Transforming Likert Scale Data into Normal Distributions in Python

In data analysis and statistical modeling, it is often useful to transform data from one scale to another. In this article, we will explore how to transform Likert scale data, commonly used in surveys, into normal distributions using Python. We will demonstrate the process using a sample dataset and provide a code implementation to achieve this transformation.

Problem Statement

Likert scale data consists of discrete values representing different levels of agreement or preference, typically ranging from 1 to 5 or 1 to 7. For certain analysis techniques and modeling purposes, it may be beneficial to convert this discrete data into a continuous scale that follows a normal distribution.

To transform Likert scale data into normal distributions, we will utilize the 'random.normalvariate()' function from the Python 'random' module. This function generates random numbers following a normal distribution, given a mean and standard deviation.

First, we define dictionaries 'Mu' and 'std' that store the mean and standard deviation values for each Likert scale category. These values can be predetermined based on domain knowledge or empirical data. Next, we create a copy of the original dataset to preserve the integrity of the original data. We iterate over each column and each cell in the dataframe using nested 'for' loops. For each cell value that matches a Likert scale category, we replace it with a newly generated random value following a normal distribution. This ensures that each cell receives a unique random value based on its corresponding Likert category.

CODE

import random

Mu = {1: 0.021, 2: 0.146, 3: 0.375, 4: 0.625, 5: 0.979}
std = {1: 0.021, 2: 0.104, 3: 0.125, 4: 0.125, 5: 0.021}

def generate_random_value(category):
    return random.normalvariate(Mu[category], std[category])

raw_data_rnd = raw_data.copy()

for col in raw_data_rnd.columns:
    for i in range(len(raw_data_rnd[col])):
        value = raw_data_rnd[col].iloc[i]
        if value in Mu.keys():
            raw_data_rnd[col].iloc[i] = generate_random_value(value)

raw_data_rnd

Future enhancements 

1. Instead of hardcoding the mean and standard deviation values in the code, you can make them configurable parameters. This allows for easier modification and adaptability to different datasets or scenarios. You can store the mean and standard deviation values in external configuration files or databases, or pass them as function arguments.
2. If your dataset contains missing values (NaNs), you can add logic to handle these values appropriately. For example, you can skip the transformation for missing values or replace them with a default value before applying the transformation.
3. In the current implementation, a new random value is generated for each cell individually. If you have a large dataset, this can be computationally expensive. To optimize performance, you can generate a batch of random values upfront and map them to the corresponding Likert scale categories.
4. The current code assumes a Likert scale range from 1 to 5. To enhance compatibility, you can modify the code to handle Likert scales with different ranges, such as 1 to 7 or custom scales. This can be achieved by extending the dictionaries Mu and std and modifying the conditional statements accordingly.
5. To promote code reusability, you can encapsulate the transformation logic in a function or class. This allows you to easily apply the transformation to multiple datasets or integrate it into larger data processing pipelines. The function or class can take parameters such as the input dataset, Likert scale range, and mean/standard deviation values, making it adaptable to various scenarios.

In this article, we explored the process of transforming Likert scale data into normal distributions using Python. By leveraging the 'random.normalvariate()' function and incorporating mean and standard deviation values for each Likert category, we were able to convert discrete Likert scale values into continuous random values that follow a normal distribution. This transformation allows us to apply statistical techniques and models that assume normally distributed data to the transformed Likert scale data. It's important to note that the transformation alters the original meaning of the Likert scale responses, and careful consideration should be given to the implications of this transformation in the context of your analysis. Remember to adapt the code to your specific dataset and ensure that you have imported the necessary libraries. Happy data analysis!