Points of Significance: Two-factor designs

Journal name:
Nature Methods
Volume:
11,
Pages:
1187–1188
Year published:
DOI:
doi:10.1038/nmeth.3180
Published online

When multiple factors can affect a system, allowing for interaction can increase sensitivity.

At a glance

Figures

  1. When studying multiple factors, main and interaction effects can be observed, shown here for two factors (A, blue; B, red) with two levels each.
    Figure 1: When studying multiple factors, main and interaction effects can be observed, shown here for two factors (A, blue; B, red) with two levels each.

    (a) The main effect is the difference between τ values (light gray), which is the response for a given level of a factor averaged over the levels of other factors. (b) The interaction effect is the difference between effects of A at the different levels of B or vice versa (dark gray, Δ). (c) Interaction effects may mask main effects.

  2. In two-factor experiments, variance is partitioned between each factor and all combinations of interactions of the factors.
    Figure 2: In two-factor experiments, variance is partitioned between each factor and all combinations of interactions of the factors.

    (a) Two common two-factor designs with 8 measurements each. In the CR scenario, each mouse is randomly assigned a single treatment. Variability among mice can be mitigated by grouping mice by similar characteristics (e.g., litter or weight). The group becomes a block. Each block is subject to all treatments. (b) Partitioning of the total sum of squares (SST; CR, 16.9; RCB, 26.4) and P values for the CR and RCB designs in a. M represents the blocking factor. Vertical axis is relative to the SST. The total d.f. in both cases = 7; all other d.f. = 1.

References

  1. Krzywinski, M. & Altman, N. Nat. Methods 11, 699700 (2014).
  2. Krzywinski, M. & Altman, N. Nat. Methods 11, 215216 (2014).
  3. Montgomery, D.C. Design and Analysis of Experiments 8th edn. (Wiley, 2012).

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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.

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