inst/help/Manova.md

In jasp-stats/jaspAnova: ANOVA Module for JASP

MANOVA

MANOVA allows the user to analyze the difference among three, or more, group means.

Assumptions

• The dependent variables are normally distributed for every group.
• The independent variables are categorical, the dependent variables are continuous.
• The population covariance matrices of each group are equal.
• The groups are independent.

Input

Assignment Box

• Dependent Variable: The variable(s) of interest. Also called the outcome variable(s).
• Fixed Factors: The variables that are manipulated/define the different groups. Also called the independent variables.

Model

• Components and model terms

  • Components: All the independent variables that can be included in the model.
  • Model terms: The independent variables included in the model. By default all the main effects and interaction effects of the specified independent variables are included in the model.

• Include intercept: display the intercept term in the MANOVA and ANOVA tables.

Additional Options

• Test: Select the statistical test to be performed for the MANOVA and how the F-ratio is approximated.

  • Pillai: Pillai's trace.
  • Wilks: Wilks' lambda. This can be interpreted as the proportion of the variance in the outcomes that is not explained by an effect.
  • Hotelling-Lawley: Hotelling-Lawley's trace.
  • Roy: Roy's largest root.

• Display:

• ANOVA tables: Outputs individual ANOVA tables per dependent variable.

• Vovk-Sellke maximum p-ratio: The bound 1/(-e p log(p)) is derived from the shape of the p-value distribution. Under the null hypothesis (H0) it is uniform (0,1), and under the alternative (H1) it is decreasing in p, e.g., a beta (α, 1) distribution, where 0 < α < 1. The Vovk-Sellke MPR is obtained by choosing the shape α of the distribution under H1 such that the obtained p-value is maximally diagnostic. The value is then the ratio of the densities at point p under H0 and H1. For example, if the two-sided p-value equals .05, the Vovk-Sellke MPR equals 2.46, indicating that this p-value is at most 2.46 times more likely to occur under H1 than under H0. More information can be found in this blogpost.

• Assumption Checks:

• Homogeneity of covariance matrices: Box's M-test for homogeneity of covariance matrices.
• Multivariate normality: Generalized Shapiro-Wilk test for multivariate normality by Villasenor-Alva and Gonzalez-Estrada (2009), using the mvShapiroTest package.

Output

MANOVA

MANOVA - test: - Cases: This column contains the independent variables, their interaction, and the residual. - df: degrees of freedom of the design. - Approx. F: Approximation of the F-ratio. The different tests can provide different approximations. - Test statistic: The test statistic, dependent on which tests are selected. - Num df: Degrees of freedom used in determining the p-values of the F statistics. - Den df: Degrees of freedom used in determining the p-values of the F statistics. - p: The p-value of the approximated F-ratio. - VS-MPR: Vovk-Sellke Maximum p-ratio.

ANOVA

ANOVA - dependent variable: - Cases: This column contains the independent variables, their interaction, and the residual. - Sum of Squares: The summed squared group-mean differences. - df: Degrees of freedom of the model. - Mean Square: The estimate of population variance (the sum of squares divided by df's). - F: The value of the F-statistic. - p: The p-value. - VS-MPR: Vovk-Sellke Maximum p-ratio.

References

• Field, A. (2009). Discovering Statistics using SPSS (3rd ed.). Sage Publishing.
• Field, A., Miles, J., & Field, Z. (2012). Discovering statistics using R. Sage Publishing.
• Villasenor-Alva, J.A. and Gonzalez-Estrada, E. (2009). A generalization of Shapiro-Wilk's test for multivariate normality. Communications in Statistics: Theory and Methods, 38, 1870-1883.

R Packages

• stats

Example

TBA

jasp-stats/jaspAnova documentation built on June 14, 2024, 6:48 p.m.