Week 5: MANOVA

• What does MANOVA stand for?

  Multivariate Analysis of Variance
• What is the primary purpose of MANOVA?

  To analyze differences among groups on multiple dependent variables simultaneously
• What is a key assumption of MANOVA regarding the dependent variables?

  The dependent variables should be related in some way
• Why is it important to consider assumptions in MANOVA?

  Assumptions ensure the validity of the results and interpretations
• What are the advantages of using MANOVA over separate ANOVAs?

  • Controls for Type I error
  • Considers the interrelationships among dependent variables
  • Provides a composite measure for analysis
• What is the minimum sample size requirement for MANOVA?

  You need more cases in each cell than the number of dependent variables
• What does multivariate normality mean in the context of MANOVA?

  Dependent variables should be drawn from normally distributed populations
• How can you test for multivariate normality in SPSS?

  Using the Shapiro-Wilk test
• What is the significance level threshold for the Shapiro-Wilk test to assume normality?

  Higher than 0.05
• What does Box's Test assess in MANOVA?

  Whether the assumption of homogeneity of covariance matrices is violated
• What is the significance level threshold for Box's Test?

  Greater than 0.001
• What does Levene's Test check in the context of MANOVA?

  Whether the assumption of equality of variance is violated
• What is the significance level threshold for Levene's Test?

  Greater than 0.05
• What is Wilks' Lambda used for in MANOVA?

  To assess the overall significance of the model
• If you obtain a significant result in MANOVA, what should you consider next?

  Conduct separate ANOVAs for each dependent variable
• What is the purpose of Tukey's tests in MANOVA?

  To determine which specific groups differ when the independent variable has more than two levels
• What are the steps to interpret MANOVA results?

  1. Descriptive Statistics
  2. Box's Test
  3. Levene's Test (if Box's M is violated)
  4. Check for Multicollinearity
  5. Conduct MANOVA Main Test
  6. Test of Between Subjects Effects
  7. Multiple Comparisons
• What is the difference between ANOVA and MANOVA?

  ANOVA tests for mean differences on a single DV, while MANOVA tests for mean differences on a combination of DVs
• Why is it inefficient to use T-tests for evaluating more than three groups?

  It increases the risk of Type I error due to multiple analyses
• What alpha value does Box's M adapt?

  0.001
• What is a null hypothesis?

  It states there is no significant effect of the independent variable on the dependent variable
• What is a Type II error?

  A Type II error is the non-rejection of a false null hypothesis
• What are the key assumptions of MANOVA?

  • Sample size: More cases than dependent variables
  • Multivariate normality: DVs should be normally distributed
  • Homogeneity of variance-covariance matrices
  • Absence of outliers
  • Linearity
  • Multicollinearity
• What should be done if the assumptions of MANOVA are violated?

  • Consider using non-parametric tests
  • Transform the data
  • Use robust statistical methods
• What is the role of Mahalanobis distance in MANOVA?

  To check for the absence of outliers
• How can you check for linearity in MANOVA?

  By using scatter plots
• What is multicollinearity in the context of MANOVA?

  It refers to high correlations among independent variables
• What is the significance of having more than one dependent variable in MANOVA?

  It allows for the analysis of interrelated outcomes simultaneously
• What happens if the MANOVA is significant?

  You should consider the individual ANOVAs for each dependent variable
• What is the purpose of Bonferroni adjustments in MANOVA?

  To control for Type I error when conducting multiple ANOVAs
• What is the relationship between MANOVA and ANOVA?

  MANOVA is an extension of ANOVA for multiple related dependent variables
• How does MANOVA control for Type I errors?

  By analyzing multiple dependent variables simultaneously rather than separately
• What is the significance of the F statistic in MANOVA?

  It indicates the ratio of variance between groups to variance within groups
• What does a significant Wilks' Lambda indicate?

  There are significant differences among the groups on the linear combination of dependent variables
• How can you determine which specific groups differ after a significant MANOVA result?

  By conducting post-hoc tests like Tukey's tests
• What is the role of descriptive statistics in MANOVA?

  To summarize the data and provide an overview before analysis
• What is the significance of the partial eta squared in MANOVA?

  It measures the effect size of the independent variable on the dependent variables
• What does a significant result in the Test of Between Subjects Effects indicate?

  That the independent variable has a significant effect on at least one dependent variable
• How does the interpretation of MANOVA results differ from that of ANOVA?

  MANOVA results require consideration of multiple dependent variables simultaneously
• What is the importance of checking for outliers in MANOVA?

  Outliers can significantly affect the results and interpretations