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, tol = 1e-7, ...)

_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.

     tol: tolerance to be used in deciding if the residuals are
          rank-deficient: see 'qr'.

     ...: 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.

     The tolerance 'tol' is applied to the QR decomposition of the
     residual correlation matrix (unless some response has essentially
     zero residuals, when it is unscaled).  Thus the default value
     guards against very highly correlated responses: it can be reduced
     but doing so will allow rather inaccurate results and it will
     normally be better to transform the responses to remove the high
     correlation.

_V_a_l_u_e:

     An object of class '"summary.manova"'.  If there is a positive
     residual degrees of freedom, this is a list with components 

row.names: The names of the terms, the row names of the 'stats' table
          if present.

      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.

     otherwise components 'row.names', 'SS' and 'Df' (degrees of
     freedom) for the terms (and not the residuals).

_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

