Pearsons-Product-Moment-Correlation-Coefficient-Pmcc gcse Edexcel

Pearson’s PMCC

What is Pearson’s product moment correlation coefficient (PMCC)?

• Pearson’s product moment correlation coefficient (PMCC) measures the strength of the linear correlation between two data sets

  • i.e., to what extent does one always go up when the other one goes up (or always go down when the other one goes up)

  • AND to what extent a scatter diagram of the data points lie along a straight line

    • This is what it means for the correlation to be linear

    • The line in question is the linear regression line for the data points

• The notation for the Pearson’s product moment correlation coefficient of a sample is usually

• Pearson’s PMCC is always a number between -1 and 1

  • i.e.

    • This is the same as for Spearman’s rank correlation coefficient

• The value of tells you about the type and strength of any correlation

  • A positive value () means there is positive correlation between the data sets

    • An value close to 1 means strong linear positive correlation

    • If , there is perfect linear positive correlation

      • i.e., the points lie exactly along a straight line that slopes ‘up to the right’ (positive gradient)

  • If is zero (), then there is no linear correlation

  • A negative value (<img alt=”r less than 0″ data-mathml=”<math ><semantics><mrow><mi>r</mi><mo>&#60;</mo><mn>0</mn></mrow><annotation encoding=”application/vnd.wiris.mtweb-params+json”>{“fontFamily”:”Times New Roman”,”fontSize”:”18″,”autoformat”:true,”toolbar”:”<toolbar ref=’general’><tab ref=’general’><removeItem ref=’setColor’/><removeItem ref=’bold’/><removeItem ref=’italic’/><removeItem ref=’autoItalic’/><removeItem ref=’setUnicode’/><removeItem ref=’mtext’ /><removeItem ref=’rtl’/><removeItem ref=’forceLigature’/><removeItem ref=’setFontFamily’ /><removeItem ref=’setFontSize’/></tab></toolbar>”}</annotation></semantics></math>” height=”22″ role=”math” src=”data:image/svg+xml;charset=utf8,%3Csvg%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%22%20xmlns%3Awrs%3D%22http%3A%2F%2Fwww.wiris.com%2Fxml%2Fmathml-extension%22%20height%3D%2222%22%20width%3D%2233%22%20wrs%3Abaseline%3D%2216%22%3E%3C!–MathML%3A%20%3Cmath%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Er%3C%2Fmi%3E%3Cmo%3E%26lt%3B%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmath%3E–%3E%3Cdefs%3E%3Cstyle%20type%3D%22text%2Fcss%22%3E%40font-face%7Bfont-family%3A’math1072b030ba126b2f4b2374f342b’%3Bsrc%3Aurl(data%3Afont%2Ftruetype%3Bcharset%3Dutf-8%3Bbase64%2CAAEAAAAMAIAAAwBAT1MvMi7iBBMAAADMAAAATmNtYXDEvmKUAAABHAAAADRjdnQgDVUNBwAAAVA