Points of significance: Importance of being uncertain

Journal name:
Nature Methods
Volume:
10,
Pages:
809–810
Year published:
DOI:
doi:10.1038/nmeth.2613
Published online

Statistics does not tell us whether we are right. It tells us the chances of being wrong.

At a glance

Figures

  1. The mean and s.d. are commonly used to characterize the location and spread of a distribution.
    Figure 1: The mean and s.d. are commonly used to characterize the location and spread of a distribution.

    When referring to a population, these measures are denoted by the symbols μ and σ.

  2. Population parameters are estimated by sampling.
    Figure 2: Population parameters are estimated by sampling.

    (a) Frequency histogram of the values in a population. (b) Three representative samples taken from the population in a, with their sample means. (c) Frequency histogram of means of all possible samples of size n = 5 taken from the population in a.

  3. The distribution of sample means from most distributions will be approximately normally distributed.
    Figure 3: The distribution of sample means from most distributions will be approximately normally distributed.

    Shown are sampling distributions of sample means for 10,000 samples for indicated sample sizes drawn from four different distributions. Mean and s.d. are indicated as in Figure 1.

  4. The mean (X̅), s. d. (s) and s.e.m. of three samples of increasing size drawn from the distribution in Figure 2a.
    Figure 4: The mean (X̅), s. d. (s) and s.e.m. of three samples of increasing size drawn from the distribution in Figure 2a.

    As n is increased, X̅ and s more closely approximate μ and σ. The s.e.m. (s/√n) is an estimate of s and measures how well the sample mean approximates the population mean.

References

  1. Huxley, T.H. in Collected Essays 8, 229 (Macmillan, 1894).
  2. vos Savant, M. Game show problem. http://marilynvossavant.com/game-show-problem (accessed 29 July 2013).
  3. Glantz, S.A. Circulation 61, 17 (1980).
  4. Huck, S.W. Statistical Misconceptions (Routledge, 2009).
  5. Ableson, R.P. Statistics as Principled Argument 27 (Psychology Press, 1995).

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Author information

Affiliations

  1. Martin Krzywinski is a staff scientist at Canada's Michael Smith Genome Sciences Centre.

  2. Naomi Altman is a Professor of Statistics at The Pennsylvania State University.

Competing financial interests

The authors declare no competing financial interests.

Author details

Supplementary information

Other

  1. Supplementary Table 1 (259 KB)

    Examples and sample calculations spreadsheet. Please note that the workbook requires that macros be enabled.

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