The field of statistics contains two types of variables: dependent and independent. Similarly, to conclude, statisticians use various types of tests out of which two of them are parametric and non-parametric tests. These are extremely broad classifications of different statistical procedures used in the vast world of statistical applications.

**Parametric vs Nonparametric**

The difference between these two tests is that one of them is dependent and the other is independent to a certain extent from parameters like mean, standard deviation, variation, and Central Limit Theorem. All of these are different parameters calculated on the data available. Although every parametric test has a nonparametric counterpart or equivalent.

Parametric statistical procedures are described as those whose results rely on the assumption of the shape of the distribution of data (Example: Normal Distribution) and about the parameters of the assumed distribution. There are different kinds of parametric tests like the t-test, Pearson coefficient of correlation, paired t-test, and many more.

Nonparametric statistical procedures are described as those whose results rely on no or few of the assumptions of the shape of the distribution of data or about the parameters of the assumed distribution. Their application is more flexible and robust as they do not depend on any kind of assumption or pre-defined conditions for the data.

**Comparison Table Between Parametric and Nonparametric**

Parameters of Comparison | Parametric | Nonparametric |

Definition | The test whose outcomes depend on the distribution is called a parametric test. | The test whose outcomes do not depend on the distribution is called a nonparametric test. |

Statistical power | Parametric tests have higher statistical power. | Nonparametric tests have lower statistical power. |

Versatility | Parametric tests are not applicable to all situations. | Nonparametric tests are more robust and can be applied to different situations. |

Central Tendency value | Mean value is the central tendency value for this test. | Median value is the central tendency value for this test. |

Type of distribution | It is used on data that follows a normal distribution. | It is used on data that follows any arbitrary distribution. |

**What is Parametric Test?**

A parametric statistical test assumes the parameters of the population and the distributions of the data it came from. The parametric test is used for quantitative data with continuous variables. The data that parametric tests are used on are measured on ratio scales measurement and follow a normal distribution.

The most widely and commonly used parametric tests are t-test (for sample size less than 30), Z-test (for sample size greater than 30), ANOVA, Pearson’s rank Correlation. The central tendency value that is taken into considerations is the mean of the distribution and is mostly applicable to a normal distribution for data. The disadvantage of this kind of this test is that since the central tendency value is mean, the data is highly prone to be affected by outliers, and thus prone to being skewed and this reduces the statistical power of this test.

Continuous distributions like the data about various heights or weights of a species over time, data about temperatures are examples where parametric tests are used. Although, due to the assumptions about the data its application is a little less versatile in real life.

**What is Nonparametric Test?**

Nonparametric tests are tests that aren’t dependent on any assumptions of the data distribution or parameters to analyze them. They are also sometimes referred to as “distribution-free tests”. Nonparametric doesn’t necessarily mean that we know nothing about the population, it means that the data is skewed or “not normally distributed”.

The reasons why we use nonparametric tests are: if the data doesn’t meet the assumptions for the population sample or when data is skewed, the population sample size is too small, or the data being analyzed is nominal or ordinal. The different types of nonparametric tests are the Sign test, Wilcoxon signed-rank test, Kruskal-Wallis test, Mann-Whitney test, Spearman rank correlation, Mood’s median test. The median value is the central tendency value.

It is more flexible in real-life applications as data found in real life is not necessarily normally distributed and is mostly clumped or non-linear. Due to their simplicity and robust nature, nonparametric tests are seen as less prone to improper use and misunderstanding. They are mostly used in populations that come in ranked order, such as movie ratings and reviews, putting up ratings for restaurants, and such. But, for data with large sample size, these tests lose a lot of their statistical power.

**Main Differences Between Parametric and Nonparametric Test**

The main difference between Parametric and Nonparametric tests is that parametric tests depend upon the data that follows certain assumptions or conditions whereas nonparametric tests need not require follow any such assumptions. Some of the other differences between the two tests are as follows:

- Parametric data follows a normal distribution whereas normal distribution follows any arbitrary distribution.
- Parametric tests apply only to variables whereas nonparametric can be applied to both attributes and variables.
- The central tendency value for the parametric test is mean and for the nonparametric test is median.
- In real-life situations, nonparametric tests pose to be better fitting alternatives than parametric tests.
- In cases where the sample size is large, parametric tests show higher statistical power than nonparametric tests.

**Conclusion**

In conclusion, parametric and nonparametric tests are both integral parts of analyzing any given data. Depending on whether it is normally distributed or not, either a parametric or nonparametric test is used. The choosing of which test to perform depends upon what kind of data we have, what the sample size is, and how much pre-requisite knowledge about the population we have.

Data having a large sample size requires a parametric test instead of nonparametric as it is more accurate. In the case of a small sample size data, the nonparametric test is preferred. No test is better than the other as both operate in different situations. As statisticians, you need to keep in mind that a nonparametric test is an alternative to a parametric test, not a substitute.

**References**

- http://people.umass.edu/~biep640w/pdf/HOSKIN%20Tonya%20Intro%20to%20Nonparametrics.pdf
- https://onlinelibrary.wiley.com/doi/abs/10.1002/j.1556-6676.1988.tb02007.x

Table of Contents