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Understanding Normal Distribution and Rank Correlation Coefficients in Statistics

This guide explores key concepts in statistics, focusing on normal distribution and rank correlation. It discusses how the normal distribution serves as a model for natural phenomena measurements and introduces rank correlation methods, including Spearman's rank correlation coefficient. The document also compares Spearman's method with the product-moment correlation coefficient, providing essential formulas and resources for further understanding. Key resources are included for practical exploration of these concepts, enhancing clarity on correlation measures.

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Understanding Normal Distribution and Rank Correlation Coefficients in Statistics

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Presentation Transcript

  1. Uncertainties 5 16.6.11

  2. Outline • Normal distribution • Rank correlation

  3. ways to think about the normal distribution • A continuous version of the binomial distribution • when N (the number of trials) is big • http://onlinestatbook.com/stat_sim/normal_approx/index.html • A model for distribution of measurements of naturally occurring phenomena • Amazing that these coincide!!

  4. Parameters of the Normal distribution • Mean • Variance = (standard deviation)squared • Try out at: • http://www.stattucino.com/berrie/dsl/index.html

  5. Luskentyre shells

  6. Ranks’ data

  7. Spearman’s rank correlation coefficient Correlation measured by ‘least squares’ line of best fit has gradient called the product-moment correlation coefficient. Spearman’s rank correlation coefficient is another measure of correlation which can be used when ranks rather than measures are given. Here is the formula: Where (d-sub-i)-squared is the difference between the two rankings squared and ‘n’ is the number of items.

  8. MEI article on correlation • Please read (at least) the first four pages of this article: • http://www.mei.org.uk/files/pdf/Spearmanrcc.pdf • After you’ve read the pages you should be clearer about the differences between the two coefficients of rank with which you are familiar.

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