**Parametric Tests**

Parametric tests are statistical tests in which we make assumptions regarding the distribution of the population. Such tests involve a specific distribution when estimating the key parameters of that distribution. For example, we may wish to estimate the mean or the compare population proportions.

**Breaking Down Parametric Tests**

When carrying out statistical tests assuming the parameter follows a specific distribution, the choice of the distribution chosen directly affects the formulation of the test statistic. For instance, if we assume that a parameter follows a normal distribution, we have to compute the z-statistic.

When conducting parametric testing, it may be necessary to approximate the normal distribution for non-normal distributions. This approximation is possible because of the central limit theorem which asserts that as the sample size increases, most non-normal distributions “tend to normalize”.

Parametric tests are generally considered to be stronger compared to nonparametric ones.

**Non-Parametric Tests**

Nonparametric tests – also called distribution-free tests by some researchers – are tests that do not make any assumption regarding the distribution of the parameter under study. Researchers use non-parametric testing when there are concerns about some quantities other than the parameter of the distribution.

Situations Where Nonparametric Tests are Appropriate

- When the median is more desirable compared to the mean

Although you can conduct a parametric test using non-normal data courtesy of the central limit theorem, there are situations where the mean may not provide a fair measure of the central tendency.

**Example**

Consider a situation where we want to establish the center of rather skewed distribution such as that of income of residents in a given city. A majority of the residents could be categorized in the middle class but the presence of just a few billionaires in a sample can greatly increase the mean income. Such a mean may not provide a very reliable/realistic measure of income. Instead, it may be more appropriate to use the median. The center of the income distribution can be better represented by the median since 50% of the residents will be above it and the remaining 50% below the same.

In summary, “outliers” affect the mean when dealing with skewed data. The median, on the other hand, sticks closer to the center of the distribution.

- When the sample size is very small

In the absence of outright normal distribution of the data, you might find that you don’t have sufficient information or sample size big enough to justify normal approximation. You might not even succeed in carrying out distribution tests such as the goodness of fit test. In such a scenario, a non-parametric test may be appropriate.

- Analysis of ordinal data

Although nonparametric tests are usually simpler to conduct compared to parametric ones, they do not have as much statistical power. Nonetheless, they provide an efficient tool for analyzing ordinal, ranked, or very skewed data.

*Reading 12 LOS 12k:*

*Distinguish between parametric and nonparametric tests and describe situations in which the use of nonparametric tests may be appropriate.*