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ANLY 715 - Fangya Tan
Paper Review:
A Procedure Whose Time has Passed?
MANOVA: Multivariate analysis of variance
Definition: Compare Multivariate Sample
Mean (More than two DV)
Application: Education, Psychology (25%)
gifted education literature
Challenges : Some paper using MANOVA for
univariate research questions rather than
multivariate questions.
• MANOVA + ANOVA Comb
Multivariate effect - ANOVA (96%) HUBERTY
AND MORRIS
Truth : MANOVA + ANOVA is illogical
Solution : MANOVA + DDA
• Controlling Type I error rates when analyzing
multiple DVs
• Repeated Measures:
Analyze repeated measurements taken from
individuals over time (lab result, vital sign)
Superior Choice: Linear Mixed Effects Model/
Multiple Imputation
Bonus Application
• MANOVA Challenges
• 1. The Actual research questions may
not be multivariate to begin with
• 2. Other statistical method can be
better suited
• 3. Some Assumptions are hard to
Satisfied
-Linearity of DV
-homogeneity of covariance matrices
(0.3-0.7)
Out of Date?
• Independent random sampling
• Linearity of the dependent variables
(Pearson)
• Multivariate normality(Kurtosis
skewness)
• Multivariate homogeneity of variance
within groups (Levene’s test)
• Multivariate homogeneity of variance
between groups (Box M)
Assumptions
ANOVA vs MANOVA
Outcome Variable
• Example: how children in public and private schools differ on three tests that measure
(1) reading, (2) mathematics, and (3) moral reasoning
• MANOVA : Whether groups differ on the variate (2 or more depend variables)
Do children in public and private differ on a variate formed using
three measured constructs?
• ANOVA : Whether three or more groups differ on the mean of depend variable.
Do children in public and private differ on mean value of
Math/reading/reasoning scores?
Alternative Solution
Maybe we can try something different!
D
Research Procedure to Consider Advantage
Mean Differences between
groups for DV
Regression with
corrections for multiple
comparison
Well understood Correct
Type I error
(Bonferoni)
Latent Mean differences
SEM
structural equation modeling
Devoid model
error intercorrelations
between DV
Repeated Measures
Mixed effect
model Multiple
computation
Missing Data
https://journals.sagepub.com/doi/full/10.1177/0016986219887200

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MANOVA paper review with example in R

  • 1. ANLY 715 - Fangya Tan Paper Review: A Procedure Whose Time has Passed?
  • 2. MANOVA: Multivariate analysis of variance Definition: Compare Multivariate Sample Mean (More than two DV) Application: Education, Psychology (25%) gifted education literature Challenges : Some paper using MANOVA for univariate research questions rather than multivariate questions.
  • 3. • MANOVA + ANOVA Comb Multivariate effect - ANOVA (96%) HUBERTY AND MORRIS Truth : MANOVA + ANOVA is illogical Solution : MANOVA + DDA • Controlling Type I error rates when analyzing multiple DVs • Repeated Measures: Analyze repeated measurements taken from individuals over time (lab result, vital sign) Superior Choice: Linear Mixed Effects Model/ Multiple Imputation Bonus Application
  • 4. • MANOVA Challenges • 1. The Actual research questions may not be multivariate to begin with • 2. Other statistical method can be better suited • 3. Some Assumptions are hard to Satisfied -Linearity of DV -homogeneity of covariance matrices (0.3-0.7) Out of Date?
  • 5. • Independent random sampling • Linearity of the dependent variables (Pearson) • Multivariate normality(Kurtosis skewness) • Multivariate homogeneity of variance within groups (Levene’s test) • Multivariate homogeneity of variance between groups (Box M) Assumptions
  • 6. ANOVA vs MANOVA Outcome Variable • Example: how children in public and private schools differ on three tests that measure (1) reading, (2) mathematics, and (3) moral reasoning • MANOVA : Whether groups differ on the variate (2 or more depend variables) Do children in public and private differ on a variate formed using three measured constructs? • ANOVA : Whether three or more groups differ on the mean of depend variable. Do children in public and private differ on mean value of Math/reading/reasoning scores?
  • 7. Alternative Solution Maybe we can try something different! D Research Procedure to Consider Advantage Mean Differences between groups for DV Regression with corrections for multiple comparison Well understood Correct Type I error (Bonferoni) Latent Mean differences SEM structural equation modeling Devoid model error intercorrelations between DV Repeated Measures Mixed effect model Multiple computation Missing Data
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