# Difference between Parametric and Non-Parametric Methods

Statistical analysis plays a crucial role in understanding and interpreting data across various disciplines. Two prominent approaches in statistical analysis are** Parametric and Non-Parametric Methods.** While both aim to draw inferences from data, they differ in their assumptions and underlying principles. This article delves into the differences between these two methods, highlighting their respective strengths and weaknesses, and providing guidance on choosing the appropriate method for different scenarios.

**Parametric Methods**

**Parametric Methods**

Parametric methods are statistical techniques that rely on specific assumptions about the underlying distribution of the population being studied. These methods typically assume that the data follows a known Probability distribution, such as the normal distribution, and estimate the parameters of this distribution using the available data.

The basic idea behind the ** Parametric method** is that there is a set of fixed parameters that are used to determine a probability model that is used in Machine Learning as well. Parametric methods are those methods for which we priory know that the population is normal, or if not then we can easily approximate it using a Normal Distribution which is possible by invoking the Central Limit Theorem.

Parameters for using the normal distribution are as follows:

- Mean
- Standard Deviation

Eventually, the classification of a method to be parametric completely depends on the presumptions that are made about a population.

**Assumptions for Parametric Methods**

**Assumptions for Parametric Methods**

Parametric methods require several assumptions about the data:

The data follows a normal (Gaussian) distribution.**Normality:**The variance of the population is the same across all groups.**Homogeneity of variance:**Observations are independent of each other.**Independence:**

**What are Parametric Methods?**

**What are Parametric Methods?**

**Statistical Tests:**Tests for the difference between the means of two independent groups.**t-test:**Tests for the difference between the means of three or more groups.**ANOVA:**Compares the variances of two groups.**F-test:**Tests for relationships between categorical variables.**Chi-square test:**Measures the strength and direction of the linear relationship between two continuous variables.**Correlation analysis:**

**Machine Learning Models:**Predicts a continuous outcome based on a linear relationship with one or more independent variables.**Linear regression:**Predicts a binary outcome (e.g., yes/no) based on a set of independent variables.**Logistic regression:**Classifies data points based on Bayes’ theorem and assuming independence between features.**Naive Bayes:**Models sequential data with hidden states and observable outputs.**Hidden Markov Models:**

some more common parametric methods available some of them are:

- Confidence interval used for – population mean along with known standard deviation.
- The confidence interval is used for – population means along with the unknown standard deviation.
- The confidence interval for population variance.
- The confidence interval for the difference of two means, with unknown standard deviation.

**Advantages of Parametric Methods**

**Advantages of Parametric Methods**

When the assumptions are met, parametric tests are generally more powerful than non-parametric tests, meaning they are more likely to detect a real effect when it exists.**More powerful:**Parametric tests require smaller sample sizes than non-parametric tests to achieve the same level of power.**More efficient:**Parametric methods provide estimates of the population mean, variance, and other parameters, which can be used for further analysis.**Provide estimates of population parameters:**

**Disadvantages of Parametric Methods**

**Disadvantages of Parametric Methods**

If the assumptions of normality, homogeneity of variance, and independence are not met, parametric tests can be invalid and produce misleading results.**Sensitive to assumptions:**Parametric methods are limited to the specific probability distribution they are based on.**Limited flexibility:**Parametric methods are not well-suited for capturing complex non-linear relationships between variables.**May not capture complex relationships:**

**Applications of Parametric Methods**

**Applications of Parametric Methods**

Parametric methods are widely used in various fields, including:

Comparing the effectiveness of different treatments.**Biostatistics:**Investigating relationships between variables.**Social sciences:**Estimating risk and return of investments.**Finance:**Analyzing the performance of systems.**Engineering:**

**Nonparametric Methods**

**Nonparametric Methods**

Non-parametric methods are statistical techniques that do not rely on specific assumptions about the underlying distribution of the population being studied. These methods are often referred to as “distribution-free” methods because they make no assumptions about the shape of the distribution.

The basic idea behind the parametric method is no need to make any assumption of parameters for the given population or the population we are studying. In fact, the methods donâ€™t depend on the population. Here there is no fixed set of parameters are available, and also there is no distribution (normal distribution, etc.) of any kind is available for use. This is also the reason that nonparametric methods are also referred to as distribution-free methods. Nowadays Non-parametric methods are gaining popularity and an impact of influence some reasons behind this fame is:

- The main reason is that there is no need to be mannered while using parametric methods.
- The second important reason is that we do not need to make more and more assumptions about the population given (or taken) on which we are working on.
- Most of the nonparametric methods available are very easy to apply and to understand also i.e. the complexity is very low.

### Assumptions of Non-Parametric Methods

Non Parametric methods require several assumptions about the data:

Data points are independent and not influenced by others.**Independence:**Data represents a random sample from the population.**Random Sampling:**Measurements are consistent across all data points.**Homogeneity of Measurement:**

**What is Non-Parametric Methods?**

**What is Non-Parametric Methods?**

**Statistical Tests:**Tests for the difference between the medians of two independent groups.**Mann-Whitney U test:**Tests for the difference between the medians of three or more groups.**Kruskal-Wallis test:**Measures the strength and direction of the monotonic relationship between two variables.**Spearman’s rank correlation:**Tests for the difference between the medians of two paired samples.**Wilcoxon signed-rank test:**

**Machine Learning Models:**Classifies data points based on the k nearest neighbors.**K-Nearest Neighbors (KNN):**Makes classifications based on a series of yes/no questions about the features.**Decision Trees:**Creates a decision boundary that maximizes the margin between different classes.**Support Vector Machines (SVM):**Can be designed with specific architectures to handle non-parametric data, such as convolutional neural networks for image data and recurrent neural networks for sequential data.**Neural networks:**

**Advantages of Non-Parametric Methods**

**Advantages of Non-Parametric Methods**

Non-parametric methods are not affected by outliers in the data, making them more reliable in situations where the data is noisy.**Robust to outliers:**Non-parametric methods can be used with a variety of data types, including ordinal, nominal, and continuous data.**Widely applicable:**Non-parametric methods are often computationally simple and easy to implement, making them suitable for a wide range of users.**Easy to implement:**

**Diadvantages of Non-Parametric Methods**

**Diadvantages of Non-Parametric Methods**

When the assumptions of parametric methods are met, non-parametric tests are generally less powerful, meaning they are less likely to detect a real effect when it exists.**Less powerful:**Non-parametric tests may require larger sample sizes than parametric tests to achieve the same level of power.**May require larger sample sizes:**Non-parametric methods provide less information about the population parameters than parametric methods.**Less information about the population:**

**Applications of Non-Parametric Methods**

**Applications of Non-Parametric Methods**

Non-parametric methods are widely used in various fields, including:

Comparing the effectiveness of different treatments.**Medicine:**Investigating relationships between variables.**Psychology:**Analyzing environmental data.**Ecology:**Developing machine learning algorithms.**Computer science:**

## Difference Between Parametric and Non-Parametric

There are several Difference between Parametric and Non-Parametric Methods are as follows:

Parametric Methods | Non-Parametric Methods |
---|---|

Parametric Methods uses a fixed number of parameters to build the model. | Non-Parametric Methods use the flexible number of parameters to build the model. |

Parametric analysis is to test group means. | A non-parametric analysis is to test medians. |

It is applicable only for variables. | It is applicable for both â€“ Variable and Attribute. |

It always considers strong assumptions about data. | It generally fewer assumptions about data. |

Parametric Methods require lesser data than Non-Parametric Methods. | Non-Parametric Methods requires much more data than Parametric Methods. |

Parametric methods assumed to be a normal distribution. | There is no assumed distribution in non-parametric methods. |

Parametric data handles â€“ Intervals data or ratio data. | But non-parametric methods handle original data. |

Here when we use parametric methods then the result or outputs generated can be easily affected by outliers. | When we use non-parametric methods then the result or outputs generated cannot be seriously affected by outliers. |

Parametric Methods can perform well in many situations but its performance is at peak (top) when the spread of each group is different. | Similarly, Non-Parametric Methods can perform well in many situations but its performance is at peak (top) when the spread of each group is the same. |

Parametric methods have more statistical power than Non-Parametric methods. | Non-parametric methods have less statistical power than Parametric methods. |

As far as the computation is considered these methods are computationally faster than the Non-Parametric methods. | As far as the computation is considered these methods are computationally slower than the Parametric methods. |

Examples: Logistic Regression, NaÃ¯ve Bayes Model, etc. | Examples: KNN, Decision Tree Model, etc. |

### Conclusion

Parametric and non-parametric methods offer distinct advantages and limitations. Understanding these differences is crucial for selecting the most suitable method for a specific analysis. Choosing the appropriate method ensures valid and reliable inferences, enabling researchers to draw insightful conclusions from their data. As statistical analysis continues to evolve, both parametric and non-parametric methods will play crucial roles in advancing knowledge across various fields.

## Frequently Asked Question(FAQs)

### Q. **What are non-parametric methods?**

**What are non-parametric methods?**

Non-parametric methods do not make any assumptions about the underlying distribution of the data. Instead, they rely on the data itself to determine the relationship between variables. These methods are more flexible than parametric methods but can be less powerful.

### Q. **What are parametric methods?**

**What are parametric methods?**

Parametric methods are statistical techniques that make assumptions about the underlying distribution of the data. These methods typically use a pre-defined functional form for the relationship between variables, such as a linear or exponential model.

### Q. What is the difference between non-parametric method and distribution free method?

Non-Parametric methods:

This includes the mean, variance, or even the shape (e.g., normal, skewed) of the distribution.No assumptions about the underlying distribution’s parameters:However, the number and nature of these parameters are flexible and not predetermined.Estimates parameters:Chi-square tests, Wilcoxon signed-rank testExamples:

### Q. **What are some common Non Parametric Methods?**

**What are some common Non Parametric Methods?**

Some common Non Parametric Methods:

- Chi-square test
- Wilcoxon signed-rank test
- Mann-Whitney U test
- Spearman’s rank correlation coefficient