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| Parametric Tests & Non-Parametric Tests |
Parametric Tests (for
example, “t” test, and “f” test) are regarded as one of the most powerful
tests. It is used during the stage of data analysis of a research work.
Parametric
Tests are used when certain basic assumptions are fulfilled. If those assumptions
are not fulfilled, that kind of tests comes under the ambit of Non-Parametric Tests (such as, chi
square test, and Mann-Whitney Test).
Following
are the basic assumptions of the parametric tests. If these assumptions are
fulfilled, then parametric tests could be used; otherwise, non-parametric tests
would be employed. Let’s discuss the basic assumptions of:
1. Normality
of Distribution: The sample (which has been drawn from the
population) must be normally distributed for parametric tests. If samples are not
normally distributed, it would not fall under the category of non-parametric
tests; that is why, non-parametric tests are also known as distribution-free tests.
2. Randomization: The
condition for selecting sample from the populations must be random.
It means any technique, which is under the category of probability sampling
technique, needs to be adopted. If samples are not selected through the process
of randomization, we cannot apply parametric tests; in that case, we would
apply non-parametric tests.
3. Homogeneity
of Variance: The samples have equal, or nearly equal, variances.
Homogeneity means sameness (in other words, more or less it should be same). For
example, if we calculate the variance of two populations from where samples are
drawn, they must have more or less same variance. If there is a wide difference among the
variance of the sample, parametric tests cannot be used; in such case,
non-parametric tests will be used.
4. Null-Hypothesis: This assumption
is pre-requisite for both parametric as well as non-parametric tests. Therefore,
this assumption is not the distinctive feature of parametric tests; this is the
common feature of both parametric and non-parametric tests.
In both
type of tests (parametric test or non-parametric test), a null-hypothesis must
be formed. A null-hypothesis states that there is no significant difference or
relationship between two or more parameters.
What are Parametric and Non-Parametric Data?
There are
two types of data which are recognized during the application of statistical
treatments. These are the following:
i. Parametric Data: It
refers to the data which are measured. As it has already been
discussed above, parametric tests assume that the data are normally (or nearly
normally) distributed. Parametric tests are applied to both interval and ratio
scaled data.
ii.Non-Parametric Data: Data
of this type are either counted (nominal) or ranked
(ordinal).
