Parametric Hypothesis Test

Context:
- It requires a random sample of data from the population (i.e. sample dataset must be independent and identically distributed).
- It requires a normal distribution (approximately) of the sample and population on the test variable.
- It requires homogeneity of variance to be true, i.e, population variances must be approximately equal in both the sample and population.
- It uses the mean value as central tendency measure.
- It can range from being a One-Tailed Hypothesis Test to being a Two-Tailed Hypothesis Test (left or right).
- It can require a continuous test variable ranging from being ratio to being interval.
Example(s)
- F-test.
- Student's t-Test.
- Pearson Correlation Test.
- ANOVA.
Counter-Example(s):
- Non-Parametric Test.
See: Test Statistic, Parametric Model, Parametric Statistics, Probability Distribution, Parametrization, Descriptive Statistics, Statistical Inference, Robust Statistics.

References

(Changing Works, 2017) ⇒ Retrieved on 2017-05-07 from http://changingminds.org/explanations/research/analysis/parametric_non-parametric.htm Copyright: Changing Works 2002-2016
- There are two types of test data and consequently different types of analysis. As the table below shows, parametric data has an underlying normal distribution which allows for more conclusions to be drawn as the shape can be mathematically described. Anything else is non-parametric.

	Parametric Statistical Tests	Non-Parametric Statistical Tests
Assumed distribution	Normally Distributed	Any
Assumed variance	Homogeneous	Any
Typical data	Ratio or Interval	Ordinal or Nominal
Data set relationships	Independent	Any
Usual central measure	Mean	Median
Benefits	Can draw more conclusions	Simplicity; Less affected by outliers

(Jim Frost, 2015) ⇒ Retrieved on 2017-05-07 from http://blog.minitab.com/blog/adventures-in-statistics-2/choosing-between-a-nonparametric-test-and-a-parametric-test Copyright ©2017 Minitab Inc. All rights Reserved.
- Nonparametric tests are like a parallel universe to parametric tests. The table shows related pairs of hypothesis tests that Minitab statistical software offers.

Parametric tests (means)	Nonparametric tests (medians)
1-sample t test	1-sample Sign, 1-sample Wilcoxon
2-sample t test	Mann-Whitney test
One-Way ANOVA	Kruskal-Wallis, Mood’s median test
Factorial DOE with one factor and one blocking variable	Friedman test

PARAMETRIC TEST	NON-PARAMETRIC TEST
Independent Sample t Test	Mann-Whitney test
Paired samples t test	Wilcoxon signed Rank test
One way Analysis of Variance (ANOVA)	Kruskal Wallis Test
One way repeated measures Analysis of Variance	Friedman's ANOVA

(Wikipedia, 2016) ⇒ https://en.wikipedia.org/wiki/Parametric_statistics Retrieved:2016-5-24.
- Parametric statistics is a branch of statistics which assumed that sample data comes from a population that follows a probability distribution based on a fixed set of parameters. Most well-known elementary statistical methods are parametricConversely a non-parametric model differs precisely in that the parameter set (or feature set in machine learning) is not fixed and can increase, or even decrease if new relevant information is collected. A parametric model as it relies on a fixed parameter set assumes more about a given population than non-parametric methods. When the assumptions are correct, parametric methods will produce more accurate and precise estimates than non-parametric methods, i.e. have more statistical power. As more is assumed when the assumptions are not correct they have a greater chance of failing, and for this reason are not a robust statistical method. On the other hand, parametric formulae are often simpler to write down and faster to compute. For this reason their simplicity can make up for their lack of robustness, especially if care is taken to examine diagnostic statistics.