Question

Q67 Enumerate the important considerations for statistical analysis with special references to parametric statistics and non-parametric statistics. [3 Marks]

Answer 1

Parametric method can be described as those that makes certain assumptions with regard to one or more of the population parameters that characterize the underlying distribution(s) for which the test is employed. IIt implies, that if a test that assumes the population distribution has a particular form (e.g., a normal distribution) and involves hypotheses about population parameters.

Non-Parametric tests do not make these kinds of assumptions about the underlying distribution(s) (but some assumptions are made and these are different for different non-parametric tests.).

To define it properly, a statistical method is Non-Parametric if it satisfies at least one of the following criteria:

• Given data is with a nominal scale of measurement.
• Given data is with an ordinal scale of measurement.
• We have data with an interval or ratio scale of measurement, where the distribution function of the random variable producing the data are unspecified (or specified except for an infinite number of unknown parameters

WHEN TO USE PARAMETRIC TESTS:

1. For skewed and non-normal distributions

Parametric tests can perform better with continuous data that are non-normal.

2. Parametric tests can perform well when the spread of each group is different

Nonparametric tests that compare groups, follow the assumption that the data for all groups must have the same spread (dispersion). If your groups have a different spread, the nonparametric tests might not provide valid results.

3. Statistical power

Parametric tests usually have more statistical power than nonparametric tests. Thus, you are more likely to detect a significant effect when one truly exists.

WHEN TO USE NON-PARAMETRIC TESTS

1. When the data is better represented by the median

For example, the center of a skewed distribution, like income, can be better measured by the median where 50% are above the median and 50% are below. If you add a few billionaires to a sample, the mathematical mean increases greatly even though the income for the typical person doesn’t change.

When your distribution is skewed enough, the mean is strongly affected by changes far out in the distribution’s tail whereas the median continues to more closely reflect the center of the distribution. For these two distributions, a random sample of 100 from each distribution produces means that are significantly different, but medians that are not significantly different.

2. Data has a small sample size

If the given data doesn't meet the sample size guidelines for the parametric tests and it is not normally distributed, it is recommended to use a nonparametric test. When you have a really small sample, you might not even be able to ascertain the distribution of your data because the distribution tests will lack sufficient power to provide meaningful results.

3. You have ordinal data, ranked data, or outliers that you can’t remove

Typical parametric tests can only assess continuous data and the results can be significantly affected by outliers. Conversely, some nonparametric tests can handle ordinal data, ranked data, and not be seriously affected by outliers. Be sure to check the assumptions for the nonparametric test because each one has its own data requirements.