Points of Significance: Nested designs

Journal name:
Nature Methods
Volume:
11,
Pages:
977–978
Year published:
DOI:
doi:10.1038/nmeth.3137
Published online

For studies with hierarchical noise sources, use a nested analysis of variance approach.

At a glance

Figures

  1. Inferences about fixed factors are different than those about random factors, as shown by box-plots of n = 10 samples across three independent experiments.
    Figure 1: Inferences about fixed factors are different than those about random factors, as shown by box-plots of n = 10 samples across three independent experiments.

    Circles indicate sample medians. Box-plot height reflects simulated measurement error (σε2 = 0.5). (a) Fixed factor levels are identical across experiments and have a systematic effect on the mean. (b) Random factor levels are samples from a population, have a random effect on the mean and contribute noise to the system (σB2= 1).

  2. Factors may be crossed or nested.
    Figure 2: Factors may be crossed or nested.

    (a) A crossed design examines every combination of levels for each fixed factor. (b) Nested design can progressively subreplicate a fixed factor with nested levels of a random factor that are unique to the level within which they are nested. (c) If a random factor can be reused for different levels of the treatment, it can be crossed with the treatment and modeled as a block. (d) A split plot design in which the fixed effects (tissue, drug) are crossed (each combination of tissue and drug are tested) but themselves nested within replicates.

  3. Data and analysis for a simulated three-factor nested experiment.
    Figure 3: Data and analysis for a simulated three-factor nested experiment.

    (a) Simulated expression levels, Xijkl, measured for a = 2 levels of factor A (control and treatment, i), b = 5 of factor B (mice, j), c = 5 of factor C (cells, k) and n = 3 technical replicates (l). Averages across factor levels are shown as horizontal lines and denoted by dots in subscript for the factor's index. Blue arrows illustrate deviations used for calculation of sum of squares (SS). Data are simulated with μc = 10 for control and μt = 11 for treatment and σB2 = 1, σC2 = 2, σε2 = 0.5 for noise at mouse, cell and technical replicate levels, respectively. Values below the figure show factor levels and averages at levels of A (Xi...) and B (Xij..). Labels for the levels of B and C are reused but represent distinct individual mice and cells. (b) Histogram of deviations (d) for each factor. Three deviations illustrated in a are identified by the same blue arrows. Nested ANOVA calculations show number of times (k) each deviation (d) contributes to SS, degrees of freedom (d.f.), mean squares (MS), F-ratio, P value and the estimated variance contribution of each factor.

References

  1. Blainey, P., Krzywinski, M. & Altman, N. Nat. Methods 11, 879880 (2014).
  2. Krzywinski, M. & Altman, N. Nat. Methods 11, 699700 (2014).
  3. Krzywinski, M. & Altman, N. Nat. Methods 11, 597598 (2014).

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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.

  3. Paul Blainey is an Assistant Professor of Biological Engineering at MIT and Core Member of the Broad Institute.

Competing financial interests

The authors declare no competing financial interests.

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Supplementary information

PDF files

  1. Supplementary tables (59 KB)

    Supplementary Tables 1–3

Additional data