Analysis Of Variance
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ASP allows you to estimate a wide variety of analysis of variance models:
- One-Way Analysis Of Variance models.
- Simple Random Block/Repeated Measures models.
- N Way Analysis Of Variance models with fixed, random, or mixed effects
and with or without a nested factor.
- N Way Random Block or Repeated Measures models with fixed, random, or
mixed effects and with or without a nested factor.
- N Way Analysis Of Variance/Random Block Covariance models.
Output from the ANALYSIS OF VARIANCE routines is generated in
- First, an analysis of variance table is displayed.
Then you are given the option of generated additional output from the
model being estimated:
Analysis Of Variance Table.
The analysis of variance table contains the sum of squares explained by each factor, the
error sum of squares, and the total sum of squares along with the degrees of freedom
associated with each of these sums of squares.
Next the mean square associated with each sum of squares is listed, as is
the F statistic with its associated probability value for the null hypothesis that the
factor level means are equal.
Expected mean squares are given for nested designs and for random and
mixed models. The denominator of the F statistics in the analysis of variance table is
also given for these models, as are the nested sums of squares when appropriate.
The analysis of variance Table for an n-way analysis contains sums of
squares, degrees of freedom, mean squares, F statistics, and probability values for the
interaction effects between factors as well as for the factors themselves. TOP
Once the factor means and effects output is exited you are given
options for additional output:
Estimates of the effects and means
of each factor level are also presented, and the
variance of each of these estimates is listed to its right. The number of
treatments that were available to estimate each factor level mean are
The output for an n-way analysis reports the effects, means,
variances and number for the interactions between individual factor levels as
well as for the factor levels themselves.
The output includes the difference between all possible factor or
treatment means, the standard error of each difference, the statistic for the level of
confidence you have chosen, this statistic times the standard error, and the lower and
upper limits for the confidence interval. A matrix indicating significant differences is
The output for these options includes the value of the linear combination,
the standard error of this value, the statistic for the level of confidence you have
chosen, this statistic times the standard error, and the lower and upper limits for the
Listing The Variance/Covariance Matrix. This
option allows you to list the variance/covariance matrix of the coefficients of the
underlying regression model from which the parameters of the analysis of variance model
are derived. The result is an algebraic representation of the underlying analysis of
variance regression model along with the variance/covariance matrix for the estimated
coefficients in this model.
List/Plot/Add Residuals To Data Matrix. This
option allows you to calculate the standardized, studentized, and jackknife residuals
along with the leverage and influence of each residual. These variables are plotted and
you are then given the option of adding these variables to the data matrix in the editor.
A table of the actual value of the dependent variable, its estimated value, and the
residual values is also displayed.
Breaking Down Residuals. This option
allows you to break down and plot the residuals in the model you are estimating by factor
and treatment means.
Plot Treatment Means. This option
allows you to break down and plot the treatment means in the model you are estimating by
the individual values of the factors.
ASP also allows you to setup an analysis of variance regression matrix
that can be subsequently altered and estimated by you. This
option allows you to specify and estimate a unique general linear model.
When the regression model is estimated the output includes an algebraic
representation of the regression equation in this model, and an analysis of variance table
that reports the regression, residual, and total sum of squares along with their
respective degrees of freedom, the regression and residual mean square, and the F
statistic and its probability value for the null hypothesis that the regression sum of
squares is zero.
You are also given the option of listing the variance/covariance matrix
for this model and of listing, plotting, etc. the residuals of the model.
ASP allows you to estimate the factor means of an analysis of variance
model without estimating the model itself. Only the factor and interaction means and
variances are estimated by this option and not the factor and interaction effects.