R/univariateData.R

In ab9sq/Rqualification: A series of function to test R against NIST data sets

#' Lew NIST univariate Data Set.
#'
#' Dataset of 200 points
#'
#' This "real world" dataset is the result of a study by H.S. Lew of the Structures
#'     Division of the Cednter for Building Technology at the National Institute of
#'     Standards & Technology (NIST). The purpose of the study was to characterize
#'     the physical behavior of steel-concrete beams under periodic load. The rsponse
#'     variable is deflection (from the rest point) of the stel-concrete beam. the 200
#'     observations were collected equi-spaced in time.
#'
#'     \tabular{lr}{
#'     \strong{Level of Difficulty} \tab Lower\cr
#'     \strong{Variables} \tab 1\cr
#'     \strong{Observations} \tab 200\cr
#'     \strong{First observation} \tab -213\cr
#'     \strong{Expected results} (as certified)\tab \cr
#'     \strong{Mean} \tab -177.435000000000\cr
#'     \strong{Standard Deviation} \tab 277.332168044316\cr
#'     \strong{Population lag-1 autocorrelation coefficient} \tab -0.307304800605679\cr}

#'
#' @format 200 observation of 1 variable:
#'
#' @source \url{http://www.itl.nist.gov/div898/strd/univ/lew.html}
#'
#' @examples
#' Lew
"Lew"


#' NumAcc4 NIST Univariate Data Set.
#'
#' Dataset of 1001 9-digit points
#'
#' This generated/fabricated dataset consists of 1001 9-digit floating-point
#'     values: a single 10000000.2, followed by 500 pairings of 10000000.1 and
#'     10000000.3. By construction, this data set has sample mean = 10000000.2
#'     (exact); sample standard deviation = .1 (exact); and sample autocorrelation
#'     coef. = -0.999 (exact). The construction was carried out based on
#'     considerations described by Simon, Stephen D. and Lesage, James P. (1989):
#'     Assessing the Accuracy of ANOVA Caluclations in Statistical Software",
#'     Computational Statistics \& data Analysis, 8, pp. 325-332.


#'
#'     \tabular{lr}{
#'     \strong{Level of Difficulty} \tab Higher\cr
#'     \strong{Variables} \tab 1\cr
#'     \strong{Observations} \tab 1001\cr
#'     \strong{First observation} \tab 100000000.2\cr
#'     \strong{Expected results} (as certified)\tab \cr
#'     \strong{Mean} \tab 10000000.2 (exact)\cr
#'     \strong{Standard Deviation} \tab 0.1 (exact)\cr
#'     \strong{Population lag-1 autocorrelation coefficient} \tab -0.999 (exact)\cr}

#'
#' @format 1001 observation of 1 variable:
#'
#' @source \url{http://www.itl.nist.gov/div898/strd/univ/numacc4.html}
#'
#' @examples
#' NumAcc4
"NumAcc4"


#' NumAcc3 NIST Univariate Data Set.
#'
#' Dataset of 1001 8-digit points
#'
#' This generated/fabricated dataset consists of 1001 8-digit floating-point
#'     values: a single 1000000.2, followed by 500 pairings of 1000000.1 and
#'     1000000.3. By construction, this data set has sample mean = 1000000.2
#'     (exact); sample standard deviation = .1 (exact); and sample autocorrelation
#'     coef. = -0.999 (exact). The construction was carried out based on
#'     considerations described by Simon, Stephen D. and Lesage, James P. (1989):
#'     Assessing the Accuracy of ANOVA Caluclations in Statistical Software",
#'     Computational Statistics \& data Analysis, 8, pp. 325-332.
#'
#'     \tabular{lr}{
#'     \strong{Level of Difficulty} \tab Average\cr
#'     \strong{Variables} \tab 1\cr
#'     \strong{Observations} \tab 1001\cr
#'     \strong{First observation} \tab 1000000.2\cr
#'     \strong{Expected results} (as certified)\tab \cr
#'     \strong{Mean} \tab 1000000.2 (exact)\cr
#'     \strong{Standard Deviation} \tab 0.1 (exact)\cr
#'     \strong{Population lag-1 autocorrelation coefficient} \tab -0.999 (exact)\cr}

#'
#' @format 1001 observation of 1 variable:
#'
#' @source \url{http://www.itl.nist.gov/div898/strd/univ/numacc3.html}
#'
#' @examples
#' NumAcc3
"NumAcc3"


#' NumAcc2 NIST Univariate Data Set.
#'
#' Dataset of 1001 2-digit points
#'
#' This generated/fabricated dataset consists of 1001 2-digit floating-point
#'      values: a single 1.2, followed by 500 pairings of 1.1 and 1.3. By
#'      construction, this data set has sample mean = 1.2 (exact); sample
#'      standard deviation = 0.1 (exact); and sample autocorrelation coef. = -0.999
#'      (exact). The construction was carried out based on considerations
#'      described by Simon, Stephen D. and Lesage, James P. (1989): Assessing
#'      the Accuracy of ANOVA Caluclations in Statistical Software", Computational
#'      Statistics \& data Analysis, 8, pp. 325-332.
#'
#'     \tabular{lr}{
#'     \strong{Level of Difficulty} \tab Average\cr
#'     \strong{Variables} \tab 1\cr
#'     \strong{Observations} \tab 1001\cr
#'     \strong{First observation} \tab 1.2\cr
#'     \strong{Expected results} (as certified)\tab \cr
#'     \strong{Mean} \tab 1.2 (exact)\cr
#'     \strong{Standard Deviation} \tab 0.1 (exact)\cr
#'     \strong{Population lag-1 autocorrelation coefficient} \tab -0.999 (exact)\cr}
#'
#' @format 101 observation of 1 variable:
#'
#' @source \url{http://www.itl.nist.gov/div898/strd/univ/numacc2.html}
#'
#' #' @examples
#' NumAcc2
"NumAcc2"


#' NumAcc1 NIST Univariate Data Set.
#'
#' Dataset of 3 8-digit points
#'
#' This generated/fabricated dataset consists of three 8-digit integers
#'     differing only in the least significant digit. The data set is: 10000002,
#'     10000001, and 10000003. By construction, this data set has sample
#'     mean = 10000002 (exact); sample standard deviation = 1 (exact); and
#'     sample autocorrelation coef. = -0.5 (exact). The construction was carried
#'     out based on considerations described by Simon, Stephen D. and Lesage,
#'     James P. (1989): Assessing the Accuracy of ANOVA Caluclations in Statistical
#'     Software", Computational Statistics \& data Analysis, 8, pp. 325-332
#'
#'     \tabular{lr}{
#'     \strong{Level of Difficulty} \tab Average\cr
#'     \strong{Variables} \tab 1\cr
#'     \strong{Observations} \tab 1001\cr
#'     \strong{First observation} \tab 10000001\cr
#'     \strong{Expected results} (as certified)\tab \cr
#'     \strong{Mean} \tab 10000002 (exact)\cr
#'     \strong{Standard Deviation} \tab 1 (exact)\cr
#'     \strong{Population lag-1 autocorrelation coefficient} \tab -0.5 (exact)\cr}

#'
#' @format 3 observation of 1 variable:
#'
#' @source \url{http://www.itl.nist.gov/div898/strd/univ/NumAcc1.html}
#'
#' #' @examples
#' NumAcc1
"NumAcc1"


#' Michelso NIST Univariate Data Set.
#'
#' Dataset of 100 points
#'
#' This "real world" dataset is the result of the classic study conducted by
#'     Michelson on the speed of light in air in 1879. The response variable is
#'     speed of light (in millions of meters per second). The data was included
#'     as part of a larger study by Dorsey, Ernest N. (1944) on the velocity of
#'     light as reported in the Transactions of the American Philosophical Society.
#'
#'     \tabular{lr}{
#'     \strong{Level of Difficulty} \tab Lower\cr
#'     \strong{Variables} \tab 1\cr
#'     \strong{Observations} \tab 100\cr
#'     \strong{First observation} \tab 299.85\cr
#'     \strong{Expected results} (as certified)\tab \cr
#'     \strong{Mean} \tab 299.852400000000\cr
#'     \strong{Standard Deviation} \tab 0.0790105478190518\cr
#'     \strong{Population lag-1 autocorrelation coefficient} \tab 0.535199668621283\cr}

#'
#' @format 100 observation of 1 variable:
#'
#' @source \url{http://www.itl.nist.gov/div898/strd/univ/Michelso.html}
#'
#' #' @examples
#' Michelso
"Michelso"


#' Mavro NIST Univariate Data Set.
#'
#' Dataset of 50 points
#'
#' This "real world" dataset is the result of a study by Radu Mavrodineaunu, a
#'     chemist at the National Institute of Standards & Technology (NIST). The
#'     purpose of the study was to determine a certified transmittance value
#'     that may be attached to the particular of filter under study. The 50
#'     transmittance valuess were collected equi-spaced in time at a sampling
#'     rate of 10 observations per second.
#'
#'     \tabular{lr}{
#'     \strong{Level of Difficulty} \tab Lower\cr
#'     \strong{Variables} \tab 1\cr
#'     \strong{Observations} \tab 50\cr
#'     \strong{First observation} \tab 2.00180\cr
#'     \strong{Expected results} (as certified)\tab \cr
#'     \strong{Mean} \tab 2.00185600000000\cr
#'     \strong{Standard Deviation} \tab 0.000429123454003053\cr
#'     \strong{Population lag-1 autocorrelation coefficient} \tab 0.937989183438248\cr}

#'
#' @format 50 observation of 1 variable:
#'
#' @source \url{http://www.itl.nist.gov/div898/strd/univ/Mavro.html}
#'
#' #' @examples
#' Mavro
"Mavro"


#' Lottery NIST Univariate Data Set.
#'
#' Dataset of 218 3-digit points
#'
#' This dataset consists of 218 3-digit numbers (from 000 to 999) resulting from
#'     the state of Maryland's Pick-3 Lottery. The data was collected for the
#'     32-week period September 3, 1989 to April 14, 1990. One 3-digit random
#'     number was drawn per day, 7 days per week for most weeks, but 6 or 5 days
#'     per week for other weeks. Interesting data-analytic questions involving
#'     the dataset are 1) are the lottery numbers uniformly distributed? and 2)
#'     is there serial correlation between lottery numbers?
#'
#'
#'     \tabular{lr}{
#'     \strong{Level of Difficulty} \tab Lower\cr
#'     \strong{Variables} \tab 1\cr
#'     \strong{Observations} \tab 218\cr
#'     \strong{First observation} \tab 162\cr
#'     \strong{Expected results} (as certified)\tab \cr
#'     \strong{Mean} \tab 518.958715596330\cr
#'     \strong{Standard Deviation} \tab 291.699727470969\cr
#'     \strong{Population lag-1 autocorrelation coefficient} \tab -0.120948622967393\cr}

#'
#' @format 218 observation of 1 variable:
#'
#' @source \url{http://www.itl.nist.gov/div898/strd/univ/lottery.html}
#'
#' #' @examples
#' Lottery
"Lottery"



#' Pi Digits NIST Univarent Data Set.
#'
#' Dataset of 5000 points
#'
#' This dataset consists of the first 5000 digits of the mathemtatical constant
#'     pi (= 3.1415926535897932384...). These 5000 digits were reported in
#'     Mathematics of Computation, January 1962, page 76. Interesting
#'     number-theoretic questions involving pi digits are 1) are the digits
#'     uniformly distributed? and 2) is there serial correlation between
#'     successive digits?
#'
#'     \tabular{lr}{
#'     \strong{Level of Difficulty} \tab Lower\cr
#'     \strong{Variables} \tab 1\cr
#'     \strong{Observations} \tab 5000\cr
#'     \strong{First observation} \tab 3\cr
#'     \strong{Expected results} (as certified)\tab \cr
#'     \strong{Mean} \tab 4.53480000000000\cr
#'     \strong{Standard Deviation} \tab 2.86733906028871\cr
#'     \strong{Population lag-1 autocorrelation coefficient} \tab -0.00355099287237972\cr}

#'
#' @format 218 observation of 1 variable:
#'
#' @source \url{http://www.itl.nist.gov/div898/strd/univ/pidigits.html}
#'
#' #' @examples
#' PiDigits
"PiDigits"