Basic Worksheet Functions
Real Statistics Functions: The following Real Statistics array functions support Two-way MANOVA. These functions are similar to those that support One-way MANOVA, as described at MANOVA Real Statistics Capabilities.
In each of the following, R1 is a cell range containing the data being analyzed (without headings except for Extract2Rows). The first column contains identifiers for one of the factors, the second column contains identifiers for the other factor and the remaining columns contain the values for the dependent variables. Note that R1 uses the same format as for one-way MANOVA except that there are now two columns for the factor identifiers instead of one.
Extract2Cov(R1, s1, s2) = covariance matrix for all the elements in R1 that match s1 and s2 in the first two columns; if s1 = “” then the pooled covariance matrix is returned.
COV2Pooled(R1) = pooled covariance matrix based on the data in R1.
Extract2Rows(R1, s1, s2, head) = an array containing all the rows in R1 that match s1 and s2 in the first two columns; if head = TRUE (default) then it is assumed that the first row in R1 contains column headings (which are included in the output)
MANOVA2_Tot(R1) = the Total (T) matrix based on the data in R1
MANOVA2_Res(R1) = the Residual (E) matrix (aka error matrix or within-subjects matrix) based on the data in R1
MANOVA2_Row(R1) = the H (hypothesis) matrix for the first factor (which we call the row factor or factor A) based on the data in R1
MANOVA2_Col(R1) = the H matrix for the second factor (which we call the column factor or factor B) based on the data in R1
MANOVA2_Int(R1) = the H matrix for the interaction between the two factors (which we call the interaction factor or factor AB) based on the data in R1
Note that range N5:O6 of Figure 4 of Two-way MANOVA Example contains the array formula =MANOVA2_Tot(A4:D27), range N9:O10 contains =MANOVA2_Row(A4:D27) and similarly for the other matrices in columns N and O. Range Q5:R6 contains the array formula =Extract2Cov(A4:D27,Q4,R4) and similarly for the next 5 matrices. Range Q29:R30 contains the array formula =COV2Pooled(A4:D27).
Wilks Test Functions
In addition, there are the following array functions that return a 6 × 1 column array containing the values: the appropriate test statistic (as described below), df1, df2, F-stat, p-value and partial eta-square effect size. If lab = TRUE (default FALSE) then an extra column of labels is appended to the output.
MANOVA2_WilksRow(R1, lab): uses Wilks test statistic on the column 1 factor
MANOVA2_WilksCol(R1, lab): uses Wilks test statistic on the column 2 factor
MANOVA2_WilksInt(R1, lab): uses Wilks test statistic on the interaction between the two factors
Pillai Test Functions
MANOVA2_PillaiRow(R1, lab): uses Pillai test statistic on the column 1 factor
MANOVA2_PillaiCol(R1, lab): uses Pillai test statistic on the column 2 factor
MANOVA2_PillaiInt(R1, lab): uses Pillai test statistic on the interaction between the two factors
Hotelling Test Functions
MANOVA2_HotelRow(R1, lab): uses Hotelling test statistic on the column 1 factor
MANOVA2_HotelCol(R1, lab): uses Hotelling test statistic on the column 2 factor
MANOVA2_HotelInt(R1, lab): uses Hotelling test statistic on the interaction between the two factors
For example, range G5:L5 in Figure 3 of Two-way MANOVA Example contains =TRANSPOSE(MANOVA2_PillaiRow(A4:D27)) and range G18:L18 contains the formula =TRANSPOSE(MANOVA2_WilksInt(A4:D27)). The other Pillai, Wilks and Hotelling values in that figure are calculated in the same way.
Roy Root Test Functions
There are the following non-array functions. If b = TRUE (default) the largest eigenvalue, lambda, for the appropriate H covariance matrix is returned; otherwise 1/(1+lambda) is returned.
MANOVA2_RoyRow(R1, b) = Roy Root for the column 1 factor
MANOVA2_RoyCol(R1, b) = Roy Root for the column 2 factor
MANOVA2_RoyInt(R1, b) = Roy Root for the interaction factor
E.g. cell G14 in Figure 3 of Two-way MANOVA Example contains the formula =MANOVA2_RoyCol(A4:D27).
Box M Test Function
The following array function returns a 5 × 1 column array containing the values: M-statistic df1, df2, F-stat and p-value. If lab = TRUE (default FALSE) then an extra column of labels is appended to the output.
MANOVA2_BOX(R1, lab): performs a Box M test for equality of the covariance matrices that correspond to the interactions between the two factors in R1.
E.g. range Z4:AA8 in Figure 5 of Two-way MANOVA Example contains the array formula =MANOVA2_BOX(A4:D27,TRUE).