**Parametric Test:**Parametric tests are those that make assumptions about the parameters (defining properties) of the population distribution from which the sample is drawn. In other words, Parametric tests are used when we have information about the population parameter or at least certain assumptions can be made regarding the characteristics of the population.

**Examples**: t-test, z-test, F-test, ANOVA test, Pearson’s coefficient of correlation.

**Non-Parametric
Test:** Non-parametric tests are normally ‘distribution-free’
and are used for non-normal variables. In contrast to Parametric test, Non-Parametric
tests are used when the researcher has no information about the population parameter,
neither he can make any assumptions about the population. **Examples:** Chi-Square Test, Mann-Whitney u-test, Wilcoxon signed-rank test**, **Wald–Wolfowitz Runs test**, **Mc-Nemar test, Mood's median
test,** **Spearman correlation coefficient.

**PARAMETRIC Vs
NON-PARAMETRIC TEST**

Parametric tests
require assumptions about the distributional characteristics of the population,
while Non-parametric tests are distribution free and do not require assumptions
so they can be used for non-normal/skewed distributions and where the group variance
is not equal.

Parametric tests
evaluate hypothesis for a particular parameter, usually the population mean,
whereas Non-parametric tests evaluate hypothesis for entire population.

In parametric test,
measurement of variables is done on **interval
or ratio scale**. On the other hand, in Non-Parametric test, the variables of
interest are calculated on **nominal or
ordinal scale**. Similarly the measure of central tendency in the parametric
test is **mean**, whereas in the case of
non-parametric test, measure of central tendency is** median**.

In the case of
parametric test, there is complete information about the population. On the
contrary, there is no information about the population distribution in non-parametric test.

Parametric test is
applicable for variables only, whereas non-parametric test can be applied for
both variables and attributes.

Parametric tests are
more powerful than non-parametric tests when the assumptions are correct.
However, non-parametric tests are easy to compute especially in the case of non-normal
data.

__Self-Check Exercises__

Answer: (C) the underlying distribution

Answer: (C) sign test

Answer: (B) Non-parametric test

Answer: (C) Median test

Answer: (B) One-way ANOVA

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