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30 Cards in this Set
- Front
- Back
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MANCOVA is similar to what analysis |
reversal of discriminant analysis DA: dvs are the groups Manova: IVs are the groups |
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univariate |
influences one variation, having one DV (Ttest, Anova, ANCOVA) |
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Bivariate |
impact or influence on two variations, having 2 DVs (pearson correlation) |
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Multivariate |
impact or influence on several variations, more than 2 DVs (manova, multiple regression) |
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difference between MANOVA & ANOVA |
manova is an extension of the ANOVA; ANOVA examines differ. on 1 continuous DV by & Independent grouping; Manova examines multiple continous DVs & bundles them into a weighted linear combinantio or composite varialbe - assess whether new combination differes by the diff. groups or levels of the IV (assess main effects & interactions) |
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MANova variables |
IVs must be categorical and DVs must be continous or scale - testing for group differences of several IVs taking into account the relationship between DVs |
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Partial Eta 2 |
shows how much variance is explained by the IV; effect size for the Manova model |
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Post Hoc Tests |
if there is a sign. difference btw groups then perform a post hoc to determine where the differnce lie. (which specific IV level significantly differs from another) |
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Multivariate F- statistic |
derived by dividing the mean sums of the squares (ss) for the source variable by the source variable mean error (ME or MSE) |
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Theories of Manova |
- sum of squares cross products matrices (SSCP) calculates the F-test - Discriminant Variates: the DVs are different - Manova Test Statistics: Wilks Lambda, Pillals-Bartlett, Hotellings T, & Roy's Greatest Characteristic Root - Independent random sampling: participants do not influence one anothers score |
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why would you use a MANOVA |
1. alternate to RM ANOVA (decrease risk for Type II error 2. increases power (whole is greater than parts) 3. To study the relationship btw several DVs 4. can reduce large #'s of DVs to subsets/linear composites of DVs (like factor analysis) 5. protection from type 1 error 6. Latent variable/multivariate testing |
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Latent variable/multivariate testing |
when you have multiple DVs in an attempt to measure one concept that best distinguish the predictors. If DBs do not represent a potential latent variable the use Bonneferonni for each DV as a separate ANOVA |
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Relationships among DVS |
1. DVs should be correlated in some way theoretically or statistically 2. if DVs are not correlated then several ANoVAs should be done instead |
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Roy Bargman Stepdown Manova (tests of main effects) |
exploratory test to main effect testing (running univariate ANoVAs for each DV) where order of entry of DVs are important -strongest correlation entered first |
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4 Multivariate TEsts (4) |
Wilks lambda(most common) Pillais-Bartlett (most robust against violations) Hotellings T (equivalent to Pillais) Roys Greatest Characteristic Root (least used) |
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Wilks lambda |
- variance not accounted for, the smaller the value the better 1- wilks lambda = R2 (variance accounted for) - if value high, it is not significant |
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Pillais Bartlett |
- variance explained/accounted for - sum of explained variance on the discriminant variates or latent variables |
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Hotellings T |
two levels for IV, no repeated measures, 2 or more DVs - use when DVs do not correlate |
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Roys Greatest Characteristic Root (least used) |
powerful but sensititve -based on 1st dimension/ most dominant discriminant root / latent variable (when looking at the factor that accounts for the most vairance -use when DVs correlate -sensitive to violation of homogeneity of variance-co |
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what is the benefit of doing an Discriminant Analysis (DA)? |
helps determine the meaning of a latent variate -doing factor analysis on DVs to see which will be in each group - look at structure matrix to identify factor loading |
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name 5 MANOVA assumptions |
1) independence of obs 2) homogeneity of variance 3) Normality (bivariate & multivariate) 4) Linearity 5) Homogeneity of variance -covariance * Homogeneity of regression |
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Homogeneity of variance |
variance between the groups must be equal - check Levenes TEst (non sign values indicates equal variance between groups) |
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Normality |
assess for skewness & outliers on scatterplots; remove any outliers (extreme values) that may affect multivariate normality - univariate: look at Kolomorgrov-Smirnoff test - multivariate: use mahalanobis distance to test for any outliers |
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Linearity |
The DVs can not be too correlated w/each other (must be btw .3 and .8) - check scatterplot to be sure no curvilinear relationship - DVs should be separate & independent of each other - we want to violate multicollinarity (it indicates no multicollinarity) |
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multicollinearitiy |
Tolerance: cut off>1 Tolerance = 1/VIF |
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Homogeneity of variance -covariance matrixes |
- several correlated to DVs - DVs should change at the same rate at each different level of the IV - check Box's M, if sign. it is violated, then use Pillais trace (+variance/variance accounted for) - if non significant, use Wilks lambda (variance not accounted for) |
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Homogeneity of regression |
rarely used only if you are giving order of the DV (i.e, step down of Manova) |
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Modified Hummel Sligo Bonferonni |
show you that Manova protects against Type 1 error and Manova is robust |
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If Manova is robust |
perform individual ANOVAs and bonneferonni correction not needed |
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Multiple DVs can |
fail the analysis bc the DVs may overlap and a poor variable will violate the asssumptions
poor power is when DVs correlate too strongly (high correlation) |
