Nonparametric statistical tests are for data with not normal distributions, i.e. when the distribution as not 'bell shaped'. One get a pretty good idea of the distribution with a histogram. The Shapiro test can be used to check if the distributions is normal or not.

If you think you need a nonparametric tests, what you really need is a Generalized Linear Model https://schmettow.github.io/New_Stats/glm.html

There are no specific conditions. See the attached screenshot for a reference

David Booth

In case that's no parameter existing.

"When do we use parametric statistics? - When do we use nonparametric statistics?"

In one approach, you should use both and, if they give contradictory answers, you should investigate why.

More seriously, you should consider:

(a) There is not always a "non-parametric" analysis available to treat a problem, particularly if you are limited to things treated in standard texts;

(b) Non-parametric and parametric approaches often treat different basic quantities, such as medians, means, median-differences, mean-differences, etc.;

(c) For some sophisticated types of analysis, there may not be a clear distinction between non-parametric and parametric approaches. For example, if one considers "bootstrapping", etc..

(d) The contradictory aims of (i) the search for optimal procedures inherent in parametric analyses and (ii) the avoidance of unnecessary/unjustified assumptions inherent in non-parametric analyses.

(e) There is a third possibility, namely graphical display of the data, that may be all that is required for some problems, but that should always be done as a starting point.

Muqdad Bashir Hussein

It does not rely on specific assumptions about the underlying probability distribution or functional form of the data. They are robust and flexible tools that can be used in various situations. scenarios where nonparametric statistics are commonly applied:

1. Unknown Distribution: Nonparametric methods are suitable when the distribution of the data is unknown or cannot be assumed to follow a specific parametric form. Nonparametric tests and estimators make fewer assumptions about the shape or parameters of the distribution, allowing for more flexible analysis.

2. Non-Normal Data: Nonparametric methods are robust to violations of normality assumptions. When the data do not follow a normal distribution or when there are outliers present, nonparametric techniques can provide reliable results. For example, nonparametric tests such as the Wilcoxon rank-sum test or the Kruskal-Wallis test can be used as alternatives to parametric tests like the t-test or ANOVA when the underlying assumptions are not met.

3. Ordinal or Categorical Data: Nonparametric methods are often used when dealing with ordinal or categorical data. These methods can handle data that are ranked or grouped into categories without assuming specific numerical values or intervals. For example, the Mann-Whitney U test is commonly used to compare two independent groups when the data are measured on an ordinal scale.

4. Small Sample Size: Nonparametric methods can provide reliable results even with small sample sizes. They do not rely on large sample approximations or assumptions about the population parameters. Nonparametric techniques such as the sign test or the Wilcoxon signed-rank test can be used for paired data analysis, even with limited observations.

5. Data Transformation: Nonparametric methods can be useful when traditional transformations to achieve normality are not successful or when pre-specified parametric models do not adequately fit the data. Nonparametric regression techniques, such as kernel regression or local polynomial regression, can be employed to model relationships between variables without assuming a specific functional form.

Good luck!!