svytable               package:survey               R Documentation

_C_o_n_t_i_n_g_e_n_c_y _t_a_b_l_e_s _f_o_r _s_u_r_v_e_y _d_a_t_a

_D_e_s_c_r_i_p_t_i_o_n:

     Contingency tables and chisquared tests of association for survey
     data.

_U_s_a_g_e:

     svytable(formula, design, Ntotal = design$fpc, round = FALSE)
     svreptable(formula, design, Ntotal = sum(weights(design, "sampling"))), round = FALSE)
     svychisq(formula, design, statistic = c("F",  "Chisq","Wald","adjWald"))
     ## S3 method for class 'svytable':
     summary(object, statistic = c("F",  "Chisq","Wald","adjWald"),...)

_A_r_g_u_m_e_n_t_s:

 formula: Model formula specifying margins for the table (using '+'
          only)

  design: survey object

statistic: See Details below

  Ntotal: A population total or set of population stratum totals to
          normalise to.

   round: Should the table entries be rounded to the nearest integer?

  object: Output from 'svytable'

     ...: Other arguments to 'summary', not used here

_D_e_t_a_i_l_s:

     The 'svytable' and 'svreptable' function compute a weighted
     crosstabulation.  If the sampling probabilities supplied to
     'svydesign' were actual probabilities (rather than relative
     probabilities) this estimates a full population crosstabulation.
     Otherwise it estimates only relative proportions and should be
     normalised to some convenient total such as 100 or 1.0 by
     specifying the 'Ntotal' argument.  If the formula has a left-hand
     side the mean or sum of this variable rather than the frequency is
     tabulated

     The 'Ntotal' argument can be either a single number or a data
     frame whose first column is the sampling strata and second column
     the population size in each stratum.  In this second case the
     'svytable' command performs `post-stratification': tabulating and
     scaling to the population within strata and then adding up the
     strata.

     As with other 'xtabs' objects, the output of 'svytable' can be
     processed by 'ftable' for more attractive display. The 'summary'
     method for 'svytable' objects calls 'svychisq' for a test of
     independence.

     'svychisq' computes first and second-order Rao-Scott corrections
     to the Pearson chisquared test, and two Wald-type tests.

     The default ('statistic="F"') is the Rao-Scott second-order
     correction.  The p-values are computed with a Satterthwaite
     approximation to the distribution.  The alternative
     'statistic="Chisq"' adjusts the Pearson chisquared statistic by a
     design effect estimate and then compares it to the chisquared
     distribution it would have under simple random sampling.

     The 'statistic="Wald"' test is that proposed by Koch et al (1975)
     and used by the SUDAAN software package. It is a Wald test based
     on the differences between the observed cells counts and those
     expected under independence. The adjustment given by
     'statistic="adjWald"' reduces the statistic when the number of
     PSUs is small compared to the number of degrees of freedom of the
     test. Rao and Thomas (1990) compare these tests and find the
     adjustment benefical.

     At the moment, 'svychisq' works only for 2-dimensional tables.

_V_a_l_u_e:

     The table commands return an 'xtabs' object, 'svychisq' returns a
     'htest' object.

_N_o_t_e:

     Rao and Scott (1984) leave open one computational issue. In
     computing `generalised design effects' for these tests, should the
     variance under simple random sampling be estimated using the
     observed proportions or the the predicted proportions under the
     null hypothesis? 'svychisq' uses the observed proportions,
     following simulations by Sribney (1998)

_R_e_f_e_r_e_n_c_e_s:

     Koch, GG, Freeman, DH, Freeman, JL (1975) "Strategies in the
     multivariate analysis of data from complex surveys" International
     Statistical Review 43: 59-78

     Rao, JNK, Scott, AJ (1984) "On Chi-squared Tests For Multiway
     Contigency Tables with Proportions Estimated From Survey Data" 
     Annals of Statistics 12:46-60.

     Sribney WM (1998) "Two-way contingency tables for survey or
     clustered data" Stata Technical Bulletin 45:33-49.

     Thomas, DR, Rao, JNK (1990) "Small-sample comparison of level and
     power for simple goodness-of-fit statistics under cluster
     sampling" JASA 82:630-636

_S_e_e _A_l_s_o:

     'xtabs', 'svyby' for tables of means, medians, etc.

_E_x_a_m_p_l_e_s:

       data(api)
       xtabs(~sch.wide+stype, data=apipop)

       dclus1<-svydesign(id=~dnum, weights=~pw, data=apiclus1, fpc=~fpc)
       summary(dclus1)

       svytable(~sch.wide+stype, dclus1)
       svychisq(~sch.wide+stype, dclus1)
       svychisq(~sch.wide+stype, dclus1, statistic="Chisq")
      svychisq(~sch.wide+stype, dclus1, statistic="adjWald")

       rclus1 <- as.svrepdesign(dclus1)
       svreptable(~sch.wide+stype, rclus1, round=TRUE)

