NMath Reference Guide

## Two |

Class TwoWayAnovaUnbalanced is the base class for performing a
two way ANOVA when the number of observations in each cell is not the
same (an unbalanced design). In this case the main and interaction effects are
interdependent, and we must obtain the marginal sum of squares associated with
each factor after all the other factors have already been included in the model
(the marginal sum of squares for each variable equals the incremental sum
of squares for that variable when it is entered into the equation last).
In terms of a regression approach to ANOVA, the marginal sum of squares due
to a factor is the sum of squares for the set of dummy variables associated
with that factor when those dummy variables are entered into the model last,
after all other dummy variables.
Classes deriving from TwoWayAnovaUnbalanced provide the ordering of
dummy regression variables and use the base class to compute the resulting
regressions and sums of squares.

Inheritance Hierarchy

SystemObject

CenterSpace.NMath.CoreTwoWayAnovaBase

CenterSpace.NMath.CoreTwoWayAnovaUnbalanced

CenterSpace.NMath.CoreTwoWayAnovaTypeI

CenterSpace.NMath.CoreTwoWayAnovaTypeII

CenterSpace.NMath.CoreTwoWayAnovaTypeIII

CenterSpace.NMath.CoreTwoWayAnovaBase

CenterSpace.NMath.CoreTwoWayAnovaUnbalanced

CenterSpace.NMath.CoreTwoWayAnovaTypeI

CenterSpace.NMath.CoreTwoWayAnovaTypeII

CenterSpace.NMath.CoreTwoWayAnovaTypeIII

Syntax

The TwoWayAnovaUnbalanced type exposes the following members.

Constructors

Name | Description | |
---|---|---|

TwoWayAnovaUnbalanced | Constructs a TwoWayAnovaUnbalanced. |

Properties

Name | Description | |
---|---|---|

AnovaTable | Gets the ANOVA table. | |

FactorARegressionFactorParameters | Gets the ANOVAs for the factor A regression parameters. | |

FactorBRegressionFactorParameters | Gets the ANOVAs for the factor B regression parameters. | |

GrandMean |
Gets the grand mean.
(Overrides TwoWayAnovaBaseGrandMean) | |

InteractionRegressionFactorParameters | Gets the ANOVAs for the interaction regression parameters. | |

RegressionInterceptParameter |
Bets the ANOVA regression parameter object associated with the
intercept parameter.
(Overrides TwoWayAnovaBaseRegressionInterceptParameter) |

Methods

Name | Description | |
---|---|---|

ComputeBalancedAnova | Computes the ANOVA in the case that the design is acutally balanced. This can greatly increase performance if an unbalanced ANOVA class is used to perform an ANOVA on a data set that is in fact balanced (same number of observations in each cell). | |

ComputeFactorSumsOfSquares(DoubleMatrix) |
Fill in the DoubleVector parameterSumsOfSquares_ with the sums of
squares for the parameters used in the regression that is used to
compute the ANOVA.
(Inherited from TwoWayAnovaBase) | |

ComputeFactorSumsOfSquares(DoubleMatrix, TwoWayAnovaUnbalancedParameterOrder, TwoWayAnovaUnbalancedParameterSlices) | Compute the factor sums of squares. | |

ComputeFactorSumsOfSquares(LinearRegression, Int32, Int32, Int32) |
Fill in the DoubleVector parameterSumsOfSquares_ with the sums of
squares for the parameters used in the regression that is used to
compute the ANOVA.
(Inherited from TwoWayAnovaBase) | |

GetCellData |
Returns all the data in a cell, as defined by the levels of the two factors
in the ANOVA.
(Inherited from TwoWayAnovaBase) | |

GetFactorSumOfSquares | For a given parameter order, retrives the sum of squares for the regression parameters associated with the last factor, or interaction, in the order. | |

GetMeanForCell |
Returns the mean for the specified cell, as defined by the levels of
the two factors in the ANOVA.
(Inherited from TwoWayAnovaBase) | |

GetMeanForFactorLevel |
Returns the mean for the specified factor level.
(Inherited from TwoWayAnovaBase) | |

GetOrderedRegression | Create the ordered linear regession object for the data and given coefficient ordering. | |

GetParameterSlices | For a give ANOVA regression factor/interaction parameter order, computes the slices to access the columns of the regression matrix for the factor and interaction parameters. | |

IncrementalSumOfSquares(LinearRegression, Int32, DoubleVector, Double) | ||

IncrementalSumOfSquares(DoubleMatrix, Int32, DoubleVector, Double, Factor, AnovaRegressionFactorParam) | Computes the incremental sum of squares when adding numParameters to the regression model. The columns corresponding these parameters are assumed to be the last numParameter columns in the given regression matrix. | |

InitializeFactorsAndCellData | Consumes the ANOVA data from a DataFrame. | |

InterceptParameterSumOfSquares |
Compte the sum of squares associated with the regression's intercept parameter.
(Inherited from TwoWayAnovaBase) | |

MakeCellData |
Fills in the cell data for a two way ANOVA from the given data frame and
column information.
(Inherited from TwoWayAnovaBase) | |

MakeFactorParameters(LinearRegression, DoubleVector, Int32, Factor) |
Create the array of AnovaRegressionFactorParam objects, one for each
regression dummy variable. The sums of squares for each of these
parameters is assumed to have been computed are are stored in the
DoubleVector instance variable parameterSumsOfSquares with
the parameters for factor A first, followed by the parameters for
factor B and starting at the given index.
(Inherited from TwoWayAnovaBase) | |

MakeFactorParameters(Factor, DoubleVector, LinearRegression, Int32, Int32) | Create the array of AnovaRegressionFactorParam objects, one for each regression dummy variable. The sums of squares for each of these parameters is assumed to have been computed are are stored in the DoubleVector instance variable parameterSumsOfSquares with the parameters for factor A first, followed by the parameters for factor B and starting at the given index. | |

MakeInteractionParameters |
Creates the array of AnovaRegressionInteractionParam objects using the
DoubleVector instance variable parameterSumsOfSquares_. The sums of
squares for the interaction parameters are assumed to begin at the
given index.
(Inherited from TwoWayAnovaBase) | |

ReorderRegressionMatrix | For a give parameter order reorders the columns of the input regression matrix so that the the columns corresponding to the parameters are in the order specified by the parameter order. |

Fields

Name | Description | |
---|---|---|

anovaTable_ | The ANOVA table. | |

cells_ |
The ANOVA data broken up into cells.
(Inherited from TwoWayAnovaBase) | |

factorA_ |
One of the factors in the ANOVA
(Inherited from TwoWayAnovaBase) | |

factorAparams_ | Anovas for the factor A regression parameters. | |

factorB_ |
The other factor in the ANOVA.
(Inherited from TwoWayAnovaBase) | |

factorBparams_ | Anovas for the factor B regression parameters. | |

grandMean_ | The mean of all the data. | |

interactionParams_ | Anovas for the interaction regression parameters. | |

interceptParameter_ | Intercept parameter values for the ANOVA regression. | |

numFactorAparams_ | Number of regression parameters for factor A. | |

numFactorBparams_ | Number of regression parameters for factor B. | |

numInteractionParams_ | Number of interaction regression parameters. | |

observations_ |
The observation vector for the regression used to compute the ANVOA.
(Inherited from TwoWayAnovaBase) |

Remarks

We will use the notion described by Scholer.
http://goanna.cs.rmit.edu.au/~fscholer/anova.php"
What follows is an excerpt.
Consider a model that includes two factors A and B; there are therefore
two main effects, and an interaction, AB. The full model is represented
by SS(A, B, AB).
Other models are represented similarly: SS(A, B) indicates the model
with no interaction, SS(B, AB) indicates the model that does not account
for effects from factor A, and so on.
It is convenient to define incremental sums of squares to represent these differences. Let
SS(AB | A, B) = SS(A, B, AB) - SS(A, B)
SS(A | B, AB) = SS(A, B, AB) - SS(B, AB)
SS(B | A, AB) = SS(A, B, AB) - SS(A, AB)
SS(A | B) = SS(A, B) - SS(B)
SS(B | A) = SS(A, B) - SS(A)
The notation shows the incremental differences in sums of squares,
for example SS(AB | A, B) represents "the sum of squares for
interaction after the main effects", and SS(A | B) is "the sum of
squares for the A main effect after the B main effect and ignoring
interactions"

See Also