Question

Answer the following questions:

What is a nonparametric test?

How does a nonparametric test differ from a parametric test?

What are the advantages and disadvantages of using a nonparametric test?

When the sign test is used, what population parameter is being tested?

Answer 1

What is a nonparametric test?

Such tests also called as distrinution free tests, distribution free methods, which do not rely on assumptions that the data are drawn from a given probability distribution. Moreover they are based on fewer assumptions.The cost of fewer assumptions is that nonparametric tests are generally less powerful than their parametric counterparts.

The nonparametric test is defined as the hypothesis test which is not based on underlying assumptions, i.e. it does not require population’s distribution to be denoted by specific parameters.

The test is mainly based on differences in medians. Hence, it is alternately known as the distribution-free test. The test assumes that the variables are measured on a nominal or ordinal level. It is used when the independent variables are non-metric.

How does a nonparametric test differ from a parametric test?

The parametric test is one which has information about the population parameter. On the other hand, the nonparametric test is one where the researcher has no idea regarding the population parameter.

In parametric test measure of central tendency is Mean and in non parametric test measure of central tendency is Median.

In parametric test information about population is completely known and in non parametric test information about population is unavailable.

What are the advantages and disadvantages of using a nonparametric test?

1]

Nonparametric tests are more robust than parametric tests. In other words, they are valid in a broader range of situations (fewer conditions of validity).

2]

They can be used for all data types, including nominal variables, interval variables, or data that has outliers or that has been measured imprecisely.

3]

Small sample sizes are acceptable.

However, they do have their disadvantages:

1]

Less powerful than parametric tests if assumptions haven’t been violated.

2]

More labor-intensive to calculate by hand (for computer calculations, this isn’t an issue).

3]

Critical value tables for many tests aren’t included in many computer software packages. This is compared to tables for parametric tests (like the z-table or t-table) which usually are included.

When the sign test is used, what population parameter is being tested?

In parametric test we used paired t test and is equivalent to sign test in non parametric test, in sign test median will be tested.