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| {{lowercase|title=d'}}
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| The '''sensitivity index''' or '''''d'''''' (pronounced 'dee-prime') is a [[statistic]] used in [[signal detection theory]]. It provides the separation between the means of the signal and the noise distributions, compared against the standard deviation of the noise distribution. For [[Normal distribution|normally distributed]] signal and noise with mean and standard deviations <math>\mu_S</math> and <math>\sigma_S</math>, and <math>\mu_N</math> and <math>\sigma_N</math>, respectively, d' is defined as:
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| : <math>d' = \frac{\mu_S - \mu_N}{\sqrt{\frac{1}{2}(\sigma_S^2 + \sigma_N^2)}}</math><ref>Samuel Gale and David Perkel. A Basal Ganglia Pathway Drives Selective Auditory Responses in Songbird Dopaminergic Neurons via Disinhibition. The Journal of Neuroscience (2010). 30(3):1027–1037</ref>
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| An estimate of d' can be also found from measurements of the hit rate and [[False alarm|false-alarm]] rate. It is calculated as:
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| ::''d''' = ''Z''(hit rate) - ''Z''(false alarm rate),<ref>MacMillan N, Creelman C (2005) Detection Theory: A User’s Guide. Lawrence Erlbaum Associates. (p.7) Retrieved from: http://books.google.co.uk/books/about/Detection_Theory.html?id=hDX65v9bReYC</ref>
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| where function ''Z''(''p''), ''p'' ∈ [0,1], is the inverse of the [[Normal distribution#Cumulative distribution function|cumulative Gaussian distribution]].
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| ''d' '' is a [[dimensionless]] statistic. A higher ''d''' indicates that the signal can be more readily detected.
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| ==See also==
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| * [[Receiver Operating Characteristic]] (R.O.C.)
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| * [[Summary Statistics]]
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| ==References==
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| {{reflist}}
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| * Wickens, Thomas D. (2001) ''Elementary Signal Detection Theory'', OUP USA. ISBN 0-19-509250-3 (Ch.2, p.20). [http://books.google.com/books?vid=ISBN0195092503&id=s3pGN_se4v0C&pg=PA22&lpg=PA22&dq=Thomas+D.+Wickens Excerpts]
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| ==External links==
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| <!-- Please see [[Wikipedia:External links]] for guidelines on appropriate external links. -->
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| *[http://wise.cgu.edu/sdtmod/index.asp Interactive signal detection theory tutorial] including calculation of d'.
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| [[Category:Detection theory]]
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| [[Category:Signal processing]]
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| [[Category:Summary statistics]]
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| {{Signal-processing-stub}}
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| {{stat-stub}}
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