Definition

Noun: A nonparametric statistic is a statistical measure or method that does not rely on data belonging to a specific, assumed population distribution (often a normal distribution). It is computed without requiring knowledge of the underlying distribution's form (e.g., normal, exponential) or its parameters (e.g., mean, variance). These methods are often used when data do not meet the assumptions of parametric tests or when the nature of the population distribution is unknown.

Usage

Nonparametric statistics are used for data analysis when parametric assumptions are violated or when dealing with ordinal data or ranks. * The researcher used a nonparametric statistic because the sample data were heavily skewed and did not follow a normal distribution. * For analyzing the survey's Likert-scale responses, a nonparametric statistic like the Mann-Whitney U test is appropriate.

Advanced Usage

• "Distribution-free methods": This is a common synonym for nonparametric statistics, emphasizing their independence from specific distributional assumptions.
• Contrast with Parametric Statistics: Nonparametric statistics are often contrasted with parametric statistics (e.g., t-test, ANOVA), which require assumptions about the population parameters and distribution.

Variants and Related Words

• Nonparametric test (n): A hypothesis test that uses nonparametric statistics (e.g., Wilcoxon signed-rank test, Kruskal-Wallis test).
• Nonparametrics (n): The field or study of nonparametric statistical methods.

Synonyms

• Distribution-free statistic
• Assumption-free method (in a specific context)

Related Phrases

• To run a nonparametric test: To perform a statistical analysis using nonparametric methods.
  • We had to run a nonparametric test because the data violated the homogeneity of variance assumption.

Noun

1. a statistic computed without knowledge of the form or the parameters of the distribution from which observations are drawn