# Yates Analysis - Output

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 interaction estimates)} " src="http://upload.wikimedia.org/math/0/c/4/0c4e66a3223edc1b5bd289f2b7e75f6c.png" />

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

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