
	Where results make sense

Topic: MANOVA

	SPSS Library: Advanced issues in using and understanding SPSS MANOVA
		MANOVA internally converts this to an average, so that the mean of the means is estimated as opposed to the sum of the means.
		MANOVA Y BY A(1,2) B(1,3) /DESIGN=A, One important point to note is that since the A and B simple main effects each involve a repartitioning of the interaction term, attempting to fit both sets of simple main effects on one DESIGN subcommand would introduce redundant effects and should thus be avoided.
		MANOVA V1 TO V6 Note that the final two rows of the contrast matrix are simply coefficient by coefficient multiples of rows two and three and two and four, respectively.
	www.ats.ucla.edu /stat/spss/library/manova.htm (6748 words)

	PA 765: MANOVA
		MANOVA is not robust when the selection of one observation depends on selection of one or more earlier ones, as in the case of before-after and other repeated measures designs.
		Put another way, MANOVA will test groups (ex., a treatment and a control group) to differ if they differ in correlation among the dependents even though their means are the same on the dependents, whereas ANOVA will fail to reject the null hypotheses of no group differences.
		Step-down MANOVA, also called the Roy-Bargman Stepdown F test, is a conservative approach to significance testing of the main effects, designed to prevent the inflation of Type I errors (thinking you have something when you do not).
	www2.chass.ncsu.edu /garson/pa765/manova.htm (3806 words)

	Multivariate Statistics - MANOVA Overview
		MANOVA, as with its univariate counterparts typically involve random assignment of participants to levels of one or more nominal independent variables; however, all participants are measured on several continuous dependent variables.
		In other words, MANOVA is a test of the significance of group differences in some m-dimensional space where each dimension is defined by linear combinations of the original set of dependent variables.
		A MANOVA is then performed in order to look for effects, and a significant linear combination of variables would indicate a significant difference between the original levels.
	www.uwsp.edu /psych/cw/statmanual/manovauses.html (983 words)

	EPA Statistical Primer - Manova (Site not responding. Last check: 2007-10-24)
		Manova tests whether the categorical variable explains a significant amount of variability in the new dependent variable.
		For the Manova model, the relative abundances of the different fish species were the dependent variables; and they used cluster assignment as the independent variable.
		Manova can require rather large sample sizes for complicated models because the number of cases in each category must be larger than the number of dependent variables.
	www.epa.gov /bioindicators/primer/manova.html (541 words)

	MANOVA (Site not responding. Last check: 2007-10-24)
		MANOVA means multiple ANOVA - multiple dependent variables to be analyzed simultaneously.
		MANOVA won't give you the interaction effects between the main effect and the repeated factor.
		MANOVA does not have the compound symmetry requirement that the one-factor repeated measures ANOVA model requires.
	carbon.cudenver.edu /~lsherry/rem/manova.html (456 words)

	MANOVA
		The main objective in using MANOVA is to determine if the response variables (student improvement in the example mentioned above), are altered by the observer’s manipulation of the independent variables.
		Linearity - MANOVA assumes that there are linear relationships among all pairs of dependent variables, all pairs of covariates, and all dependent variable-covariate pairs in each cell.
		It is simply a MANOVA where the artificial DVs are initially adjusted for differences in one or more covariates.
	online.sfsu.edu /~efc/classes/biol710/manova/manovanew.htm (1488 words)

	SPSS Library: MANOVA and GLM
		Unlike MANOVA, GLM does not use specifications of contrast types from the user to determine what parameters are to be estimated (contrast results are available in GLM, but they are produced after the initial parameter estimation phase; in MANOVA, the design matrix is actually built from the contrasts specified by the user or by defaults).
		That is, the MANOVA design matrix can be constructed from the more general GLM design matrix by factoring the GLM matrix into the product of two matrices: the MANOVA design or basis matrix, and a contrast matrix whose rows show the interpretations of the parameter estimates produced by use of the MANOVA design matrix.
		MANOVA handles this by reparameterizing the model, using a method that is sometimes referred to as using sum to 0 restrictions (note that each A column in the design matrix sums to 0).
	www.ats.ucla.edu /stat/spss/library/manglm.htm (2705 words)

	MANOVA
		MANOVA is useful in experimental situations where at least some of the independent variables are manipulated.
		Because in MANOVA there are multiple DVs, a column matrix (vector) of values for each DV is used.
		MANOVA works well in situations where there are moderate correlations between DVs.
	online.sfsu.edu /~efc/classes/biol710/manova/manova.htm (1240 words)

	Power via MANOVA (Site not responding. Last check: 2007-10-24)
		You must input the mean for each group at each time, the common pooled standard deviation at each time, and the correlation matrix among time points (over all subjects).
		MANOVA assumes alpha is.05, and F tests are always two-sided.
		The MANOVA procedure is no longer supported by SPSS, so you won't find it in the recent manuals or help files.
	www.nur.utexas.edu /researchlab/papers/powermanova.html (656 words)

	SPSS MANOVA (Site not responding. Last check: 2007-10-24)
		MANOVA can be used to carry out a range of analyses.
		Because of this, the number of dependent variables on the MANOVA specification is necessarily an integral multiple of the product of the number of levels of the within-subjects factors.
		To request power values, specify the appropriate keywords after the POWER subcommand, along with the type of test (either F or T), and the significance level at which the power is to be calculated.
	www.personal.psu.edu /faculty/k/r/krm10/MANOVA.html (1804 words)

	[No title]
		The PA independent variable was a physical attractiveness manipulation: the female defendant presented to the mock jurors was “beautiful,” “average,” or “ugly.” The second independent variable was CRIME, the type of crime the defendant committed, a burglary (theft of items from victim’s room) or a swindle (conned the male victim).
		The MANOVA produced the test for a multivariate interaction by obtaining eigenvalue(s) (ratio of SSeffect / SSerror) for the weighted linear combination(s) of the dependent variables that maximized that effect.
		Well, were we now to do two oneway MANOVAs, one at each level of crime, to find the multivariate effect of PA upon our DVs, those two MANOVAs would each construct two roots (weights for the DVs) that maximize the eigenvalues for their own data.
	core.ecu.edu /psyc/wuenschk/MV/MANOVA/MANOVA2.doc (1776 words)

	Lesson 6: MANOVA (Site not responding. Last check: 2007-10-24)
		The MANOVA model is to look at a series of normally-distributed, dependent variable as they are influenced by one or more independent factors.
		Note that there is a function on both sides of the equation, MANOVA does indeed build a function on that side that maximally separates the groups.
		This is the MANOVA variate - you are looking at the influence of the independent variable(s) on this variate, which is a linear combination of the dependent variables.
	www.colorado.edu /epob/epob4640mwalker/lect6.html (1304 words)

	MANOVA (Site not responding. Last check: 2007-10-24)
		The MANOVA is chiefly used in one of four related situations.
		The assumptions of the MANOVA are straight foreword generalizations from those of the ANOVA: multivariate normalcy, multivariate homogeneity of variance and covariance and independent random sampling.
		The MANOVA, like the ANOVA, is robust against moderate violations of multivariate normalcy and multivariate homogeneity of variance, especially when the sample are all about the same size.
	bill.psyc.anderson.edu /exdes/ex10.html (1782 words)

	MANOVA (Site not responding. Last check: 2007-10-24)
		In more recent versions of SPSS, MANOVA and MANCOVA are found under "GLM" (General Linear Model).
		The multivariate formula for F is based not only on the sum of squares between and within groups, as in ANOVA, but also on the sum of crossproducts -- that is, it takes covariance into account as well as group means.
		If the overall F-test shows the centroid (vector) of means of the dependent variables is not the same for all the groups formed by the categories of the independent variables, tests of group differences are used to explore the nature of the group differences.
	www.public.asu.edu /~hyanik/as/manova.htm (925 words)

	Hair5 Nts 6b
		MANOVA is applied in any of the experimental designs encountered in univariate statistics; for a review see Against all Odds #12 (Design of Experiments) and #13 (Blocking & Sampling).
		The F criterion for univariate ANOVA is proportional to A/W, where W = within-groups sum of squares and A = among groups sum of squares.
		Analogously, the test criteria for multivariate MANOVA are measures of the size of the matrix A W
	www.uic.edu /classes/idsc/ids470/hair5ed/nts06b.htm (1256 words)

	Stata help for manova
		Reporting detail report categorical variable value mappings ------------------------------------------------------------------------- bootstrap, by, jackknife, and statsby may be used with manova; see prefix.
		The manova command fits multivariate analysis-of-variance (MANOVA) and multivariate analysis-of-covariance (MANCOVA) models for balanced and unbalanced designs, including designs with missing cells, and for factorial, nested, or mixed designs, or designs involving repeated measures.
		manova y1 y2 = a b c ab ac b*c.
	www.stata.com /help.cgi?manova (404 words)

	manova()
		If the response is univariate (has only one column), manova() is equivalent to anova().
		The results are the same as if the i-th row of the response and all X-variables (variates and dummy variables and their products), including the constant vector were multiplied by sqrt(Wts[i]) and a least squares fit (without an intercept) computed.
		manova() or manova(,weights:Wts) (no model supplied) uses the model used by the most recent GLM command such as manova(), anova(), or poisson().
	www.stat.umn.edu /macanova/html_help/node222.htm (578 words)

	[No title]
		Even experienced users of ANOVA and MANOVA techniques are often puzzled by the differences in results that sometimes occur when performing a MANOVA on, for example, three variables as compared to a univariate ANOVA on the sum of the three variables.
		This "insight" is the reason why MANOVA methods are increasingly applied to test the significance of univariate repeated measures factors with more than two levels.
		There are instances (designs) when the MANOVA approach cannot be applied; specifically, when there are few subjects in the design and many levels on the repeated measures factor, there may not be enough degrees of freedom to perform the multivariate analysis.
	www.statsoftinc.com /textbook/stanman.html (5994 words)

	470nts5b.htm
		Before Multiple Discriminant Analysis (MDA) is applied, MANOVA is done as a preliminary test to see if there are actually differences between/among the groups.
		MANOVA is applied in any of the experimental designs encountered in univariate statistics.
		Suppose a survey is taken at 2 schools and at 3 classrooms in each.
	www.uic.edu /classes/idsc/ids470/972/470nts5b.htm (922 words)

	Repeated Measures ANOVA Using SPSS MANOVA (Stat-38) (Site not responding. Last check: 2007-10-24)
		The document first explains when one should use such a procedure; then describes the terminology used here; gives a sample research problem; and finally, in a detailed example, shows how to use the SPSS procedure.
		When SPSS executes this MANOVA command, the first several pages of output will be lists of means and standard deviations for the within-subjects variables.
		When there are more than two levels of a within-subjects factor, SPSS MANOVA prints out two different sets of within-subjects hypothesis tests.
	www.utexas.edu /acits/docs/stat38.html (4682 words)

	MANOVA -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-24)
		Under normality assumptions about ((computer science) the occurrence of an incorrect result produced by a computer) error distributions, the counterpart of the sum of squares due to error has a (additional info and facts about Wishart distribution) Wishart distribution.
		Analagous to ANOVA, MANOVA is based on the product of model variance matrix and
		Invariance considerations imply the MANOVA statistic should be a measure of magnitude of the (additional info and facts about singular value decomposition) singular value decomposition of this matrix product, but there is no unique choice owing to the multi-dimensional nature of the alternative hypothesis.
	www.absoluteastronomy.com /encyclopedia/m/ma/manova5.htm (345 words)

	MANOVA Power Analysis available in PASS
		It computes power for three MANOVA test statistics: Wilks’ lambda, Pillai-Bartlett trace, and Hotelling-Lawley trace.
		MANOVA is an extension of common analysis of variance (ANOVA).
		In MANOVA, the number of response variables is increased to two or more.
	www.ncss.com /passmanova.html (116 words)

	manova (Site not responding. Last check: 2007-10-24)
		Perform a one-way multivariate analysis of variance (MANOVA).
		The goal is to test whether the p-dimensional population means of data taken from
		The LR test statistic (Wilks' Lambda) and approximate p-values are computed and displayed.
	octave.sourceforge.net /index/f/manova.html (69 words)

	Information Technology Services
		Furthermore, SPSS MANOVA displays the adjusted means in the scale of the transformation used for the repeated measures analysis.
		For the second MANOVA run, you must first "center" the covariate by subtracting the grand mean for the covariate from each observation's value on the covariate.
		Note that you should NOT interpret the remainder of the MANOVA output from this second analysis.
	www.utexas.edu /its/rc/answers/spss/spss40.html (452 words)

	MANOVAMAP: Graphical Representation of MANOVA in Marketing Research (ResearchIndex)
		Abstract: A graphical representation of the multivariate analysis of variance (MANOVA) is proposed.
		This representation, termed a "MANOVAMAP," shows the magnitude of MANOVA model effects and their statistical significance in an easily interpreted statistical graphic.
		The use and construction of MANOVAMAPs is discussed for an empirical example, and is compared with both a traditional MANOVA analysis of the data, and a traditional graphical analysis based upon centroid plots.
	citeseer.ist.psu.edu /novak94manovamap.html (724 words)

	ED230B/C: MANOVA
		11 5.636364 3.546907.7 10.3 manova y1 y2 y3 = grp Number of obs = 33 W = Wilks' lambda L = Lawley-Hotelling trace P = Pillai's trace R = Roy's largest root Source
		We see from these results that variables y1 and y3 display significant effects when looking at the differences by groups 1 and 2 and 1 and 3.
		use http://www.gseis.ucla.edu/courses/data/hsb2 manova read math science = female prog female*prog Number of obs = 200 W = Wilks' lambda L = Lawley-Hotelling trace P = Pillai's trace R = Roy's largest root Source
	www.gseis.ucla.edu /courses/ed230bc1/cnotes1/man1.html (677 words)

	MATLAB Central - Newsreader - MANOVA, # of IVs (Site not responding. Last check: 2007-10-24)
		MATLAB Central - Newsreader - MANOVA, # of IVs
		MATLAB Central > comp.soft-sys.matlab > archive > MANOVA, # of IVs
		E-mail me when replies are made to this thread
	newsreader.mathworks.com /WebX?14@100.RToQa50xhD9.1@.eecc2c2 (288 words)

	UIUC HF: Research Projects (Site not responding. Last check: 2007-10-24)
		Performance changes that occur between IPC#1 to IPC#2 will be analyzed using a Chi-Square test for each of the three groups.
		The McNemar intervening activity statistic, MANOVA and ANOVA will be used where appropriate for analysis of the results.
		Principal components and factor analysis techniques will be used to analyze objective performance metrics derived from FDR and PCATD and FTD output data.
	www.humanfactors.uiuc.edu /research/projects.asp (4891 words)

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