Linear correlation

From Wikiversity

Linear correlations involve straight-line relationships between two variables. The correlation between variables 1 and 2 is denoted by r₁₂.

Subject classification: this is a mathematics resource .

Completion status: this resource is ~50% complete.

This figure illustrates a variety of different types of bivariate relations, including a range of positive and negative linear relations.

[edit] Introduction

The degree of linear relationship between two variables can be represented in terms of a Venn Diagram. Perflectly overlapping circles would indicate a correlation of 1, and non-overlapping circles would represent a correlation of 0.

When we ask questions such as "Is X related to Y?", "Does X predict Y?", and "Does X account for Y"?, we are interested in measuring and better understanding the relationship between two variables.

To answer such questions quantitatively, a variety of bivariate correlational statistics (including chi-square, phi/Cramer's V, Spearman's rho/Kendall's tau-b, and the product-moment correlation) can be appropriate, depending on the level of measurement. In addition, all correlational analyses should be accompanied by appropriate graphs, such as clustered bar charts, scatterplots, and error-bar charts.

However, one of the most commonly calculated indices of bivariate relationship is the Pearson or product-moment correlation which indicates the degree of linear (straight-line) relationship or correspondence between two variables.

[edit] Test yourself

This is a pre-quiz to see what you already know.

• Introductory quiz

[edit] Lesson

Currently, the best way to study this topic is to read through several of the external links, until you have a reasonable understanding of what correlation is, what its used for, and how it is interpreted.

Then try the correlational guess exercises.

Finally, using a statistics package of your choice, you should complete the correlational data analysis exercises.

[edit] Activity

Check out Correlation Explore and then, when you're ready, try Correlation Guess

• Correlation Explore
• Correlation Guess

Rate yourself:

• < 10 / 50 (more study needed)
• 10 - 15 / 50 (you're getting there)
• 15 - 20 / 50 (solid effort)
• 20 - 25 / 50 (very well done)
• 25 / 50 (excellent)

[edit] Data analysis exercises

• Data analysis tutorial
• For more information, see data analysis exercises.

[edit] See also

[edit] Wikipedia

• Correlation
• Kendall's tau rank correlation coefficient
• Pearson product-moment correlation coefficient
• Spearman's rank correlation coefficient

[edit] External links

• Correlation (Annis, 2008)
• Correlation (Garson, 2008)
• Correlation (Plonsky, 2006)
• Correlation (Trochim, 2006)
• Correlation coefficient (Hopkins, 2000)
• Lecture - Linear correlation (Neill, 2008)
• Rank order correlation (Lowry, 2008)
• Tutorial - Linear correlation (Neill, 2008)
• Understanding correlation (Rummel, 1976)