summary.manova             package:stats             R Documentation

_S_u_m_m_a_r_y _M_e_t_h_o_d _f_o_r _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 'summary' method for class '"manova"'.

_U_s_a_g_e:

     ## S3 method for class 'manova':
     summary(object,
             test = c("Pillai", "Wilks", "Hotelling-Lawley", "Roy"),
             intercept = FALSE, ...)

_A_r_g_u_m_e_n_t_s:

  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.

     ...: further arguments passed to or from other methods.

_D_e_t_a_i_l_s:

     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).

     The table gives a transformation of the test statistic which has
     approximately an F distribution.  The approximations used follow
     S-PLUS and SAS (the latter apart from some cases of the
     Hotelling-Lawley statistic), but many other distributional
     approximations exist: see Anderson (1984) and Krzanowski and
     Marriott (1994) for further references.  All four approximate F
     statistics are the same when the term being tested has one degree
     of freedom, but in other cases that for the Roy statistic is an
     upper bound.

_V_a_l_u_e:

     A list with components 

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

Eigenvalues: A matrix of eigenvalues.

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

_R_e_f_e_r_e_n_c_e_s:

     Anderson, T. W. (1994) _An Introduction to Multivariate
     Statistical Analysis._ Wiley.

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

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

     Krzanowski, W. J. and Marriott, F. H. C. (1994) _Multivariate
     Analysis. Part I: Distributions, Ordination and Inference._ Edward
     Arnold.

_S_e_e _A_l_s_o:

     'manova', 'aov'

_E_x_a_m_p_l_e_s:

     ## Example on producing plastic film 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, length=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
     summary(fit)               # same F statistics as single-df terms

