The following calculations are needed when
finding Pearson's product moment correlation coefficient or pmcc:
S_{xx} = \displaystyle \sum x^2 - \frac{(\sum x)^2}{n}
S_{yy} = \displaystyle \sum y^2 - \frac{(\sum y)^2}{n}
S_{xy} = \displaystyle \sum xy - \frac{(\sum x)(\sum y)}{n}
S_{xx} = \displaystyle \sum x^2 - \frac{(\sum x)^2}{n}
S_{yy} = \displaystyle \sum y^2 - \frac{(\sum y)^2}{n}
S_{xy} = \displaystyle \sum xy - \frac{(\sum x)(\sum y)}{n}
Summary/Background
The pmcc can be found using:
r = \displaystyle \frac{S_{xy} }{\sqrt{S_{xx} S_{yy} } }
r = \displaystyle \frac{S_{xy} }{\sqrt{S_{xx} S_{yy} } }
Karl Pearson FRS (27 March 1857 – 27 April 1936) established the discipline of mathematical statistics. A sesquicentenary conference was held in London on 23 March 2007, to celebrate the 150th anniversary of his birth.
In 1911 he founded the world's first university statistics department at University College London. He was a proponent of eugenics, and a protege and biographer of Sir Francis Galton. He was also a socialist. Pearson was instrumental in the development of regression and correlation theory. One of his classic data sets (originally collected by Galton) involves the regression of sons' height upon that of their fathers'. Pearson built a 3-dimensional model of this data set (which remains in the care of the Statistical Science Department) to illustrate the ideas. The Pearson product-moment correlation coefficient is named after him, and it was the first important "effect size" to be introduced into statistics.
In 1911 he founded the world's first university statistics department at University College London. He was a proponent of eugenics, and a protege and biographer of Sir Francis Galton. He was also a socialist. Pearson was instrumental in the development of regression and correlation theory. One of his classic data sets (originally collected by Galton) involves the regression of sons' height upon that of their fathers'. Pearson built a 3-dimensional model of this data set (which remains in the care of the Statistical Science Department) to illustrate the ideas. The Pearson product-moment correlation coefficient is named after him, and it was the first important "effect size" to be introduced into statistics.
Software/Applets used on this page
This question appears in the following syllabi:
Syllabus | Module | Section | Topic | Exam Year |
---|---|---|---|---|
AQA A-Level (UK - Pre-2017) | S1 | Correlation and Regression | Correlation | - |
AQA A2 Maths 2017 | Statistics | Correlation and Regression | Product Moment Correlation Coefficient | - |
AQA AS Further Maths 2017 | Statistics | Extra | Product Moment Correlation Coefficient | - |
AQA AS/A2 Further Maths 2017 | Statistics | Extra | Product Moment Correlation Coefficient | - |
AQA AS/A2 Maths 2017 | Statistics | Correlation and Regression | Product Moment Correlation Coefficient | - |
CCEA A-Level (NI) | S2 | Correlation and Regression | Correlation | - |
Edexcel A-Level (UK - Pre-2017) | S1 | Correlation and Regression | Correlation | - |
Edexcel A2 Maths 2017 | Statistics | Regression and Correlation | Product Moment Correlation Coefficient | - |
Edexcel AS Further Maths 2017 | Further Statistics 2 | Correlation | Product Moment Correlation Coefficient | - |
Edexcel AS/A2 Further Maths 2017 | Further Statistics 2 | Correlation | Product Moment Correlation Coefficient | - |
Edexcel AS/A2 Maths 2017 | Statistics | Regression and Correlation | Product Moment Correlation Coefficient | - |
I.B. Higher Level | 7 | Correlation and Regression | Correlation | - |
OCR A-Level (UK - Pre-2017) | S1 | Correlation and Regression | Correlation | - |
OCR A2 Maths 2017 | Statistics | Using and Testing Correlation Coefficient | Product Moment Correlation Coefficient | - |
OCR AS Further Maths 2017 | Statistics | Correlation | Product Moment Correlation Coefficient | - |
OCR MEI A2 Maths 2017 | Statistics | Using and Testing Correlation Coefficient | Product Moment Correlation Coefficient | - |
OCR MEI AS Further Maths 2017 | Statistics A | Correlation | Product Moment Correlation Coefficient | - |
OCR-MEI A-Level (UK - Pre-2017) | S2 | Correlation and Regression | Correlation | - |
Pre-U A-Level (UK) | Prob | Correlation and Regression | Correlation | - |
Scottish (Highers + Advanced) | HS | Correlation and Regression | Correlation | - |
Scottish Highers | S | Correlation and Regression | Correlation | - |
Universal (all site questions) | C | Correlation and Regression | Correlation | - |