Wilcoxon matched pair sign test using Python

by | Feb 9, 2023 | Statistics For Machine Learning

What is the Wilcoxon matched pair sign test?

The Wilcoxon matched pair sign test is a non-parametric hypothesis test that is used to compare the medians of two dependent samples.

For example, let’s say there are 10 rabbits. A certain treatment is provided to the rabbits. And the weights of the rabbits before and after the treatment are recorded.

Now, we want to know whether the difference in the medians of the weights of the rabbits before and after the treatment is statistically significant.

The Wilcoxon matched pair sign test is the non-parametric alternative of the paired t-test. We perform the Wilcoxon matched pair sign test when the data is not distributed normally.

How is the Wilcoxon matched pair sign test performed?

Let’s say we are given the weights of 10 rabbits before and after a certain treatment. And we want to know whether the difference between the medians of the rabbits before and after treatment is statistically significant. To do so, we need to perform the following steps:

1. We will first find out the difference between two weights for each rabbit before and after the treatment.

2. Then, we will rank the absolute differences in ascending order.

3. If the difference associated with two or more ranks is the same, we will replace the ranks with the average rank. For example, if the difference associated with ranks 2, 3, and 4 are the same, we will replace ranks 2, 3, and 4 with the average of 2, 3, and 4, which is 3.

4. We will then assign a sign with each rank. If the difference associated with a rank is positive, we will assign a positive sign. And if the difference associated with a rank is negative, we will assign a negative sign.

5. We will now calculate W+ and W-. W+ is the sum of positive ranks, and W- is the sum of negative …

Facebooktwitterredditpinterestlinkedinmail

Calculate the pseudoinverse of a matrix using Python

What is the pseudoinverse of a matrix? We know that if A is a square matrix with full rank, then A-1 is said to be the inverse of A if the following condition holds: $latex AA^{-1}=A^{-1}A=I $ The pseudoinverse or the Moore-Penrose inverse of a matrix is a...

Cholesky decomposition using Python

What is Cholesky decomposition? A square matrix A is said to have Cholesky decomposition if it can be written as a product of a lower triangular matrix and its conjugate transpose. $latex A=LL^{*} $ If all the entries of A are real numbers, then the conjugate...

Tensor Hadamard Product using Python

In one of our previous articles, we already discussed what the Hadamard product in linear algebra is. We discussed that if A and B are two matrices of size mxn, then the Hadamard product of A and B is another mxn matrix C such that: $latex H_{i,j}=A_{i,j} \times...

Perform tensor addition and subtraction using Python

We can use numpy nd-array to create a tensor in Python. We can use the following Python code to perform tensor addition and subtraction. import numpy A = numpy.random.randint(low=1, high=10, size=(3, 3, 3)) B = numpy.random.randint(low=1, high=10, size=(3, 3, 3)) C =...

How to create a tensor using Python?

What is a tensor? A tensor is a generalization of vectors and matrices. It is easily understood as a multidimensional array. For example, in machine learning, we can organize data in an m-way array and refer it as a data tensor. Data related to images, sounds, movies,...

How to combine NumPy arrays using horizontal stack?

We can use the hstack() function from the numpy module to combine two or more NumPy arrays horizontally. For example, we can use the following Python code to combine three NumPy arrays horizontally. import numpy A = numpy.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) B =...

How to combine NumPy arrays using vertical stack?

Let’s say we have two or more NumPy arrays. We can combine these NumPy arrays vertically using the vstack() function from the numpy module. For example, we can use the following Python code to combine three NumPy arrays vertically. import numpy A = numpy.array([[1, 2,...

Singular Value Decomposition (SVD) using Python

What is Singular Value Decomposition (SVD)? Let A be an mxn rectangular matrix. Using Singular Value Decomposition (SVD), we can decompose the matrix A in the following way: $latex A_{m \times n}=U_{m \times m}S_{m \times n}V_{n \times n}^T $ Here, U is an mxm matrix....

Eigen decomposition of a square matrix using Python

Let A be a square matrix. Let’s say A has k eigenvalues λ1, λ2, ... λk. And the corresponding eigenvectors are X1, X2, ... Xk. $latex X_1=\begin{bmatrix} x_{11} \\ x_{21} \\ x_{31} \\ ... \\ x_{k1} \end{bmatrix} \\ X_2=\begin{bmatrix} x_{12} \\ x_{22} \\ x_{32} \\ ......

How to calculate eigenvalues and eigenvectors using Python?

In our previous article, we discussed what eigen values and eigenvectors of a square matrix are and how we can calculate the eigenvalues and eigenvectors of a square matrix mathematically. We discussed that if A is a square matrix, then $latex (A- \lambda I) \vec{u}=0...

Amrita Mitra

Author

Ms. Amrita Mitra is an author, who has authored the books “Cryptography And Public Key Infrastructure“, “Web Application Vulnerabilities And Prevention“, “A Guide To Cyber Security” and “Phishing: Detection, Analysis And Prevention“. She is also the founder of Asigosec Technologies, the company that owns The Security Buddy.

0 Comments

Submit a Comment

This site uses Akismet to reduce spam. Learn how your comment data is processed.

Not a premium member yet?

Please follow the link below to buy The Security Buddy Premium Membership.

Featured Posts

Translate »