Spearmans-Rank-Correlation-Coefficient gcse Edexcel

Spearman’s Rank Basics

What is Spearman’s rank correlation coefficient?

• Spearman’s rank correlation coefficient measures the strength of the 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)

  • It is not always easy to see this clearly on a scatter diagram

• The notation for the Spearman’s rank correlation coefficient of a sample is

• Spearman’s rank correlation coefficient is always a number between -1 and 1

  • i.e.

• 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 positive correlation

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

  • A negative value (<img alt=”straight r subscript straight S less than 0″ data-mathml=”<math ><semantics><mrow><msub><mi mathvariant=”normal”>r</mi><mi mathvariant=”normal”>S</mi></msub><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=”28″ 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%2228%22%20width%3D%2239%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%3Cmsub%3E%3Cmi%20mathvariant%3D%22normal%22%3Er%3C%2Fmi%3E%3Cmi%20mathvariant%3D%22normal%22%3ES%3C%2Fmi%3E%3C%2Fmsub%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%2CAAEAAAAMAIAAAwBAT1MvMi7iBBMAAADMAAAATmNtYXDEvmKUAAABHAAAADRjdnQgDVUNBwAAAVAAAAA6Z2x5ZoPi2VsAAAGMAAAAzGhlYWQQC2qxAAACWAAAADZoaGVhCGsXSAAAApAAAAAkaG10eE2rRkcAAAK0AAAACGxvY2EAHTwYAAACvAAAAAxtYXhwBT0FPgAAAsgAAAAgbmFtZaBxlY4AAALoAAABn3Bvc3QB9wD6AAAEiAAAACBwcmVwa1uragAABKgAAAAUAAADSwGQAAUAAAQABAAAAAAABAAEAAAAAAAAAQEAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAACAgICAAAAAg1UADev96AAAD6ACWAAAAAAACAAEAAQAAABQAAwABAAAAFAAEACAAAAAEAAQAAQAAADz%2F%2FwAAADz%2F%2F%2F%2FFAAEAAAAAAAABVAMsAIABAABWACoCWAIeAQ4BLAIsAFoBgAKAAKAA1ACAAAAAAAAAACsAVQCAAKsA1QEAASsABwAAAAIAVQAAAwADqwADAAcAADMRIRElIREhVQKr%2FasCAP4AA6v8VVUDAAACAIAAVQKAAqsABQALAGwYsEEaALEAABMQsQAG5LEAARMQsAk8sQEF9bAKPLAAELEFA%2FWxAgXtsQQD9bEDBe2wChCxCwP1sQgF7bEGA%2FWxBwXtAbAMELEBA%2FayCQAKPDw8sQUE9bICCAs8PDyxBAT1sgYHAzw8PLENA%2BYTBwUXNScBNQ0BFzeBAQEA%2F%2F8BAP8A%2FwAB%2FwGrVoCAVoABKlaAgFaAAAEAAAABAADVeM5BXw889QADBAD%2F%2F%2F%2F%2F1joTc%2F%2F%2F%2F%2F%2FWOhNzAAD%2FIASAA6sAAAAKAAIAAQAAAAAAAQAAA%2Bj%2FagAAF3AAAP%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%2F)format(‘truetype’)%3Bfont-weight%3Anormal%3Bfont-style%3An