# Non-parametric tests: Normal approximations

## Non-parametric Tests

• Non-parametric tests are statistical methods used when the data does not meet the assumptions of parametric tests, such as normally distributed observations.
• They can be applied to data at the nominal or ordinal level, or to interval data which has not met the assumptions for parametric tests.

## Features of Non-parametric Tests

• Non-parametric tests, unlike parametric tests, do not require assumptions about population parameters (hence the name ‘non-parametric’).
• They do not assume that the outcome variable fits any particular distribution, like the normal distribution.

## Normal Approximations

• Normal approximation involves approximating a binomial distribution to a normal distribution, under certain conditions.
• This method is used when dealing with large dataset - the main condition being that both np and n(1-p) are greater than 5, where n is the sample size and p is the probability of success.
• The central limit theorem states that if we have a large number of independent, identically distributed variables, then the distribution of their mean will approach a normal distribution, regardless of the shape of their individual distributions.

## When to Use Normal Approximations

• When the sample size is large, it becomes tedious to use the binomial formula for calculations. We can instead approximate the binomial distribution to a normal one.
• This kind of approximation makes analyses much simpler and manageable.

## Benefit of Using Non-parametric Tests

• Non-parametric tests are beneficial in cases where it may not be reasonable to make the assumptions necessary for parametric tests.
• They are also useful when the measurement level of the variable is not high enough to justify the use of parametric tests.
• Although they might not be as powerful (in statistical terms) when the conditions for parametric tests are met, non-parametric tests are robust and reliable.

## Common Non-parametric Tests

• Some commonly used non-parametric tests include the Mann-Whitney U test, Kruskal-Wallis test, Spearman’s rank correlation test and Chi-square test.
• The choice of which non-parametric test to use depends upon the nature of the data and the comparison being made.