📚 Topic Summary
In statistical modeling, many techniques rely on certain assumptions about the data, such as normality, linearity, and homoscedasticity (constant variance). Often, real-world data violates these assumptions. Data transformation involves applying mathematical functions to the data to better meet these assumptions. Common transformations include logarithmic, square root, and Box-Cox transformations. By transforming the data, we aim to improve the validity and reliability of our statistical analyses.
🧠 Part A: Vocabulary
Match the following terms with their definitions:
- Term: Normality
- Term: Homoscedasticity
- Term: Linearity
- Term: Log Transformation
- Term: Box-Cox Transformation
- Definition: A transformation used to stabilize variance and normalize data.
- Definition: A transformation that involves taking the logarithm of the data values.
- Definition: The assumption that the residuals have a normal distribution.
- Definition: The assumption that the variance of the residuals is constant across all levels of the independent variable.
- Definition: The assumption that the relationship between the independent and dependent variables can be represented by a straight line.
(Match the terms to the correct definitions.)
📝 Part B: Fill in the Blanks
Data ______________ is a process used to make data more suitable for statistical analysis. Common types include ______________ transformations, which are helpful when data is skewed. The ______________ transformation is used to stabilize variance, while ______________ helps in achieving normality. Always check your ______________ after applying any transformations.
🧪 Part C: Critical Thinking
Explain a scenario where a log transformation would be appropriate and why. What are the potential drawbacks of using data transformations?