Population Total, Mean, Variance, and Standard Deviation
Population Total, Mean, Variance, and Standard Deviation
DESCRIPTION:
This function calculates estimates of the population total, mean, variance, and
standard deviation of a response variable, where the response variable may be
defined for either a discrete or an extensive resource. In addition the
standard error of the population estimates and confidence bounds are
calculated.
the final adjusted weight (inverse of the sample inclusion
probability) for each site, which is either the weight for a
single-stage sample or the stage two weight for a two-stage sample.
x
x-coordinate for location for each site, which is either the
x-coordinate for a single-stage sample or the stage two
x-coordinate for a two-stage sample. The default is NULL.
y
y-coordinate for location for each site, which is either the
y-coordinate for a single-stage sample or the stage two
y-coordinate for a two-stage sample. The default is NULL.
OPTIONAL ARGUMENTS:
stratum
the stratum for each site. The default is NULL.
cluster
the stage one sampling unit (primary sampling unit or cluster)
code for each site. The default is NULL.
N.cluster
the number of stage one sampling units in the resource, which
is required for calculation of finite and continuous population
correction factors for a two-stage sample. For a stratified sample
this variable must be a vector containing a value for each stratum and
must have the names attribute set to identify the stratum codes. The
default is NULL.
wgt1
the final adjusted stage one weight for each site. The default
is NULL.
x1
the stage one x-coordinate for location for each site. The default
is NULL.
y1
the stage one y-coordinate for location for each site. The default
is NULL.
popsize
the known size of the resource - the total number of sampling
units of a discrete resource or the measure of a continuous resource,
which is required for calculation of finite and continuous population
correction factors for a single-stage sample. This variable is also
used to adjust estimators for the known size of a resource. For a
stratified sample this variable must be a vector containing a value
for each stratum and must have the names attribute set to identify the
stratum codes. The default is NULL.
stage1size
the known size of the stage one sampling units of a two-
stage sample, which is required for calculation of finite and
continuous population correction factors for a two-stage sample and
must have the names attribute set to identify the stage one sampling
unit codes. For a stratified sample, the names attribute must be set
to identify both stratum codes and stage one sampling unit codes using
a convention where the two codes are separated by the # symbol, e.g.,
"Stratum 1#Cluster 1". The default is NULL.
support
the support value for each site - the value one (1) for a
site from a discrete resource or the measure of the sampling unit
associated with a site from a continuous resource, which is required
for calculation of finite and continuous population correction
factors. The default is NULL.
swgt
the size-weight for each site, which is the stage two size-weight
for a two-stage sample. The default is NULL.
swgt1
the stage one size-weight for each site. The default is NULL.
unitsize
the known sum of the size-weights of the resource, which for a
stratified sample must be a vector containing a value for each stratum
and must have the names attribute set to identify the stratum codes.
The default is NULL.
vartype
the choice of variance estimator, where "Local" = local mean
estimator and "SRS" = SRS estimator. The default is "Local".
conf
the confidence level. The default is 95%.
check.ind
a logical value that indicates whether compatability
checking of the input values is conducted, where TRUE = conduct
compatibility checking and FALSE = do not conduct compatibility
checking. The default is TRUE.
warn.ind
a logical value that indicates whether warning messages were
generated, where TRUE = warning messages were generated and FALSE = warning
messages were not generated. The default is NULL.
warn.df
a data frame for storing warning messages. The default is
NULL.
warn.vec
a vector that contains names of the population type, the
subpopulation, and an indicator. The default is NULL.
VALUE:
A data frame containing the estimates and confidence bounds.
SIDE EFFECTS:
None
DETAILS:
The Horvitz-Thompson estimator is used to calculate the total, variance, and
standard deviation estimates. The Horvitz-Thompson ratio estimator, i.e., the
ratio of two Horvitz-Thompson estimators, is used to calculate the mean
estimate. Variance estimates are calculated using either the local mean
variance estimator or the simple random sampling (SRS) variance
estimator. The choice of variance estimator is subject to user control. The
local mean variance estimator requires the x-coordinate and the
y-coordinate of each site. The SRS variance estimator uses the
independent random sample approximation to calculate joint inclusion
probabilities. Confidence bounds are calculated using a Normal
distribution multiplier. The function can accommodate a stratified sample.
For a stratified sample, separate estimates and standard errors are calculated
for each stratum, which are used to produce estimates and standard errors for
all strata combined. Strata that contain a single value are removed. For a
stratified sample, when either the size of the resource or the sum of the size-
weights of the resource is provided for each stratum, those values are used as
stratum weights for calculating the estimates and standard errors for all
strata combined. For a stratified sample when neither the size of the resource
nor the sum of the size-weights of the resource is provided for each stratum,
estimated values are used as stratum weights for calculating the estimates and
standard errors for all strata combined. The function can accomodate
single-stage and two-stage samples for both stratified and unstratified
sampling designs. Finite population and continuous population correction
factors can be utilized in variance estimation. The function checks for
compatibility of input values and removes missing values.
Diaz-Ramos, S., D.L. Stevens, Jr., and A.R. Olsen. (1996). EMAP
Statistical Methods Manual. EPA/620/R-96/XXX. Corvallis, OR: U.S.
Environmental Protection Agency, Office of Research and Development, National
Health Effects and Environmental Research Laboratory, Western Ecology
Division.
EXAMPLES:
z <- rnorm(100, 10, 1)
wgt <- runif(100, 10, 100)
total.est.fcn(z, wgt, vartype="SRS")
x <- runif(100)
y <- runif(100)
total.est.fcn(z, wgt, x, y)