# Data Transformation (Variable Transformation)

The data transformation is a rescaling of the data using a function or some mathematical operation on each observation. When data are very strongly skewed (negative or positive), we sometimes transform the data so that they are easier to model. In another way, if variable(s) does not fit a normal distribution then one should try a DatavTransformation to fit the assumption of using a parametric statistical test.

The most common data transformation is log (or natural log) transformation, which is often applied when most of the data values cluster around zero relative to the larger values in the data set and all of the observations are positive.

## Data Transformation Techniques

Variable transformation can also be applied to one or more variables in scatter plot, correlation, and regression analysis to make the relationship between the variables more linear; hence it is easier to model with a simple method. Other transformations than log are square root, reciprocal, etc.

### Reciprocal Transformation

The reciprocal transformation $x$ to $\frac{1}{x}$ or $(-\frac{1}{x})$ is a very strong transformation with a drastic effect on the shape of the distribution. Note that this transformation cannot be applied to zero values, but can be applied to negative values. Reciprocal transformation is not useful unless all of the values are positive and reverses the order among values of the same sign i.e. largest becomes smallest etc.

### Logarithmic Transformation

The logarithm $x$ to log (base 10) (or natural log, or log base 2) is another strong transformation that affects the shape of the distribution. Logarithmic transformation is commonly used for reducing right skewness, but cannot be applied to negative or zero values.

### Square Root Transformation

The square root x to $x^{\frac{1}{2}}=\sqrt(x)$ transformation has a moderate effect on the distribution shape and is weaker than the logarithm. Square root transformation can be applied to zero values but not negative values.

The purpose of data transformation are:

• Convert data from one format or structure to another (like changing a messy spreadsheet into a table).
• Clean and prepare data for analysis (fixing errors, inconsistencies, and missing values).
• Standardize data for easier integration and comparison (making sure all your data uses the same units and formats).

### Goals of transformation

The goals of transformation may be

• one might want to see the data structure differently
• one might want to reduce the skew that assists in modeling
• one might want to straighten a nonlinear (curvilinear) relationship in a scatter plot. In other words, a transformation may be used to have approximately equal dispersion, making data easier to handle and interpret

There are many techniques used in data transformation, these techniques are:

• Cleaning and Filtering: Identifying and removing errors, missing values, and duplicates.
• Data Normalization: Ensuring data consistency across different fields.
• Aggregation: Summarizing data by combining similar values.

The Benefits of data tranformation and data clean are:

• Improved data quality: Less errors and inconsistencies lead to more reliable results.
• Easier analysis: Structured data is easier to work with for data analysts and scientists.
• Better decision-making: Accurate insights from clean data lead to better choices.

Data transformation is a crucial step in the data pipeline, especially in tasks like data warehousing, data integration, and data wrangling.

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