Correlation: Dependent and independent variables

Correlation: Dependent and independent variables

Correlation: An Overview

  • Correlation is a statistical technique used to determine the relationship between two or more variables.
  • Correlation measures the degree to which two variables move in relation to each other.
  • It provides quantitative measurements of the statistical dependence between these variables.

Dependent and Independent Variables

  • In correlation analysis, the variables are classified as either dependent or independent.
  • A dependent variable is the one being tested or measured in a study. Its value depends on other variables.
  • An independent variable is the one that is manipulated or changed in a study. Its values are independent.
  • For example, in an experiment studying the effect of hours of study on exam scores, hours of study would be the independent variable and exam scores the dependent variable.

Types of Correlations

  • Positive Correlation: Both variables increase or decrease together. A value close to +1 indicates a strong positive correlation.
  • Negative Correlation: As one variable increases, the other decreases. A value close to -1 indicates a strong negative correlation.
  • Zero or No Correlation: There is no relationship between the variables. A value close to 0 indicates no correlation.

Pearson’s Correlation Coefficient

  • The most commonly used method to measure correlation is the Pearson correlation coefficient, also termed as Pearson’s r.
  • It provides a value between -1 and +1, inclusive.
  • Pearson’s correlation coefficient assumes that the relationship between the variables is linear and that both variables are normally distributed.

Limitations of Correlation

  • Correlation does not imply causation. Just because two variables are correlated, doesn’t mean that changes in one variable causes changes in the other.
  • It may not be able to detect non-linear relationships. Just because a correlation is near 0, doesn’t mean that no relationship exists.
  • Correlation doesn’t handle multiple relationships well. There might be other variables affecting the dependent variable that are not considered.

Correlation and Further Mathematics

  • Understanding correlation and the difference between dependent and independent variables is fundamental in statistics.
  • It’s important to know when to use correlation, interpret its results, and understand its limitations.
  • Mastering this concept cultivates skills in data analysis, statistical reasoning, and critical thinking.