manova                 package:base                 R Documentation

_M_u_l_t_i_v_a_r_i_a_t_e _A_n_a_l_y_s_i_s _o_f _V_a_r_i_a_n_c_e

_D_e_s_c_r_i_p_t_i_o_n:

     A class of multivariate analysis of variance and a `summary'
     method.

_U_s_a_g_e:

     manova(...)
     summary.manova(object,
                    test = c("Pillai", "Wilks", "Hotelling-Lawley", "Roy"),
                    intercept = FALSE)

_A_r_g_u_m_e_n_t_s:

     ...: Arguments to be passed to `aov'

  object: An object of class `"manova"' or an `aov' object with
          multiple responses.

    test: The name of the test statistic to be used. Partial matching
          is used so the name can be abbreviated.

intercept: logical. If `TRUE', the intercept term is included in the
          table.

_D_e_t_a_i_l_s:

     Class `"manova"' differs from class `"aov"' in selecting a
     different `summary' method.  Function `manova' calls `aov' and
     then add class `"manova"' to the result object for each stratum.

     The `summary.manova' method uses a multivariate test statistic for
     the summary table.  Wilks' statistic is most popular in the
     literature, but the default Pillai-Bartlett statistic is
     recommended by Hand and Taylor (1987).

_V_a_l_u_e:

     A list with components 

      SS: A names list of sums of squares and product matrices.

Eigenvalues: A matrix of eigenvalues, 

   stats: A matrix of the statistics, approximate F value and degrees
          of freedom.

_A_u_t_h_o_r(_s):

     B.D. Ripley

_R_e_f_e_r_e_n_c_e_s:

     Krzanowski, W. J. (1988) Principles of Multivariate Analysis. A
     User's Perspective. Oxford.

     Hand, D. J. and Taylor, C. C.  (1987) Multivariate Analysis of
     Variance and Repeated Measures. Chapman and Hall.

_S_e_e _A_l_s_o:

     `aov'

_E_x_a_m_p_l_e_s:

     ## Example on producing plastic filem from Krzanowski (1998, p. 381)
     tear <- c(6.5, 6.2, 5.8, 6.5, 6.5, 6.9, 7.2, 6.9, 6.1, 6.3,
               6.7, 6.6, 7.2, 7.1, 6.8, 7.1, 7.0, 7.2, 7.5, 7.6)
     gloss <- c(9.5, 9.9, 9.6, 9.6, 9.2, 9.1, 10.0, 9.9, 9.5, 9.4,
                9.1, 9.3, 8.3, 8.4, 8.5, 9.2, 8.8, 9.7, 10.1, 9.2)
     opacity <- c(4.4, 6.4, 3.0, 4.1, 0.8, 5.7, 2.0, 3.9, 1.9, 5.7,
                  2.8, 4.1, 3.8, 1.6, 3.4, 8.4, 5.2, 6.9, 2.7, 1.9)
     Y <- cbind(tear, gloss, opacity)
     rate <- factor(gl(2,10), labels=c("Low", "High"))
     additive <- factor(gl(2, 5, len=20), labels=c("Low", "High"))

     fit <- manova(Y ~ rate * additive)
     summary.aov(fit)           # univariate ANOVA tables
     summary(fit, test="Wilks") # ANOVA table of Wilks' lambda

