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Analyzing Statistical Significance

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Computational Cancer Biology

Part of the book series: SpringerBriefs in Electrical and Computer Engineering ((BRIEFSCONTROL))

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Abstract

In this chapter we review some popular methods for estimating the statistical significance of various conclusions that can be drawn from experimental data. These include the \(\chi ^2\)-text, the Kolmogorov–Smirnov (K–S) test for goodness of fit, the ‘student’ \(t\)-test for testing the null hypothesis that two sets of data have the same mean, Significance Analysis for Microarrays (SAM), Pattern Analysis for Microarrays (PAM) and Gene Set Enhancement Analysis (GSEA).

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Notes

  1. 1.

    Note that the Glivenko-Cantelli lemma does not require \(\varPhi _X(\cdot )\) to be continuous.

  2. 2.

    Strictly speaking, we should first define a \(\sigma \)-algebra \(\mathcal{S}\) of subsets of \(X\) and assume that \(\mathcal{A}\subseteq \mathcal{S}\). Such details are glossed over here but the treatment in [9] is quite precise.

  3. 3.

    We mostly follow the notation in [11], in which the letter S in various fonts is used to denote various quantities. The reader is therefore urged to pay careful attention.

References

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Authors and Affiliations

  1. Bioengineering Department, The University of Texas at Dallas, 800 W. Campbell Road, Richardson, TX, 75080-3021, USA

    Mathukumalli Vidyasagar

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  1. Mathukumalli Vidyasagar
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Correspondence to Mathukumalli Vidyasagar .

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Vidyasagar, M. (2012). Analyzing Statistical Significance. In: Computational Cancer Biology. SpringerBriefs in Electrical and Computer Engineering(). Springer, London. https://doi.org/10.1007/978-1-4471-4751-0_2

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  • DOI: https://doi.org/10.1007/978-1-4471-4751-0_2

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  • Publisher Name: Springer, London

  • Print ISBN: 978-1-4471-4750-3

  • Online ISBN: 978-1-4471-4751-0

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