Data

Data Transformation (Variable Transformation)

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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.

Data Transformation

The purpose of data transformation is:

  • 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
Data Transformation (Variable Transformation)

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.

Benefits of Data Transformation

The Benefits of data transformation and data cleaning are:

  • Improved data quality: Fewer 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.
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Data transformation is a crucial step in the data pipeline, especially in tasks like data warehousing, data integration, and data wrangling.

FAQS about Data Transformation

  • What is data transformation?
  • When data transformation is done?
  • What is the most common data transformation?
  • What is the reciprocal Data Transformation?
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  • What is a logarithmic transformation?
  • When logarithmic transformation is not applied to the data?
  • What is the square root transformation?
  • When square root transformation cannot be applied?
  • What is the main purpose of data transformation?
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  • What is the data normalization?
  • What is the data aggregation?
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Introduction to R Language

Primary and Secondary Data (2014)

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Data

Before learning about primary and Secondary Data, let us first understand the term Data in Statistics.

The facts and figures which can be numerically measured are studied in statistics. Numerical measures of the same characteristics are known as observation and collection of observations is termed as data. Data are collected by individual research workers or by organizations through sample surveys or experiments, keeping in view the objectives of the study. The data collected may be (i) Primary Data and (ii) Secondary Data.

Primary and Secondary Data in Statistics

The difference between primary and secondary data in Statistics is that Primary data is collected firsthand by a researcher (organization, person, authority, agency or party, etc.) through experiments, surveys, questionnaires, focus groups, conducting interviews, and taking (required) measurements, while the secondary data is readily available (collected by someone else) and is available to the public through publications, journals, and newspapers.

Primary and Secondary Data

Primary Data

Primary data means the raw data (data without fabrication or not tailored data) that has just been collected from the source and has not gone through any kind of statistical treatment like sorting and tabulation. The term primary data may sometimes be used to refer to first-hand information.

Sources of Primary Data

The sources of primary data are primary units such as basic experimental units, individuals, and households. The following methods are used to collect data from primary units usually and these methods depend on the nature of the primary unit. Published data and the data collected in the past are called secondary data.

  • Personal Investigation
    The researcher experiments or surveys himself/herself and collects data from it. The collected data is generally accurate and reliable. This method of collecting primary data is feasible only in the case of small-scale laboratories, field experiments, or pilot surveys and is not practicable for large-scale experiments and surveys because it takes too much time.
  • Through Investigators
    The trained (experienced) investigators are employed to collect the required data. In the case of surveys, they contact the individuals and fill in the questionnaires after asking for the required information, whereas a questionnaire is an inquiry form having many questions designed to obtain information from the respondents. This method of collecting data is usually employed by most organizations and it gives reasonably accurate information but it is very costly and may be time-consuming too.
  • Through Questionnaire
    The required information (data) is obtained by sending a questionnaire (printed or soft form) to the selected individuals (respondents) (by mail) who fill in the questionnaire and return it to the investigator. This method is relatively cheap as compared to the “through investigator” method but the non-response rate is very high as most of the respondents don’t bother to fill in the questionnaire and send it back to the investigator.
  • Through Local Sources
    The local representatives or agents are asked to send requisite information and provide the information based on their own experience. This method is quick but it gives rough estimates only.
  • Through Telephone
    The information may be obtained by contacting the individuals by telephone. It is Quick and provides the accurate required information.
  • Through Internet
    With the introduction of information technology, people may be contacted through the Internet and individuals may be asked to provide pertinent information. Google Survey is widely used as an online method for data collection nowadays. There are many paid online survey services too.

It is important to go through the primary data and locate any inconsistent observations before it is given a statistical treatment.

Secondary Data

Data that has already been collected by someone, may be sorted, tabulated, and has undergone a statistical treatment. It is fabricated or tailored data.

Sources of Secondary Data

The secondary data may be available from the following sources:

  • Government Organizations
    Federal and Provincial Bureau of Statistics, Crop Reporting Service-Agriculture Department, Census and Registration Organization etc.
  • Semi-Government Organization
    Municipal committees, District Councils, Commercial and Financial Institutions like banks etc
  • Teaching and Research Organizations
  • Research Journals and Newspapers
  • Internet

Data Structure in R Language