Yates Analysis - Output


A Yates analysis generates the following output.

  • A factor identifier (from Yates order). The specific identifier will vary depending on the program used to generate the Yates analysis. Dataplot, for example, uses the following for a 3-factor model.
1 = factor 1
2 = factor 2
3 = factor 3
12 = interaction of factor 1 and factor 2
13 = interaction of factor 1 and factor 3
23 = interaction of factor 2 and factor 3
123 = interaction of factors 1, 2, and 3
  • A ranked list of important factors. That is, least squares estimated factor effects ordered from largest in magnitude (most significant) to smallest in magnitude (least significant).
  • A t-value for the individual factor effect estimates. The t-value is computed as

t = frac{e}{s_e}

where e is the estimated factor effect and se is the standard deviation of the estimated factor effect.

  • The residual standard deviation that results from the model with the single term only. That is, the residual standard deviation from the model

textrm{response} = textrm{constant} + 0.5 X_i

where Xi is the estimate of the ith factor or interaction effect.

  • The cumulative residual standard deviation that results from the model using the current term plus all terms preceding that term. That is,

textrm{response} = textrm{constant} + 0.5 mathrm{(all effect estimates down to and including the effect of interest)}

This consists of a monotonically decreasing set of residual standard deviations (indicating a better fit as the number of terms in the model increases). The first cumulative residual standard deviation is for the model

textrm{response} = textrm{constant}

where the constant is the overall mean of the response variable. The last cumulative residual standard deviation is for the model

textrm{response} = textrm{constant} + 0.5 mathrm{(all factor and <a href=interaction estimates)} " src="http://upload.wikimedia.org/math/0/c/4/0c4e66a3223edc1b5bd289f2b7e75f6c.png" />

This last model will have a residual standard deviation of zero.

Read more about this topic:  Yates Analysis

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