of parametric and nonparametric statistical tests?

###### Wiki User

###### 2007-07-18 23:07:01

Parametric statistical tests assume that your data are normally

distributed (follow a classic bell-shaped curve). An example of a

parametric statistical test is the Student's t-test.

Non-parametric tests make no such assumption. An example of a

non-parametric statistical test is the Sign Test.

## Related Questions

###### Asked in Public Health and Safety

### What is the difference between parametric and nonparametric statistical tests in Health care?

Parametric tests draw conclusions based on the data that are
drawn from populations that have certain distributions.
Non-parametric tests draw fewer conclusions about the data set. The
majority of elementary statistical methods are parametric because
they generally have larger statistical outcomes. However, if the
necessary conclusions cannot be drawn about a data set,
non-parametric tests are then used.

###### Asked in Statistics, Standardized Tests

### What is the difference between parametric and non parametric?

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.

###### Asked in Education

### What are the advantages and disadvantages of nonparametric statistics compared to the parametric statistics?

Non-Parametric statistics are statistics where it is not
assumed that the population fits any parametrized distributions.
Non-Parametric statistics are typically applied to populations that
take on a ranked order (such as movie reviews receiving one
to four stars). The branch of
http://www.answers.com/topic/statistics known as non-parametric
statistics is concerned with non-parametric
http://www.answers.com/topic/statistical-model and non-parametric
http://www.answers.com/topic/statistical-hypothesis-testing.
Non-parametric models differ from
http://www.answers.com/topic/parametric-statistics-1 models in that
the model structure is not specified a priori but is instead
determined from data. The term nonparametric is not meant to
imply that such models completely lack parameters but that the
number and nature of the parameters are flexible and not fixed in
advance. Nonparametric models are therefore also called
distribution free or parameter-free. * A
http://www.answers.com/topic/histogram is a simple nonparametric
estimate of a probability distribution *
http://www.answers.com/topic/kernel-density-estimation provides
better estimates of the density than histograms. *
http://www.answers.com/topic/nonparametric-regression and
http://www.answers.com/topic/semiparametric-regression methods have
been developed based on
http://www.answers.com/topic/kernel-statistics,
http://www.answers.com/topic/spline-mathematics, and
http://www.answers.com/topic/wavelet. Non-parametric (or
distribution-free) inferential statistical methods
are mathematical procedures for statistical hypothesis testing
which, unlike http://www.answers.com/topic/parametric-statistics-1,
make no assumptions about the
http://www.answers.com/topic/frequency-distribution of the
variables being assessed. The most frequently used tests
include

###### Asked in Statistics

### Why are nonparametric tests not the first choice in statistical procedures?

There are several reasons, including the following, in no
particular order:
I suspect that many or most people learn the parametric
alternatives first, or learn mainly the parameteric
alternatives.
When the correct conditions hold, the parametric alternatives
provide the best power.
In some situations, such as the more complicated ANOVA and
related methods, there are no nonparametric alternatives.
Often data that do not appear to satisfy the requirements for
parametric procedures can be transformed so that they do, more or
less.
Parametric procedures have been shown to be robust in the face
of departures from the assumptions on which they were based, in
many cases.

###### Asked in Statistics, Education, Standardized Tests

### What is the difference between parametric and nonparametric statistical tests?

Parametric are the usual tests you learn about.
Non-parametric tests are used when something is very "wrong"
with your data--usually that they are very non-normally
distributed, or N is very small. There are a variety of ways of
approaching non-parametric statistics; often they involve either
rank-ordering the data, or "Monte-Carlo" random sampling or
exhaustive sampling from the data set.
The whole idea with non-parametrics is that since you can't
assume that the usual distribution holds (e.g., the X² distribution
for the X² test, normal distribution for t-test, etc.), you use the
calculated statistic but apply a new test to it based only on the
data set itself.

###### Asked in Statistics, Definitions, Standardized Tests

### Distingnish between parametric and nonparametric statistics. Why the parametric statistics are considered more powerful than the nonparametric statistics. Explain.?

Parametric statistical tests assume that the data belong to some
type of probability distribution. The normal distribution is
probably the most common. That is, when graphed, the data follow a
"bell shaped curve".
On the other hand, non-parametric statistical tests are often
called distribution free tests since don't make any assumptions
about the distribution of data. They are often used in place of
parametric tests when one feels that the assumptions of the have
been violated such as skewed data.
For each parametric statistical test, there is one or more
nonparametric tests. A one sample t-test allows us to test whether
a sample mean (from a normally distributed interval variable)
significantly differs from a hypothesized value. The nonparametric
analog uses the One sample sign test In one sample sign
test,
we can compare the sample values to the a hypothesized median
(not a mean). In other words we are testing a population median
against a hypothesized value k. We set up the hypothesis so that +
and - signs are the values of random variables having equal size. A
data value is given a plus if it is greater than the hypothesized
mean, a negative if it is less, and a zero if it is equal.
he sign test for a population median can be left tailed, right
tailed, or two tailed. The null and alternative hypothesis for each
type of test will be one of the following:
Left tailed test: H0: median ≥ k and H1: median < k
Right tailed test: H0: median ≤ k and H1: median > k
Two tailed test: H0: median ≠ k and H1: median = k
To use the sign test, first compare each entry in the sample to
the hypothesized median k.
If the entry is below the median, assign it a - sign.
If the entry is above the median, assign it a + sign.
If the entry is equal to the median, assign it a 0.
Then compare the number of + and - signs. The 0′s are
ignored.
If there is a large difference in the number of + and - signs,
then it is likely that the median is different from the
hypothesized value and the null hypothesis should be rejected.
When using the sign test, the sample size n is the total number
of + and - signs.
If the sample size > 25, we use the standard normal
distribution to find the critical values and we find the test
statistic by plugging n and x into a formula that can be found on
the link.
When n ≤ 25, we find the test statistic x, by using the smaller
number of + or - .
So if we had 10 +'s and 5 -'s, the test statistic x would be 5.
The zeros are ignored.
I will provided a link to some nonparametric test that goes into
more detail. The information about the Sign Test was just given as
an example of one of the simplest nonparametric test so one can see
how these tests work The Wilcoxon Rank Sum Test, The Mann-Whitney U
test and the Kruskal-Wallis Test are a few more common
nonparametric tests. Most statistics books will give you a list of
the pros and cons of parametric vs noparametric tests.

###### Asked in Statistics

### Who uses parametric modeling?

In a sense, and whether they realise it or not, thousands of
researchers are using parametric modelling whenever they employ
t-tests, F-tests, chi-square tests, or any of the myriad other
tests in common use. All of these are based on parametric
models.
There is also a large class of scientists, including
physicists, chemists, experimental psychologists, biologists,
astronomers and others, that make heavy use of parametric models to
describe systems that they have encountered.

###### Asked in College Degrees, Graduate Degrees, Masters of Business Administration MBA

### Is math required for an MBA HR degree?

Typically, you will find some type of business statistical
analysis, and/or tests and measurements.
Typically, you will find some type of business statistical
analysis, and/or tests and measurements.
Typically, you will find some type of business statistical
analysis, and/or tests and measurements.
Typically, you will find some type of business statistical
analysis, and/or tests and measurements.
Typically, you will find some type of business statistical
analysis, and/or tests and measurements.
Typically, you will find some type of business statistical
analysis, and/or tests and measurements.

###### Asked in Statistics

### How do you compare parametric and non-parametric analysis?

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.

###### Asked in Math and Arithmetic, Statistics, Definitions

### What is Parametric and Non-Parametric Statistics?

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.
In both cases, it is possible to look at measures of central
tendency (mean, for example) and spread (variance) and, based on
these, to carry out tests and make inferences.