Type:	Package
Title:	Functions for Wayne W. Daniel's Biostatistics, Tenth Edition
Version:	0.2.6
Date:	2024-10-15
Description:	Functions to accompany Wayne W. Daniel's Biostatistics: A Foundation for Analysis in the Health Sciences, Tenth Edition.
License:	GPL-2
Encoding:	UTF-8
Depends:	R (≥ 4.4)
Imports:	cli, e1071, methods, pracma, vcd
Suggests:	BSDA, car, DescTools, mblm, psych, reshape2, robslopes, survival
Language:	en-US
LazyData:	true
LazyDataCompression:	xz
RoxygenNote:	7.3.2
NeedsCompilation:	no
Packaged:	2024-10-15 18:05:44 UTC; tingtingzhan
Author:	Tingting Zhan [aut, cre, cph]
Maintainer:	Tingting Zhan <tingtingzhan@gmail.com>
Repository:	CRAN
Date/Publication:	2024-10-15 20:40:02 UTC

Functions for Wayne W. Daniel's Biostatistics (Tenth Edition)

Description

Functions and examples to accompany Wayne W. Daniel's Biostatistics: A Foundation for Analysis in the Health Sciences, Tenth Edition, Wiley, ISBN: 978-1-119-62550-6.

https://www.wiley.com/en-us/Biostatistics:+A+Foundation+for+Analysis+in+the+Health+Sciences,+10th+Edition-p-9781119625506

Data sets from 10th edition https://bcs.wiley.com/he-bcs/Books?action=resource&bcsId=7849&itemId=1118302796&resourceId=30373.

Resources from 11th edition https://bcs.wiley.com/he-bcs/Books?action=index&bcsId=11491&itemId=1119496578, with errata of data.

Author(s)

Maintainer: Tingting Zhan tingtingzhan@gmail.com (ORCID) [copyright holder]

Chapter 1: Introduction to Biostatistics

Description

Functions and examples for Chapter 1, Introduction to Biostatistics.

Usage

sampleRow(x, size, replace = FALSE, prob = NULL)

Arguments

Value

Function sampleRow returns a data.frame, a simple random sample from the input.

See Also

sample.int

Examples

library(DanielBiostatistics10th)
# To run a line of code, use shortcut
# Command + Enter: Mac and RStudio Cloud
# Control + Enter: Windows, Mac and RStudio Cloud
# To clear the console
# Control + L: Windows, Mac and RStudio Cloud

# Example 1.4.1; Page 8 (10th ed), Page 7 (11th ed)
class(EXA_C01_S04_01) # `EXA_C01_S04_01` is a 'data.frame' (a specific class defined in R)
dim(EXA_C01_S04_01) # dimension, number-row and number-column
head(EXA_C01_S04_01, n = 8L) # first `n` rows of a 'data.frame'
names(EXA_C01_S04_01) # column names of a 'data.frame'
EXA_C01_S04_01$AGE # use `$` to obtain one column from a 'data.frame' 
sampleRow(EXA_C01_S04_01, size = 10L, replace = FALSE) # to answer Example 1.4.1

# Example 1.4.2; Page 11 (10th ed), Page 10 (11th ed)
EXA_C01_S04_01[seq.int(from = 4L, to = 166L, by = 18L), ]

Chapter 2: Descriptive Statistics

Description

Functions and examples for Chapter 2, Descriptive Statistics.

Usage

print_stats(x, na.rm = TRUE)

print_freqs(x, breaks, include.lowest = TRUE, right = TRUE)

Arguments

Details

Function print_freqs prints the (relative) frequencies and cumulative (relative) frequencies, from a numeric input vector, specified interval breaks as well as open/close status of the ends of the intervals.

Function print_stats prints the simple statistics of the input observations, such as sample size, mean, median, (smallest) mode, variance, standard deviation, coefficient of variation (if all observations are non-negative), quartiles, inter-quartile range (IQR), range, skewness and kurtosis. A histogram is also printed.

Value

Function print_freqs returns a freqs object, for which a show method is defined.

Function print_stats does not have a returned value.

See Also

cut.default table cumsum mean.default median.default Mode var sd quantile skewness kurtosis

Examples

library(DanielBiostatistics10th)

# Example 2.2.1; Page 20 (10th ed), Page 19 (11th ed)
head(EXA_C01_S04_01)
class(age <- EXA_C01_S04_01$AGE) # 'integer'
sort(age) # Table 2.2.1

# Example 2.3.1; Page 23 (10th ed); Page 22 (11th ed)
(r231 = print_freqs(age, breaks = seq.int(from=30, to=90, by=10), right = FALSE)) # Table 2.3.2
# The open/close of interval ends is determined by textbook using 30-39, 40-49, etc.

# Example 2.4.1-2.4.6; Page 38-42 (10th ed); Page 30-34 (11th ed)
# Example 2.5.1-2.5.3; Page 44-46 (10th ed); Page 35-41 (11th ed)
print_stats(age)

# Example 2.5.4 (omitted); Page 49 (10th ed), Page 41 (11th ed)

# Example 2.5.5; Page 50 (10th ed)
head(EXA_C02_S05_05)
boxplot(EXA_C02_S05_05$GRF, main = c('Example 2.5.5 (10th ed)'))
print_stats(EXA_C02_S05_05$GRF)
print_freqs(EXA_C02_S05_05$GRF, breaks = seq.int(10, 45, by = 5))

Chapter 3: Some Basic Probability Concepts

Description

Examples in Chapter 3, Some Basic Probability Concepts.

Value

No function defined for Chapter 3.

Examples

library(DanielBiostatistics10th)

# Example 3.4.1-3.4.9; Page 69-75 (10th ed), Page 61-67 (11th ed)
(d341 = matrix(c(28L, 19L, 41L, 53L, 35L, 38L, 44L, 60L), ncol = 2L, dimnames = list(
  FamilyHx = c('none', 'Bipolar', 'Unipolar', 'UniBipolar'), Onset = c('Early', 'Late'))))
class(d341) # 'matrix', i.e., a two-dimensional 'array'
addProbs(d341)
addProbs(d341, margin = 2L)
addProbs(d341, margin = 1L)

# Example 3.5.1; Page 81 (10th ed), Page 72 (11th ed)
(d351 = matrix(c(495L, 14L, 5L, 436L), nrow = 2L, dimnames = list(
  Alzheimer = c('No', 'Yes'), Test = c('Negative', 'Positive'))))
print(binTab(d351), prevalence = .113)

Chapter 4: Probability Distributions

Description

Examples in Chapter 4, Probability Distributions.

Value

No function defined for Chapter 4.

Examples

library(DanielBiostatistics10th)

# Example 4.2.1-4.2.7; Page 93-97 (10th ed), Page 81-85 (11th ed)
(d421 = rep(1:8, times = c(62L, 47L, 39L, 39L, 58L, 37L, 4L, 11L)))
print_freqs(d421) # Table 4.2.1, 4.2.2, Table 4.2.3

# Example 4.2.8; Page 98 (10th ed), Page 85 (11th ed)
mean(d421)
sd(d421)
var(d421)

# ?dbinom # 'd' for binomial 'density'; calculate Prob(X = x)
# ?pbinom # 'p' for binomial 'probability' 
# `lower.tail = TRUE` (default), calculate Prob(X <= x)
# `lower.tail = FALSE`, calculate Prob(X > x)

# Example 4.3.1; Page 99 (10th ed)
dbinom(x = 3L, size = 5L, prob = .858)
# Example 4.3.1; Page 87 (11th ed) 
dbinom(x = 3L, size = 5L, prob = .899)

# Example 4.3.2; Page 103 (10th ed), Page 90 (11th ed)
dbinom(x = 4L, size = 10L, prob = .14)

# Example 4.3.3; Page 103 (10th ed), Page 91 (11th ed)
(pL = pbinom(q = 5L, size = 25L, prob = .1, lower.tail = TRUE)) # (a) P(X <= 5L)
(pU = pbinom(q = 5L, size = 25L, prob = .1, lower.tail = FALSE)) # (b) P(X > 5L)
pL + pU # = 1

# Example 4.3.4; Page 105 (10th ed), Page 92 (11th ed) 
dbinom(x = 7L, size = 12L, prob = .55)
pbinom(q = 5L, size = 12L, prob = .55)
pbinom(q = 7L, size = 12L, prob = .55, lower.tail = FALSE)

# Example 4.4.1; Page 110 (10th ed), Page 97 (11th ed) 
dpois(x = 3L, lambda = 12) 

# Example 4.4.2; Page 110 (10th ed), Page 98 (11th ed) 
ppois(q = 2L, lambda = 12, lower.tail = FALSE)

# Example 4.4.3; Page 110 (10th ed), Page 98 (11th ed) 
ppois(q = 1L, lambda = 2) 

# Example 4.4.4; Page 111 (10th ed), Page 98 (11th ed) 
dpois(x = 3L, lambda = 2)

# Example 4.4.5; Page 112 (10th ed), Page 98 (11th ed) 
ppois(q = 5L, lambda = 2, lower.tail = FALSE)

# Example 4.6.1; Page 119 (10th ed), Page 106 (11th ed) 
pnorm(q = 2)

# Example 4.6.2; Page 120 (10th ed), Page 106 (11th ed) 
pnorm(2.55) - pnorm(-2.55)
1 - 2 * pnorm(-2.55) # alternative solution

# Example 4.6.3; Page 121 (10th ed), Page 107 (11th ed) 
pnorm(1.53) - pnorm(-2.74)

# Example 4.6.4; Page 121 (10th ed), Page 107 (11th ed) 
pnorm(2.71, lower.tail = FALSE)

# Example 4.6.5; Page 122 (10th ed), Page 107 (11th ed) 
pnorm(2.45) - pnorm(.84)

# Example 4.7.1; Page 122 (10th ed), Page 109 (11th ed) 
pnorm(q = 3, mean = 5.4, sd = 1.3)
pnorm(q = (3-5.4)/1.3) # manual solution

# Example 4.7.2; Page 125 (10th ed), Page 111 (11th ed) 
pnorm(q = 649, mean = 491, sd = 119) - pnorm(q = 292, mean = 491, sd = 119)

# Example 4.7.3; Page 122 (10th ed), Page 111 (11th ed) 
1e4L * pnorm(q = 8.5, mean = 5.4, sd = 1.3, lower.tail = FALSE)

Chapter 5, 6 and 7

Description

Functions for Chapter 5, Some Important Sampling Distributions, Chapter 6, Estimation and Chapter 7, Hypothesis Testing.

Usage

aggregated_z(
  xbar,
  n,
  sd,
  null.value,
  alternative = c("two.sided", "less", "greater"),
  conf.level = 0.95,
  ...
)

aggregated_t(
  xbar,
  xsd,
  n,
  null.value,
  var.equal = FALSE,
  alternative = c("two.sided", "less", "greater"),
  conf.level = 0.95,
  ...
)

prop_CLT(
  x,
  n,
  obs,
  xbar = x/n,
  null.value,
  alternative = c("two.sided", "less", "greater"),
  conf.level = 0.95,
  ...
)

aggregated_var(
  xsd,
  n,
  null.value,
  alternative = c("two.sided", "less", "greater"),
  conf.level = 0.95,
  ...
)

Arguments

Details

Function aggregated_z performs one- or two-sample z-test using the aggregated statistics of sample mean(s) and sample size(s) when null.value is provided. Otherwise, only the confidence interval based on z-distribution is computed.

Function aggregated_t performs one- or two-sample t-test using the aggregated statistics of sample mean(s), sample standard deviation(s) and sample size(s) when null.value is provided. Otherwise, only the confidence interval based on t-distribution is computed.

Function prop_CLT performs one- or two-sample z-test on proportion(s), using Central Limit Theorem when null.value is provided. Otherwise, only the confidence interval based on z-distribution is computed.

Function aggregated_var performs one-sample \chi^2-test on variance, or two-sample F-test on variances, using the aggregated statistics of sample standard deviation(s) and sample size(s) when null.value is provided. Otherwise, only the confidence interval based on \chi^2- or F-distribution is computed.

Value

Function aggregated_z returns an 'htest' object when null.value is provided, otherwise returns a length-two numeric vector.

Function aggregated_t returns an htest object when null.value is provided, otherwise returns a length-two numeric vector.

Function prop_CLT returns an htest object when null.value is provided, otherwise returns a length-two numeric vector.

Function aggregated_var returns an htest object when null.value is provided, otherwise returns a length-two numeric vector.

See Also

t.test prop.test var.test

Examples

library(DanielBiostatistics10th)

# Example 5.3.2; Page 142 (10th ed)
aggregated_z(xbar = 190, sd = 12.7, n = 10L, null.value = 185.6, alternative = 'greater')

# Example 5.3.3; 
# Page 143 (10th ed)
pnorm(125, mean = 120, sd = 15/sqrt(50)) - pnorm(115, mean = 120, sd = 15/sqrt(50))
aggregated_z(125, sd = 15, n = 50L, null.value = 120, alternative = 'less')$p.value - 
  aggregated_z(115, sd = 15, n = 50L, null.value = 120, alternative = 'less')$p.value
# Page 127 (11th ed)
aggregated_z(110, sd = 20, n = 50L, null.value = 100, alternative = 'less')$p.value - 
  aggregated_z(95, sd = 20, n = 50L, null.value = 100, alternative = 'less')$p.value

# Example 5.4.1; Page 145 (10th ed), Page 129 (11th ed) 
aggregated_z(xbar = c(92, 105), sd = 20, n = 15L, null.value = 0, alternative = 'less') 

# Example 5.4.2; Page 148 (10th ed), 
aggregated_z(xbar = 20, sd = c(15, 20), n = c(35L, 40L), null.value = c(45, 30), 
  alternative = 'greater')

# Example 5.5.1; Page 150 (10th ed), 
prop_CLT(xbar = .4, n = 150L, null.value = .357, alternative = 'greater')

# Example 5.5.2; Page 152 (10th ed), 
prop_CLT(xbar = .45, n = 200L, null.value = .51, alternative = 'less')

# Example 5.6.1; Page 155 (10th ed), 
prop_CLT(xbar = .1, null.value = c(.28, .21), n = c(100L, 100L), alternative = 'greater')

# Example 5.6.2; Page 155 (10th ed), 
prop_CLT(xbar = .05, null.value = c(.34, .26), n = c(250L, 200L), alternative = 'less')

# Example 6.2.1; Page 166 (10th ed), Page 147 (11th ed)
aggregated_z(xbar = 22, n = 10L, sd = sqrt(45))

# Example 6.2.2; Page 168 (10th ed), Page 149 (11th ed)
aggregated_z(xbar = 84.3, n = 15L, sd = sqrt(144), conf.level = .99)

# Example 6.2.3; Page 168 (10th ed), Page 150 (11th ed)
aggregated_z(xbar = 17.2, n = 35L, sd = 8, conf.level = .9)

# Example 6.2.4; Page 169 (10th ed), Page 150 (11th ed)
head(EXA_C06_S02_04)
aggregated_z(xbar = mean(EXA_C06_S02_04$ACTIVITY), n = nrow(EXA_C06_S02_04), sd = sqrt(.36))

# Example 6.3.1; Page 173 (10th ed), 
aggregated_t(xbar = 250.8, xsd = 130.9, n = 19L)

# Example 6.4.1; Page 177 (10th ed), 
aggregated_z(xbar = c(4.5, 3.4), sd = sqrt(c(1, 1.5)), n = c(12L, 15L))

# Example 6.4.2; Page 178 (10th ed), 
aggregated_z(xbar = c(4.3, 13), sd = c(5.22, 8.97), n = c(328L, 64L), conf.level = .99)

# Example 6.4.3; Page 180 (10th ed), 
aggregated_t(xbar = c(4.7, 8.8), xsd = c(9.3, 11.5), n = c(18L, 10L), var.equal = TRUE)

# Example 6.4.4; Page 181 (10th ed), 
aggregated_t(xbar = c(4.7, 8.8), xsd = c(9.3, 11.5), n = c(18L, 10L)) 
# Welch slightly different from Cochran; textbook explained on Page 182

# Example 6.5.1; Page 185 (10th ed), 
prop_CLT(xbar = .18, n = 1220L)

# Example 6.6.1; Page 187 (10th ed), 
prop_CLT(x = c(31L, 53L), n = c(68L, 255L), conf.level = .99)

# Example 6.7.1; Page 190 (10th ed), 
(n_671 = uniroot(f = function(n, sd, level = .95) {
  qnorm(1-(1-level)/2) * sd/sqrt(n) - 5 # half-width of CI <= 5 grams
}, interval = c(0, 2e2), sd = 20)$root)
ceiling(n_671)

# Example 6.8.1; Page 192 (10th ed), 
(n_681 = uniroot(f = function(n, p, level = .95) {
  qnorm(1-(1-level)/2) * sqrt(p*(1-p)/n) - .05
}, interval = c(0, 1e3), p = .35)$root)
ceiling(n_681)

# Example 6.9.1; Page 196 (10th ed), 
d691 = c(9.7, 12.3, 11.2, 5.1, 24.8, 14.8, 17.7)
sqrt(aggregated_var(xsd = sd(d691), n = length(d691)))

# Example 6.10.1; Page 200 (10th ed), 
aggregated_var(xsd = c(8.1, 5.9), n = c(16L, 4L))

# Example 7.2.1; Page 222 (10th ed); Page 201 (11th ed)
aggregated_z(xbar = 27, sd = sqrt(20), n = 10L, null.value = 30)

# Example 7.2.2; Page 226 (10th ed); Page 204 (11th ed)
aggregated_z(xbar = 27, sd = sqrt(20), n = 10L, null.value = 30, alternative = 'less')

# Example 7.2.3; Page 228 (10th ed); Page 206 (11th ed)
head(EXA_C07_S02_03)
t.test(EXA_C07_S02_03$DAYS, mu = 15)

# Example 7.2.4; Page 231 (10th ed); Page 209 (11th ed)
aggregated_z(xbar = 146, sd = 27, n = 157L, null.value = 140, alternative = 'greater')

# Example 7.2.5; Page 232 (10th ed); Page 210 (11th ed)
d725 = c(33.38, 32.15, 34.34, 33.95, 33.46, 34.13, 33.99, 34.10, 33.85, 
  34.23, 34.45, 34.19, 33.97, 32.73, 34.05)
t.test(d725, mu = 34.5)

# Example 7.3.1; Page 237 (10th ed), Page 213 (11th ed) 
aggregated_z(xbar = c(4.5, 3.4), sd = sqrt(c(1, 1.5)), n = c(12L, 15L), null.value = 0)

# Example 7.3.2; Page 239 (10th ed), Page 215 (11th ed) 
head(EXA_C07_S03_02)
with(EXA_C07_S03_02, t.test(x = CONTROL, y = SCI, alternative = 'less', var.equal = TRUE))

# Example 7.3.3; Page 240 (10th ed), Page 217 (11th ed) 
aggregated_t(xbar = c(19.16, 9.53), xsd = c(5.29, 2.69), n = c(15L, 30L), null.value = 0)

# Example 7.3.4; Page 242 (10th ed), Page 219 (11th ed) 
aggregated_z(xbar = c(59.01, 46.61), sd = c(44.89, 34.85), n = c(53L, 54L), null.value = 0,
  alternative = 'greater')

# Example 7.4.1; Page 251 (10th ed), Page 226 (11th ed) 
head(EXA_C07_S04_01)
with(EXA_C07_S04_01, t.test(x = POSTOP, y = PREOP, alternative = 'greater', paired = TRUE))

# Example 7.5.1; Page 258 (10th ed), Page 232 (11th ed) 
prop_CLT(x = 24L, n = 301L, null.value = .063, alternative = 'greater') 

# Example 7.6.1; Page 261 (10th ed), Page 235 (11th ed) 
prop_CLT(x = c(24L, 11L), n = c(44L, 29L), null.value = 0, alternative = 'greater')

# Example 7.7.1; Page 264 (10th ed), Page 238 (11th ed) 
head(EXA_C07_S07_01)
aggregated_var(xsd = sd(EXA_C07_S07_01$mass), n = 16L, null.value = 600)

# Example 7.8.1; Page 268 (10th ed), Page 242 (11th ed) 
aggregated_var(xsd = c(30.62, 11.37), n = 6L, null.value = 1, alternative = 'greater')

# Example 7.8.2; Page 270 (10th ed), 
with(EXA_C07_S03_02, var.test(x = CONTROL, y = SCI))

Chapter 7: Power Curve

Description

Functions for Chapter 7, Hypothesis Testing.

Usage

power_z(
  x,
  null.value,
  sd,
  n,
  alternative = c("two.sided", "less", "greater"),
  sig.level = 0.05
)

Arguments

Details

Function power_z calculates the powers at each element of the alternative parameters \mu_1, for one-sample z-test

• H_0: \mu = \mu_0 vs. H_A: \mu \neq \mu_0, if alternative = 'two.sided'

• H_0: \mu \leq \mu_0 vs. H_A: \mu > \mu_0, if alternative = 'greater'

• H_0: \mu \geq \mu_0 vs. H_A: \mu < \mu_0, if alternative = 'less'

Value

Function power_z returns a 'power_z' object, which inherits from 'power.htest' class.

See Also

power.t.test

Examples

library(DanielBiostatistics10th)

# Example 7.9.1; Page 272 (10th ed), Page 245 (11th ed) 
(p791 = power_z(seq.int(from = 16, to = 19, by = .5), null.value = 17.5, sd = 3.6, n = 100L))
# Table 7.9.1

# Example 7.9.2; Page 276 (10th ed), Page 248 (11th ed) 
(p792 = power_z(seq.int(from = 50, to = 70, by = 5), null.value = 65, sd = 15, n = 20L, 
                sig.level = .01, alternative = 'less'))

# Example 7.10.1; Page 278 (10th ed), 
(n_d7101 <- uniroot(f = function(x) {
  power_z(55, null.value = 65, sd = 15, n = x, sig.level = .01, alternative = 'less')$power - .95
}, interval = c(0, 50))$root)
power_z(55, null.value = 65, sd = 15, n = ceiling(n_d7101), sig.level = .01, alternative = 'less')

Chapter 8: Analysis of Variance

Description

Examples for Chapter 8, Analysis of Variance.

Value

No function defined for Chapter 8.

Examples

library(DanielBiostatistics10th)

# Example 8.2.1; Page 318 (10th ed), Page 280 (11th ed)
head(EXA_C08_S02_01)
boxplot(selenium ~ type, data = EXA_C08_S02_01, main = 'Figure 8.2.7')
(aov_d821 = aov(selenium ~ type, data = EXA_C08_S02_01)) 
# ?stats::aov # analysis-of-variance model
anova(aov_d821) 
# ?stats::anova # ANOVA table

# Example 8.2.2; Page 325 (10th ed), Page 286 (11th ed)
(tukey_d822 <- TukeyHSD(aov_d821, conf.level = 0.95)) # Figure 8.2.8
plot(tukey_d822)

# Example 8.3.1; Page 339 (10th ed), Page 298 (11th ed)
head(EXA_C08_S03_01)
head(d831 <- within(EXA_C08_S03_01, expr = {
  ageGroup = structure(ageGroup, levels = c('<20', '20s', '30s', '40s', '>50'), class = 'factor')
}))
(aov_831 = aov(time ~ method + ageGroup, data = d831))
anova(aov_831)

# Example 8.4.1; Page 348 (10th ed), Page 307 (11th ed)
head(EXA_C08_S04_01)
head(d841 <- within(EXA_C08_S04_01, expr = {
  SUBJ = factor(SUBJ)
  TIME = structure(TIME, levels = c('Baseline', '1-Mon', '3-Mon', '6-Mon'), class = 'factor')
}))
(aov_841 = aov(FUNC ~ SUBJ + TIME, data = d841))
anova(aov_841)

# Example 8.4.2; Page 352 (10th ed), Page 310 (11th ed)
# (optional; out of the scope of this course)
head(EXA_C08_S04_02)
names(EXA_C08_S04_02)[3:6] = c('baseline', '2wk', '4wk', '6wk')
head(d842a <- within(EXA_C08_S04_02, expr = {
  subject = factor(subject)
  treatment = structure(treatment, levels = c('placebo', 'aloe_juice'), class = 'factor')
}))
head(d842b <- reshape2::melt(d842a, id.vars = c('subject', 'treatment'), 
                             variable.name = 'time', value.name = 'OralScores'))
# Hypothesis: 
# Main effect of 'treatment';
# Main effect of 'time';
# Interaction between 'treatment' and 'time'
(aov_842 = aov(OralScores ~ treatment * time + Error(subject), data = d842b))
class(aov_842)
summary(aov_842)
# Section 'Error: subject' in R output
# .. is Figure 8.4.4 'Tests of Between-Subjects Effects' (without the row of 'Intercept')
# .. 'treatment' row: effect of treatment at **baseline** (i.e. reference time), 
# ... degree-of-freedom (dof) = 2-1 = 1
# .. 'Residuals' row: residual at baseline, dof = (25-1) - (2-1) = 23
# .. It's important to note that 'treatment' is a **between-subject factor**.
# Section 'Error: Within' in R output
# .. is Figure 8.4.4 'Tests of Within-Subjects Effects'
# .. 'time' row: effect of time within subject for placebo (i.e. reference treatment), dof = 4-1 = 3
# .. 'treatment:time' row: interation of treatment and time, dof = (2-1)*(4-1) = 3
# .. 'Residuals' row: residual at 2wk, 4wk and 6wk, dof = (4-1)*23 = 69 
# ... [(4-1) timepoints, 23 dof at each timepoints]
# Analysis Interpretation
# .. No signif. diff. detected between placebo vs. aloe at baseline (p = .815)
# .. No signif. diff. detected in the trends over time between placebo vs. aloe (p = .974)
# .. Signif. diff. detected among the four timepoints, for either placebo or aloe pts (p = 3e-7)
# R code below creates an equivalent ANOVA model
anova(aov(OralScores ~ treatment * time + subject, data = d842b))
# .. 'subject' is considered as a block factor 

# Example 8.5.2; Page 364 (10th ed), Page 321 (11th ed)
head(EXA_C08_S05_02)
head(d852 <- within(EXA_C08_S05_02, expr = {
  A = structure(A, levels = c('Cardiac', 'Cancer', 'CVA', 'Tuberculosis'), class = 'factor')
  B = structure(B, levels = c('20s', '30s', '40s', '50+'), class = 'factor')
}))
(aov_852 = aov(HOME ~ A * B, data = d852))
anova(aov_852)
summary(lm(HOME ~ A * B, data = d852)) 
# produces alpha, beta and (alpha beta)'s in the formulation 

Chapter 9: Simple Linear Regression and Correlation

Description

Examples in Chapter 9, Simple Linear Regression and Correlation.

Value

No function defined for Chapter 9.

Examples

library(DanielBiostatistics10th)

# Example 9.3.1; Page 417 (10th ed), Page 358 (11th ed) 
head(EXA_C09_S03_01)
names(EXA_C09_S03_01)[2:3] = c('Waist', 'AT')
plot(AT ~ Waist, data = EXA_C09_S03_01, 
     xlab = 'Waist circumference (cm), X', 
     ylab = 'Deep abdominal AT area (cm2), Y', 
     main = 'Figure 9.3.1')
m931 = lm(AT ~ Waist, data = EXA_C09_S03_01)
plot(AT ~ Waist, data = EXA_C09_S03_01, 
     xlab = 'Waist circumference (cm), X', 
     ylab = 'Deep abdominal AT area (cm2), Y', 
     main = 'Figure 9.3.3'); abline(m931, col = 'red', lty = 2)

# Example 9.4.1; Page 432 (10th ed), Page 372 (11th ed) 
anova(m931) # Table 9.4.1. Page 434 (10th ed)

# Example 9.4.2; Page 436 (10th ed), Page 375 (11th ed)
summary(m931)
confint(m931) # Page 438 (10th ed)

# (omitted) Example 9.4.3; Page 376 (11th ed) 

# (optional)
# Example 9.4.3; Page 440 (10th ed)
# Example 9.4.4; Page 379 (11th ed)
plot(m931, which = 1, main = 'Figure 9.4.8 (10th) or 9.4.9 (11th)')

# Example 9.7.1; Page 447 (10th ed), Page 386 (11th ed) 
head(EXA_C09_S07_01)
plot(CV ~ HEIGHT, data = EXA_C09_S07_01, 
     xlab = 'Height (cm)', 
     ylab = 'Cv (units)', 
     main = 'Figure 9.7.2')
m971 = lm(CV ~ HEIGHT, data = EXA_C09_S07_01)
summary(m971); anova(m971) # Figure 9.7.3; Page 450 (10th ed)

# Example 9.7.2; Page 452 (10th ed), Page 390 (11th ed) 
cor(EXA_C09_S07_01); 
cor.test(~ CV + HEIGHT, data = EXA_C09_S07_01) # Figure 9.7.4, 9.7.5

# Page 453, When the Hypothesized rho Is a Nonzero Value
# R does not have a function to do this

Chapter 10: Multiple Regression and Correlation

Description

Examples for Chapter 10, Multiple Regression and Correlation.

Value

No function defined for Chapter 10.

Examples

library(DanielBiostatistics10th)

# Example 10.3.1; Page 493 (10th ed), Page 419 (11th ed) 
head(EXA_C10_S03_01)
pairs(EXA_C10_S03_01, main = 'Figure 10.3.1')
m1031 = lm(CDA ~ AGE + EDLEVEL, data = EXA_C10_S03_01)
summary(m1031)

# Example 10.4.1; Page 502 (10th ed), Page 428 (11th ed) 
# .. see 'Multiple R-squared' (not 'Adjusted R-squared')

# Example 10.4.2; Page 504 (10th ed), Page 429 (11th ed) 
# .. see 'F-statistic'

# Example 10.4.3; Page 505 (10th ed), Page 430 (11th ed) 
# .. see 'Coefficients:'

# confidence interval for beta's; Page 506 (10th ed), Page 431 (11th ed) 
confint(m1031)

# Example 10.5.1; Page 509 (10th ed), Page 434 (11th ed) 
(newd_1031 = data.frame(AGE = 68, EDLEVEL = 12))
predict(m1031, newdata = newd_1031, interval = 'prediction')
predict(m1031, newdata = newd_1031, interval = 'confidence')

# Example 10.6.1; Page 511 (10th ed), Page 436 (11th ed) 
head(EXA_C10_S06_01)
pairs(EXA_C10_S06_01, main = 'Scatter Plot Matrix, Example 10.6.1')
m1061 = lm(W ~ P + S, data = EXA_C10_S06_01)
summary(m1061)
confint(m1061)
anova(m1061)

# (optional)
# Example 10.6.2; Page 515 (10th ed), Page 440 (11th ed)  
psych::partial.r(EXA_C10_S06_01, x = 2:3, y = 1L)

Chapter 11: Regression Analysis: Some Additional Techniques

Description

Examples in Chapter 11, Regression Analysis: Some Additional Techniques.

Value

No function defined for Chapter 11.

Examples

library(DanielBiostatistics10th)

# Example 11.1.1; Page 540, 
head(EXA_C11_S01_01)
head(log(EXA_C11_S01_01$conc, base = 10))
head(EXA_C11_S01_01$logConc)

# Example 11.1.2; Page 542, 
head(EXA_C11_S01_02)
cor.test(~ sbp + weight, data = EXA_C11_S01_02)
cor.test(~ sbp + bmi, data = EXA_C11_S01_02) 

# Example 11.2.1; Page 545, 
head(EXA_C11_S02_01)
d1121 = within(EXA_C11_S02_01, expr = {
  SMOKE = as.logical(SMOKE)
})
xlab1121 = 'Length of gestation (weeks)'; ylab1121 = 'Birth weight (grams)'
car::scatterplot(GRAMS ~ WEEKS | SMOKE, data = d1121, regLine = FALSE, smooth = FALSE,
            xlab = xlab1121, ylab = ylab1121, main = 'Figure 11.2.1')
m1121 = lm(GRAMS ~ WEEKS + SMOKE, data = d1121)
summary(m1121) # Figure 11.2.2
confint(m1121)
car::scatterplot(GRAMS ~ WEEKS | SMOKE, data = d1121, regLine = FALSE, smooth = FALSE,
            xlab = xlab1121, ylab = ylab1121, main = 'Figure 11.2.3')
(cf1121 = m1121$coefficients)
abline(a = cf1121[1L], b = cf1121[2L], col = 'blue') # regression line for non-smoking mothers
abline(a = cf1121[1L] + cf1121[3L], b = cf1121[2L], col = 'magenta') 

# Example 11.2.3; Page 551, 
d1123 = within(EXA_C11_S02_03, expr = {
  METHOD = factor(METHOD, levels = c('C', 'A', 'B')) # textbook designated 'C' as reference level
})
summary(m1123 <- lm(EFFECT ~ AGE * METHOD, data = d1123)) # Figure 11.2.5
confint(m1123)
car::scatterplot(EFFECT ~ AGE | METHOD, data = d1123, smooth = FALSE,
            xlab = 'Age', ylab = 'Treatment effectiveness', main = 'Figure 11.2.6')

# Example 11.3.1; Page 561, 
head(EXA_C11_S03_01)
names(EXA_C11_S03_01) = c('JOBPER', 'ASRV', 'ENTH', 'AMB', 'COMM', 'PROB', 'INIT')
summary(m1131_raw <- lm(JOBPER ~ ASRV + ENTH + AMB + COMM + PROB + INIT, data = EXA_C11_S03_01))
# summary(m1131 <- MASS::stepAIC(m1131_raw, direction = 'backward'))
# the stepwise selection criterion used in MINITAB is not necessarily AIC

# Example 11.4.1; Page 572, 
addmargins(d1141 <- array(c(92L, 21L, 15L, 20L), dim = c(2L, 2L), dimnames = list(
  OCAD = c('Present', 'Absent'), Sex = c('Male', 'Female')))) # Table 11.4.2
(d1141a = within(as.data.frame.table(as.table(d1141)), expr = {
  OCAD = (OCAD == 'Present')
  Sex = factor(Sex, levels = c('Female', 'Male'))
}))
m1141 = glm(OCAD ~ Sex, family = binomial, weights = Freq, data = d1141a)
summary(m1141) # Figure 11.4.1
exp(m1141$coefficients[2L]) # exp(beta_M)
exp(confint(m1141)) # confidence interval of exp(beta)
predict(m1141, newdata = data.frame(Sex = setNames(nm = c('Male', 'Female'))), type = 'response')

# Example 11.4.2; Page 573, 
head(EXA_C11_S04_02)
summary(m1142 <- glm(ATT ~ AGE, family = binomial, data = EXA_C11_S04_02)) # Figure 11.4.2
exp(m1142$coefficients[2L])
exp(confint(m1142))
car::Anova(m1142) # Optional

# Example 11.4.3; Page 576, 
head(REV_C11_24)
summary(glm(ONSET ~ HIAA + TRYPT, family = binomial, data = REV_C11_24)) # Figure 11.4.4
# Predictor TRYPT should be removed from model due to p-value \approx 1 
summary(glm(ONSET ~ HIAA, family = binomial, data = REV_C11_24)) 

# Example 11.4.4-11.4.5; Page 578-579
DescTools::PseudoR2(m1142, which = 'CoxSnell')
DescTools::PseudoR2(m1142, which = 'Nagelkerke')

Chapter 12: \chi^2 Distribution and the Analysis of Frequencies

Description

Functions for Chapter 12, The Chi-Square Distribution and the Analysis of Frequencies.

Usage

print_OE(O, prob)

Arguments

Value

Function print_OE prints a table with observed and expected frequencies, as well as the category-wise \chi^2 statistics. A double vector of the category-wise \chi^2 statistics is returned invisibly.

Examples

library(DanielBiostatistics10th)

# Example 12.3.1; Page 605 (10th ed)
d1231_b = c(-Inf, seq.int(from = 125, to = 275, by = 25), Inf)
(d1231 = setNames( # Table 12.3.1
  c(1L, 3L, 8L, 18L, 6L, 4L, 4L, 3L), 
  nm = levels(cut(double(), breaks = d1231_b, right = FALSE, include.lowest = TRUE))))
chi1231 = print_OE(d1231, prob = diff.default(pnorm(q = d1231_b, mean = 198.67, sd = 41.31)))
pchisq(sum(chi1231), df = length(d1231) - 3L, lower.tail = FALSE)
# -3L: three restrictions (explained on Page 608)
# (1) making sum(xo) == sum(xe)
# (2) estimating mean
# (3) estimating sd

# Example 12.3.2; Page 609 (10th ed), 
# 100 doctors, 25 patients per doctor
d1232 = c(5L, 6L, 8L, 10L, 10L, 15L, 17L, 10L, 10L, 9L, 0L)
o1232 = setNames(c(sum(d1232[1:2]), d1232[-(1:2)]), nm = c('0-1', 2:9, '10 or more'))
(p1232 = sum((0:10) * d1232) / (25 * 100)) # binomial `prob`
chi1232 = print_OE(o1232, prob = c(
  pbinom(1L, size = 25L, prob = p1232),
  dbinom(2:9, size = 25L, prob = p1232),
  pbinom(9, size = 25L, prob = p1232, lower.tail = FALSE)))
pchisq(sum(chi1232), df = length(o1232) - 2L, lower.tail = FALSE)
# -2L: two restrictions (explained on Page 611)
# (1) making sum(o) == sum(e)
# (2) estimating p1232

# Example 12.3.3; Page 611 (10th ed), 
d1233 = c(5L, 14L, 15L, 23L, 16L, 9L, 3L, 3L, 1L, 1L, 0L)
o_1233 = setNames(c(d1233[1:8], sum(d1233[-(1:8)])), nm = c(0:7, '8 or more'))
p_1233 = c(dpois(0:7, lambda = 3), # lambda = 3 is provided by the textbook
           ppois(7L, lambda = 3, lower.tail = FALSE))
chi1233 = print_OE(o_1233, prob = p_1233)
pchisq(sum(chi1233), df = length(o_1233) - 1L, lower.tail = FALSE)
# -1L: one restrictions
# (1) making sum(xo) == sum(xe)
chisq.test(o_1233, p = p_1233) # equivalent # warning on any(E < 5)

# Example 12.3.4; Page 614 (10th ed), Page 531 (11th ed) 
d1234 = c('Dec 05' = 62L, 'Jan 06' = 84L, 'Feb 06' = 17L, 'Mar 06' = 16L, 'Apr 06' = 21L)
print_OE(d1234) # Figure 12.3.2
chisq.test(d1234) 

# Example 12.3.5; Page 616 (10th ed), Page 533 (11th ed) 
d1235 = c(dominant = 43L, heterozygous = 125L, recessive = 32L)
print_OE(d1235, prob = c(1, 2, 1))
chisq.test(d1235, p = c(1, 2, 1), rescale.p = TRUE)

# Example 12.4.1; Page 621 (10th ed)
addmargins(d1241 <- array(c(260L, 15L, 7L, 299L, 41L, 14L), dim = c(3L, 2L), dimnames = list(
  Race = c('White', 'Black', 'Other'), FolicAcid = c('TRUE', 'FALSE'))))
chisq.test(d1241) # ?stats::chisq.test

# Example 12.4.2; Page 626 (10th ed), 
addmargins(d1242 <- array(c(131L, 14L, 52L, 36L), dim = c(2L, 2L), dimnames = list(
  Type = c('Faller', 'Non-Faller'), LifestyleChange = c('TRUE', 'FALSE'))))
chisq.test(d1242, correct = FALSE)
chisq.test(d1242, correct = TRUE) # Yates's Correction

# Example 12.5.1; Page 631 (10th ed), 
addmargins(d1251 <- array(c(21L, 19L, 75L, 77L), dim = c(2L, 2L), dimnames = list(
  Group = c('Narcoleptic', 'Healthy'), Migraine = c('TRUE', 'FALSE'))))
(chisq_1251 = chisq.test(d1251, correct = FALSE))
if (FALSE) {
  # (optional) using test on two proportions
  # only equivalent for 2*2 contingency table
  (clt_1251 = prop_CLT(x = c(21L, 19L), n = 96L, null.value = 0))
  all.equal.numeric(unname(clt_1251$statistic^2), unname(chisq_1251$statistic))
}

# Example 12.6.1; Page 638 (10th ed), 
addmargins(d1262 <- array(c(2L, 8L, 7L, 4L), dim = c(2L, 2L), dimnames = list(
  Group = c('PI Naive', 'PA Experienced'), Regimen2yr = c('TRUE', 'FALSE'))))
fisher.test(d1262)

# Example 12.7.1; Page 644 (10th ed), 
addmargins(d1271 <- array(c(22L, 18L, 216L, 199L), dim = c(2L, 2L), dimnames = list(
  Exercising = c('Extreme', 'No'), PretermLabor = c('Cases', 'Noncases'))))
DescTools::RelRisk(d1271, conf.level = .95) # 95% CI for relative risk
fisher.test(d1271) # 95% CI for odds ratio

# Example 12.7.2; Page 647 (10th ed), 
addmargins(d1272 <- array(c(64L, 68L, 342L, 3496L), dim = c(2L, 2L), dimnames = list(
  SmkPregnancy = c('Smoked Throughout', 'Never Smoked'), Obesity = c('Cases', 'Noncases'))))
fisher.test(d1272)

# Example 12.7.3-12.7.4; Page 650-652 (10th ed), 
(d1273 <- array(c(21L, 16L, 11L, 6L, 50L, 18L, 14L, 6L), dim = c(2L, 2L, 2L), dimnames = list(
  HTN = c('Present', 'Absent'), OCAD = c('Cases', 'Controls'), Age = c('<=55', '>55'))))
addmargins(d1273, margin = 1:2) # Table 12.7.6
mantelhaen.test(d1273)

Chapter 13: Nonparametric and Distribution-Free Statistics

Description

Examples for Chapter 13, Nonparametric and Distribution-Free Statistics.

Value

No function defined for Chapter 13.

Examples

library(DanielBiostatistics10th)

# Example 13.3.1; Page 673, 
d1331 = c(4, 5, 8, 8, 9, 6, 10, 7, 6, 6)
BSDA::SIGN.test(d1331, md = 5)

# Example 13.3.2; Page 677, 
head(EXA_C13_S03_02)
with(EXA_C13_S03_02, BSDA::SIGN.test(x = X, y = Y, alternative = 'less'))

# Example 13.4.1; Page 683, 
d1341 = c(4.91, 4.10, 6.74, 7.27, 7.42, 7.50, 6.56, 4.64, 5.98, 3.14, 3.23, 5.80, 6.17, 5.39, 5.77)
wilcox.test(d1341, mu = 5.05)

# Example 13.5.1; Page 686, 
head(EXA_C13_S05_01)
(med1351 = median(unlist(EXA_C13_S05_01), na.rm = TRUE)) # common median
addmargins(t1351 <- with(EXA_C13_S05_01, expr = {
  tmp <- cbind(Urban = table(URBAN < med1351), Rural = table(RURAL < med1351, useNA = 'no'))
  rownames(tmp) <- paste('Number of scores', c('above', 'below'), 'median')
  tmp
})) # Table 13.5.2
chisq.test(t1351, correct = FALSE)

# Example 13.6.1; Page 691, 
head(EXA_C13_S06_01)
with(EXA_C13_S06_01, wilcox.test(X, Y, exact = FALSE, alternative = 'less'))

# Example 13.7.1; Page 699, 
head(EXA_C13_S07_01)
ks.test(EXA_C13_S07_01$GLUCOSE, y = pnorm, mean = 80, sd = 6)

# Example 13.8.1; Page 705 (10th ed), Page 611 (11th ed) 
(d1381 = data.frame(Air = c(12.22, 28.44, 28.13, 38.69, 54.91),
                    Benzaldehyde = c(3.68, 4.05, 6.47, 21.12, 3.33),
                    Acetaldehyde = c(54.36, 27.87, 66.81, 46.27, 30.19))) # Table 13.8.1
with(data = reshape2::melt(
  data = d1381, 
  id.vars = NULL, 
  value.name = 'Eosinophil', 
  variable.name = 'Exposure'
), expr = kruskal.test(x = Eosinophil, g = Exposure))

# Example 13.8.2; Page 708 (10th ed), Page 613 (11th ed) 
head(EXA_C13_S08_02)
with(data = reshape2::melt(
  data = EXA_C13_S08_02, 
  id.vars = NULL, 
  value.name = 'Value', 
  variable.name = 'Hospital'
), expr = kruskal.test(x = Value, g = Hospital))

# Example 13.9.1; Page 713 (10th ed); Page 618 (11th ed)
head(EXA_C13_S09_01)
m1391 = as.matrix(EXA_C13_S09_01[LETTERS[1:3]], rownames.force = TRUE)
names(dimnames(m1391)) = c('Therapist', 'Model')
m1391 # Table 13.9.1
friedman.test(m1391)

# Example 13.9.2; Page 715 (10th ed); Page 620 (11th ed) 
head(EXA_C13_S09_02)
m1392 = as.matrix(EXA_C13_S09_02[LETTERS[1:4]], rownames.force = TRUE)
names(dimnames(m1392)) = c('Animal', 'Dose')
m1392 # Table 13.9.2
friedman.test(m1392)

# Example 13.10.1; Page 720, 
head(EXA_C13_S10_01)
with(EXA_C13_S10_01, cor.test(X, Y, method = 'spearman'))

# Example 13.10.2; Page 722, 
head(EXA_C13_S10_02)
with(EXA_C13_S10_02, cor.test(V2, V3, method = 'spearman', exact = FALSE))

# Example 13.11.1-13.11.2; Page 728-729, 
testosterone <- c(230, 175, 315, 290, 275, 150, 360, 425)
citricAcid <- c(421, 278, 618, 482, 465, 105, 550, 750)
robslopes::TheilSen(x = citricAcid, y = testosterone)
# textbook uses *central* median of ordered pairs, while ?robslopes::TheilSen uses *upper* median
summary(mblm::mblm(testosterone ~ citricAcid, repeated = FALSE)) # Figure 13.11.1 (11th ed)

Chapter 14: Survival Analysis

Description

Examples for Chapter 14, Survival Analysis.

Value

No function defined for Chapter 14.

Examples

library(DanielBiostatistics10th)

# Example 14.3.1; Page 756 (10th ed), Page 652 (11th ed) 
head(EXA_C14_S03_01)
head(d1431 <- within(EXA_C14_S03_01, expr = {
  TIME = .difftime(TIME, units = 'months')
  OS = survival::Surv(time = TIME, event = (VITAL != 'ned'))
}))
class(d1431$OS) # 'Surv'
head(d1431$OS)
summary(sf_1431 <- survival::survfit(OS ~ TUMOR, data = d1431)) # Table 14.3.2
plot(sf_1431, lty = 2:3, xlab = 'month', ylab = 'OS', main = 'Figure 14.3.1'); legend(
  x = 250, y = .9, legend = c('High', 'Low'), lty = 2:3)

# Example 14.4.1; Page 764 (10th ed), Page 659 (11th ed) 
survival::survdiff(OS ~ TUMOR, data = d1431)

# Example 14.5.1; Page 769 (10th ed), Page 663 (11th ed)  
head(EXA_C14_S05_01)
head(d1451 <- within(EXA_C14_S05_01, expr = {
  time = .difftime(time, units = 'weeks')
  PFS = survival::Surv(time, status)
  drug = relevel(structure(drug, levels = c('Opiate', 'Other'), class = 'factor'), ref = 'Other')
}))
summary(model1_1451 <- survival::coxph(PFS ~ drug + age, data = d1451))
# 'Opiate' has higher hazard compared to Drug='Other' (hazard ratio (HR) = 9.407, p < .001)
# With 'proportional hazard' assumption, 
# ... we don't need to discuss Opiate vs. Other at any specific time point
confint(model1_1451)
# 'age' is not significant (p = .772), so it should be removed from the model
summary(model2_1451 <- survival::coxph(PFS ~ drug, data = d1451))
confint(model2_1451)
# 'Opiate' has higher hazard compared to Drug='Other' (hazard ratio (HR) = 9.923, p < .001)
plot(survival::survfit(PFS ~ drug, data = d1451), lty = 2:3, 
     xlab = 'weeks', ylab = 'PFS', main = 'Figure 14.5.1'); legend(
  x = 35, y = .9, legend = c('Other', 'Opiate'), lty = 2:3)

Example Data

Description

Example Data

Usage

EXA_C01_S04_01

EXA_C02_S05_05

EXA_C06_S02_04

EXA_C07_S02_03

EXA_C07_S03_02

EXA_C07_S04_01

EXA_C07_S07_01

EXA_C08_S02_01

EXA_C08_S03_01

EXA_C08_S04_01

EXA_C08_S04_02

EXA_C08_S05_02

EXA_C09_S03_01

EXA_C09_S07_01

EXA_C10_S03_01

EXA_C10_S06_01

EXA_C11_S01_01

EXA_C11_S01_02

EXA_C11_S02_01

EXA_C11_S02_03

EXA_C11_S03_01

EXA_C11_S04_02

EXA_C11_S05_01

EXA_C12_S02_03

EXA_C13_S03_02

EXA_C13_S05_01

EXA_C13_S06_01

EXA_C13_S07_01

EXA_C13_S08_02

EXA_C13_S09_01

EXA_C13_S09_02

EXA_C13_S10_01

EXA_C13_S10_02

EXA_C14_S03_01

EXA_C14_S05_01

Format

An object of class data.frame with 189 rows and 2 columns.

An object of class data.frame with 20 rows and 1 columns.

An object of class data.frame with 35 rows and 1 columns.

An object of class data.frame with 17 rows and 2 columns.

An object of class data.frame with 10 rows and 2 columns.

An object of class data.frame with 12 rows and 2 columns.

An object of class data.frame with 17 rows and 1 columns.

An object of class data.frame with 144 rows and 2 columns.

An object of class data.frame with 15 rows and 3 columns.

An object of class data.frame with 72 rows and 3 columns.

An object of class data.frame with 25 rows and 6 columns.

An object of class data.frame with 80 rows and 3 columns.

An object of class data.frame with 109 rows and 3 columns.

An object of class data.frame with 155 rows and 2 columns.

An object of class data.frame with 71 rows and 3 columns.

An object of class data.frame with 29 rows and 3 columns.

An object of class data.frame with 25 rows and 3 columns.

An object of class data.frame with 15 rows and 4 columns.

An object of class data.frame with 100 rows and 4 columns.

An object of class data.frame with 36 rows and 3 columns.

An object of class data.frame with 30 rows and 7 columns.

An object of class data.frame with 184 rows and 2 columns.

An object of class data.frame with 45 rows and 4 columns.

An object of class data.frame with 90 rows and 2 columns.

An object of class data.frame with 12 rows and 3 columns.

An object of class data.frame with 16 rows and 2 columns.

An object of class data.frame with 15 rows and 2 columns.

An object of class data.frame with 36 rows and 1 columns.

An object of class data.frame with 10 rows and 5 columns.

An object of class data.frame with 9 rows and 4 columns.

An object of class data.frame with 16 rows and 5 columns.

An object of class data.frame with 20 rows and 3 columns.

An object of class data.frame with 35 rows and 3 columns.

An object of class data.frame with 39 rows and 4 columns.

An object of class data.frame with 40 rows and 5 columns.

Exercise Data

Description

Exercise Data

Usage

EXR_C02_S03_01

EXR_C02_S03_02

EXR_C02_S03_03

EXR_C02_S03_04

EXR_C02_S03_05

EXR_C02_S03_06

EXR_C02_S03_07

EXR_C02_S03_08

EXR_C02_S03_09

EXR_C02_S03_11

EXR_C02_S03_12

EXR_C02_S05_03

EXR_C02_S05_06

EXR_C06_S02_05

EXR_C06_S04_10

EXR_C06_S09_07

EXR_C06_S10_07

EXR_C07_S02_13

EXR_C07_S02_15

EXR_C07_S02_16

EXR_C07_S03_03

EXR_C07_S03_04

EXR_C07_S03_05

EXR_C07_S03_10

EXR_C07_S03_11

EXR_C07_S03_12

EXR_C07_S04_01

EXR_C07_S04_02

EXR_C07_S04_03

EXR_C07_S04_04

EXR_C07_S08_07

EXR_C08_S02_01

EXR_C08_S02_02

EXR_C08_S02_03

EXR_C08_S02_04

EXR_C08_S02_05

EXR_C08_S02_06

EXR_C08_S02_07

EXR_C08_S03_01

EXR_C08_S03_02

EXR_C08_S03_03

EXR_C08_S03_04

EXR_C08_S03_05

EXR_C08_S04_01

EXR_C08_S04_02

EXR_C08_S04_03

EXR_C08_S04_06

EXR_C08_S05_01

EXR_C08_S05_02

EXR_C08_S05_03

EXR_C08_S05_04

EXR_C09_S03_02

EXR_C09_S03_03

EXR_C09_S03_04

EXR_C09_S03_06

EXR_C09_S03_07

EXR_C09_S07_01

EXR_C09_S07_02

EXR_C09_S07_04

EXR_C09_S07_05

EXR_C09_S07_06

EXR_C10_S03_01

EXR_C10_S03_02

EXR_C10_S03_03

EXR_C10_S03_04

EXR_C10_S03_05

EXR_C10_S03_06

EXR_C10_S06_01

EXR_C10_S06_02

EXR_C10_S06_03

EXR_C10_S06_04

EXR_C11_S02_01

EXR_C11_S02_02

EXR_C11_S02_03

EXR_C11_S02_04

EXR_C11_S03_01

EXR_C11_S03_02

EXR_C11_S03_03

EXR_C11_S04_01

EXR_C11_S04_02

EXR_C11_S05_01

EXR_C11_S05_02

EXR_C11_S05_04

EXR_C13_S05_01

EXR_C13_S05_02

EXR_C13_S06_01

EXR_C13_S06_02

EXR_C13_S06_03

EXR_C13_S07_02

EXR_C13_S08_01

EXR_C13_S08_02

EXR_C13_S08_03

EXR_C13_S08_04

EXR_C13_S08_05

EXR_C13_S08_06

EXR_C13_S09_01

EXR_C13_S09_02

EXR_C13_S09_03

EXR_C13_S10_01

EXR_C13_S10_02

EXR_C13_S10_03

EXR_C13_S10_04

EXR_C13_S10_05

EXR_C13_S10_06

EXR_C14_S03_01

EXR_C14_S03_02

EXR_C14_S04_03

Format

An object of class data.frame with 90 rows and 1 columns.

An object of class data.frame with 159 rows and 1 columns.

An object of class data.frame with 29 rows and 1 columns.

An object of class data.frame with 53 rows and 1 columns.

An object of class data.frame with 45 rows and 1 columns.

An object of class data.frame with 60 rows and 1 columns.

An object of class data.frame with 155 rows and 1 columns.

An object of class data.frame with 30 rows and 1 columns.

An object of class data.frame with 50 rows and 2 columns.

An object of class data.frame with 216 rows and 1 columns.

An object of class data.frame with 109 rows and 1 columns.

An object of class data.frame with 30 rows and 1 columns.

An object of class data.frame with 20 rows and 1 columns.

An object of class data.frame with 16 rows and 1 columns.

An object of class data.frame with 32 rows and 2 columns.

An object of class data.frame with 20 rows and 1 columns.

An object of class data.frame with 26 rows and 2 columns.

An object of class data.frame with 20 rows and 1 columns.

An object of class data.frame with 50 rows and 1 columns.

An object of class data.frame with 21 rows and 1 columns.

An object of class data.frame with 63 rows and 2 columns.

An object of class data.frame with 174 rows and 2 columns.

An object of class data.frame with 82 rows and 2 columns.

An object of class data.frame with 24 rows and 2 columns.

An object of class data.frame with 20 rows and 2 columns.

An object of class data.frame with 90 rows and 2 columns.

An object of class data.frame with 15 rows and 2 columns.

An object of class data.frame with 66 rows and 2 columns.

An object of class data.frame with 11 rows and 2 columns.

An object of class data.frame with 20 rows and 2 columns.

An object of class data.frame with 23 rows and 2 columns.

An object of class data.frame with 329 rows and 2 columns.

An object of class data.frame with 96 rows and 2 columns.

An object of class data.frame with 113 rows and 2 columns.

An object of class data.frame with 164 rows and 2 columns.

An object of class data.frame with 29 rows and 2 columns.

An object of class data.frame with 90 rows and 2 columns.

An object of class data.frame with 178 rows and 2 columns.

An object of class data.frame with 96 rows and 3 columns.

An object of class data.frame with 10 rows and 5 columns.

An object of class data.frame with 20 rows and 3 columns.

An object of class data.frame with 16 rows and 3 columns.

An object of class data.frame with 12 rows and 3 columns.

An object of class data.frame with 40 rows and 3 columns.

An object of class data.frame with 35 rows and 3 columns.

An object of class data.frame with 48 rows and 3 columns.

An object of class data.frame with 20 rows and 6 columns.

An object of class data.frame with 24 rows and 3 columns.

An object of class data.frame with 72 rows and 3 columns.

An object of class data.frame with 44 rows and 3 columns.

An object of class data.frame with 13 rows and 3 columns.

An object of class data.frame with 10 rows and 2 columns.

An object of class data.frame with 17 rows and 2 columns.

An object of class data.frame with 90 rows and 2 columns.

An object of class data.frame with 22 rows and 2 columns.

An object of class data.frame with 27 rows and 2 columns.

An object of class data.frame with 20 rows and 2 columns.

An object of class data.frame with 90 rows and 2 columns.

An object of class data.frame with 18 rows and 2 columns.

An object of class data.frame with 30 rows and 2 columns.

An object of class data.frame with 15 rows and 2 columns.

An object of class data.frame with 35 rows and 3 columns.

An object of class data.frame with 100 rows and 4 columns.

An object of class data.frame with 10 rows and 3 columns.

An object of class data.frame with 20 rows and 3 columns.

An object of class data.frame with 25 rows and 3 columns.

An object of class data.frame with 20 rows and 8 columns.

An object of class data.frame with 40 rows and 4 columns.

An object of class data.frame with 12 rows and 3 columns.

An object of class data.frame with 15 rows and 3 columns.

An object of class data.frame with 15 rows and 6 columns.

An object of class data.frame with 44 rows and 3 columns.

An object of class data.frame with 100 rows and 3 columns.

An object of class data.frame with 17 rows and 3 columns.

An object of class data.frame with 90 rows and 3 columns.

An object of class data.frame with 100 rows and 8 columns.

An object of class data.frame with 35 rows and 7 columns.

An object of class data.frame with 68 rows and 7 columns.

An object of class data.frame with 4 rows and 3 columns.

An object of class data.frame with 184 rows and 2 columns.

An object of class data.frame with 45 rows and 4 columns.

An object of class data.frame with 45 rows and 5 columns.

An object of class data.frame with 90 rows and 3 columns.

An object of class data.frame with 30 rows and 2 columns.

An object of class data.frame with 30 rows and 2 columns.

An object of class data.frame with 70 rows and 2 columns.

An object of class data.frame with 17 rows and 2 columns.

An object of class data.frame with 83 rows and 2 columns.

An object of class data.frame with 30 rows and 1 columns.

An object of class data.frame with 232 rows and 2 columns.

An object of class data.frame with 15 rows and 2 columns.

An object of class data.frame with 53 rows and 2 columns.

An object of class data.frame with 22 rows and 2 columns.

An object of class data.frame with 44 rows and 2 columns.

An object of class data.frame with 22 rows and 3 columns.

An object of class data.frame with 9 rows and 4 columns.

An object of class data.frame with 15 rows and 11 columns.

An object of class data.frame with 10 rows and 6 columns.

An object of class data.frame with 15 rows and 3 columns.

An object of class data.frame with 10 rows and 3 columns.

An object of class data.frame with 20 rows and 2 columns.

An object of class data.frame with 20 rows and 2 columns.

An object of class data.frame with 30 rows and 2 columns.

An object of class data.frame with 17 rows and 3 columns.

An object of class data.frame with 53 rows and 3 columns.

An object of class data.frame with 62 rows and 2 columns.

An object of class data.frame with 50 rows and 4 columns.

Student's and Welch–Satterthwaite Equation

Description

To determine the degree of freedom, as well as the standard error, of two-sample t-statistic, with or without the equal-variance assumption.

Usage

Gosset_Welch(
  s1,
  s0,
  c1 = 1,
  c0 = 1,
  v1 = s1^2,
  v0 = s0^2,
  n1,
  n0,
  var.equal = FALSE
)

Arguments

Details

If v_1=v_0 is assumed, the standard error of two-sample t-statistic from William Sealy Gosset (a.k.a., Student) satisfies that s^2_{\bar\Delta}=s^2_p(1/n_1+1/n_0), with degree-of-freedom \text{df} = n_1+n_0-2, where s_p is the pooled standard deviation,

s^2_p=\dfrac{(n_1-1)v_1+(n_0-1)v_0}{n_1+n_0-2}

If v_1\neq v_0, the standard error of two-sample t-statistic satisfies that s^2_{\bar\Delta}=v_1/n_1 + v_0/n_0, with degree of freedom (Welch–Satterthwaite equation),

\text{df} = \dfrac{\left(\dfrac{v_1}{n_1}+\dfrac{v_0}{n_0}\right)^2}{\dfrac{(v_1/n_1)^2}{n_1-1}+\dfrac{(v_0/n_0)^2}{n_0-1}}

Value

Function Gosset_Welch returns a numeric scalar or vector of the degree of freedom, with attributes,

attr(., 'stderr')

numeric scalar or vector, standard error s_{\bar\Delta};

attr(., 'stderr2')

numeric scalar or vector, standard error squared s^2_{\bar\Delta}, included for downstream compute-intensive functions.

References

Student's t-test by William Sealy Gosset, doi:10.1093/biomet/6.1.1.

Welch–Satterthwaite equation by Bernard Lewis Welch doi:10.1093/biomet/34.1-2.28 and F. E. Satterthwaite doi:10.2307/3002019.

Examples

x = rnorm(32L, sd = 1.6); y = rnorm(57L, sd = 2.1)
vx = var(x); vy = var(y); nx = length(x); ny = length(y)
t.test(x, y, var.equal = FALSE)[c('parameter', 'stderr')]
Gosset_Welch(v1 = vx, v0 = vy, n1 = nx, n0 = ny, var.equal = FALSE)
t.test(x, y, var.equal = TRUE)[c('parameter', 'stderr')]
Gosset_Welch(v1 = vx, v0 = vy, n1 = nx, n0 = ny, var.equal = TRUE)

Large Data

Description

Large Data

Usage

LDS_C02_NCBIRTH800

LDS_C06_BABYWGTS

LDS_C06_BOYHGTS

LDS_C06_CHOLEST

LDS_C07_HEADCIRC

LDS_C07_HEMOGLOB

LDS_C07_MANDEXT

LDS_C07_PCKDATA

LDS_C07_PROTHROM

LDS_C08_CSFDATA

LDS_C08_LSADATA

LDS_C08_MEDSCORES

LDS_C08_RBCDATA

LDS_C08_SACEDATA

LDS_C08_SERUMCHO

LDS_C09_CALCIUM

LDS_C09_CEREBRAL

LDS_C09_HYPERTEN

LDS_C10_LTEXER

LDS_C10_RESPDIS

LDS_C10_RISKFACT

LDS_C10_STERLENGTH

LDS_C11_AQUATICS

LDS_C11_TEACHERS

LDS_C11_WGTLOSS

LDS_C12_SMOKING

LDS_C13_KLETTER

Format

An object of class data.frame with 800 rows and 14 columns.

An object of class data.frame with 1200 rows and 2 columns.

An object of class data.frame with 1000 rows and 2 columns.

An object of class data.frame with 1000 rows and 2 columns.

An object of class data.frame with 1000 rows and 3 columns.

An object of class data.frame with 1000 rows and 2 columns.

An object of class data.frame with 1000 rows and 2 columns.

An object of class data.frame with 1005 rows and 3 columns.

An object of class data.frame with 1000 rows and 2 columns.

An object of class data.frame with 300 rows and 6 columns.

An object of class data.frame with 350 rows and 5 columns.

An object of class data.frame with 582 rows and 4 columns.

An object of class data.frame with 350 rows and 4 columns.

An object of class data.frame with 400 rows and 5 columns.

An object of class data.frame with 347 rows and 4 columns.

An object of class data.frame with 100 rows and 13 columns.

An object of class data.frame with 1050 rows and 3 columns.

An object of class data.frame with 1050 rows and 3 columns.

An object of class data.frame with 248 rows and 5 columns.

An object of class data.frame with 1200 rows and 6 columns.

An object of class data.frame with 1000 rows and 6 columns.

An object of class data.frame with 1162 rows and 4 columns.

An object of class data.frame with 142 rows and 7 columns.

An object of class data.frame with 212 rows and 7 columns.

An object of class data.frame with 1185 rows and 3 columns.

An object of class data.frame with 1200 rows and 6 columns.

An object of class data.frame with 168 rows and 3 columns.

Review Exercise Data

Description

Review Exercise Data

Usage

REV_C02_13

REV_C02_15

REV_C02_16

REV_C02_19

REV_C02_29

REV_C06_22

REV_C06_23

REV_C06_28

REV_C07_18

REV_C07_19

REV_C07_22

REV_C07_24

REV_C07_29

REV_C07_40

REV_C07_41

REV_C07_42

REV_C07_43

REV_C07_44

REV_C07_45

REV_C07_46

REV_C07_47

REV_C07_48

REV_C07_49

REV_C07_50

REV_C07_51

REV_C07_52

REV_C07_53

REV_C07_54

REV_C07_55

REV_C08_13

REV_C08_14

REV_C08_15

REV_C08_16

REV_C08_17

REV_C08_18

REV_C08_19

REV_C08_20

REV_C08_21

REV_C08_22

REV_C08_23

REV_C08_24

REV_C08_25

REV_C08_31

REV_C08_32

REV_C08_33

REV_C08_39

REV_C08_40

REV_C08_41

REV_C08_42

REV_C08_43

REV_C08_44

REV_C08_45

REV_C08_46

REV_C08_47

REV_C08_48

REV_C08_49

REV_C08_50

REV_C08_51

REV_C08_52

REV_C08_53

REV_C08_54

REV_C08_55

REV_C08_56

REV_C08_57

REV_C08_58

REV_C08_59

REV_C08_60

REV_C08_61

REV_C08_62

REV_C08_63

REV_C08_64

REV_C08_65

REV_C08_66

REV_C09_16

REV_C09_17

REV_C09_18

REV_C09_19

REV_C09_20

REV_C09_21

REV_C09_22

REV_C09_23

REV_C09_24

REV_C09_25

REV_C09_29

REV_C09_30

REV_C09_31

REV_C09_32

REV_C09_33

REV_C09_34

REV_C09_35

REV_C09_36

REV_C09_37

REV_C09_38

REV_C09_39

REV_C09_40

REV_C09_41

REV_C09_42

REV_C09_43

REV_C09_44

REV_C09_45

REV_C09_46

REV_C10_06

REV_C10_07

REV_C10_08

REV_C10_09

REV_C10_10

REV_C10_11

REV_C10_17

REV_C10_18

REV_C10_19

REV_C11_14

REV_C11_15

REV_C11_16

REV_C11_17

REV_C11_18

REV_C11_22

REV_C11_23

REV_C11_24

REV_C11_25

REV_C11_26

REV_C11_27

REV_C11_28

REV_C11_29

REV_C13_06

REV_C13_08

REV_C13_09

REV_C13_10

REV_C13_13

REV_C13_15

REV_C13_16

REV_C13_17

REV_C13_18

REV_C13_19

REV_C13_20

REV_C13_21

REV_C13_22

REV_C13_23

REV_C13_24

REV_C13_25

REV_C13_26

REV_C13_27

REV_C13_28

REV_C13_29

REV_C14_11

REV_C14_12

Format

An object of class data.frame with 50 rows and 1 columns.

An object of class data.frame with 28 rows and 1 columns.

An object of class data.frame with 53 rows and 2 columns.

An object of class data.frame with 22 rows and 1 columns.

An object of class data.frame with 107 rows and 1 columns.

An object of class data.frame with 27 rows and 2 columns.

An object of class data.frame with 28 rows and 2 columns.

An object of class data.frame with 110 rows and 2 columns.

An object of class data.frame with 107 rows and 3 columns.

An object of class data.frame with 107 rows and 3 columns.

An object of class data.frame with 76 rows and 2 columns.

An object of class data.frame with 37 rows and 2 columns.

An object of class data.frame with 12 rows and 2 columns.

An object of class data.frame with 8 rows and 3 columns.

An object of class data.frame with 11 rows and 3 columns.

An object of class data.frame with 10 rows and 6 columns.

An object of class data.frame with 31 rows and 2 columns.

An object of class data.frame with 98 rows and 4 columns.

An object of class data.frame with 15 rows and 11 columns.

An object of class data.frame with 17 rows and 2 columns.

An object of class data.frame with 66 rows and 2 columns.

An object of class data.frame with 51 rows and 2 columns.

An object of class data.frame with 22 rows and 2 columns.

An object of class data.frame with 28 rows and 4 columns.

An object of class data.frame with 22 rows and 2 columns.

An object of class data.frame with 24 rows and 2 columns.

An object of class data.frame with 55 rows and 2 columns.

An object of class data.frame with 17 rows and 2 columns.

An object of class data.frame with 50 rows and 2 columns.

An object of class data.frame with 75 rows and 2 columns.

An object of class data.frame with 91 rows and 2 columns.

An object of class data.frame with 48 rows and 3 columns.

An object of class data.frame with 36 rows and 3 columns.

An object of class data.frame with 52 rows and 3 columns.

An object of class data.frame with 74 rows and 4 columns.

An object of class data.frame with 162 rows and 3 columns.

An object of class data.frame with 56 rows and 2 columns.

An object of class data.frame with 30 rows and 3 columns.

An object of class data.frame with 54 rows and 3 columns.

An object of class data.frame with 31 rows and 2 columns.

An object of class data.frame with 30 rows and 3 columns.

An object of class data.frame with 60 rows and 3 columns.

An object of class data.frame with 28 rows and 1 columns.

An object of class data.frame with 48 rows and 1 columns.

An object of class data.frame with 25 rows and 2 columns.

An object of class data.frame with 18 rows and 10 columns.

An object of class data.frame with 30 rows and 3 columns.

An object of class data.frame with 24 rows and 2 columns.

An object of class data.frame with 14 rows and 8 columns.

An object of class data.frame with 24 rows and 5 columns.

An object of class data.frame with 16 rows and 14 columns.

An object of class data.frame with 90 rows and 2 columns.

An object of class data.frame with 20 rows and 5 columns.

An object of class data.frame with 18 rows and 3 columns.

An object of class data.frame with 34 rows and 2 columns.

An object of class data.frame with 24 rows and 3 columns.

An object of class data.frame with 20 rows and 5 columns.

An object of class data.frame with 36 rows and 3 columns.

An object of class data.frame with 65 rows and 2 columns.

An object of class data.frame with 11 rows and 2 columns.

An object of class data.frame with 22 rows and 8 columns.

An object of class data.frame with 41 rows and 2 columns.

An object of class data.frame with 14 rows and 8 columns.

An object of class data.frame with 119 rows and 2 columns.

An object of class data.frame with 173 rows and 2 columns.

An object of class data.frame with 192 rows and 2 columns.

An object of class data.frame with 24 rows and 2 columns.

An object of class data.frame with 32 rows and 2 columns.

An object of class data.frame with 14 rows and 12 columns.

An object of class data.frame with 30 rows and 2 columns.

An object of class data.frame with 60 rows and 2 columns.

An object of class data.frame with 20 rows and 2 columns.

An object of class data.frame with 15 rows and 2 columns.

An object of class data.frame with 29 rows and 2 columns.

An object of class data.frame with 89 rows and 2 columns.

An object of class data.frame with 31 rows and 5 columns.

An object of class data.frame with 19 rows and 2 columns.

An object of class data.frame with 16 rows and 2 columns.

An object of class data.frame with 15 rows and 2 columns.

An object of class data.frame with 12 rows and 2 columns.

An object of class data.frame with 16 rows and 2 columns.

An object of class data.frame with 20 rows and 2 columns.

An object of class data.frame with 10 rows and 2 columns.

An object of class data.frame with 85 rows and 2 columns.

An object of class data.frame with 27 rows and 2 columns.

An object of class data.frame with 25 rows and 2 columns.

An object of class data.frame with 9 rows and 3 columns.

An object of class data.frame with 25 rows and 2 columns.

An object of class data.frame with 19 rows and 5 columns.

An object of class data.frame with 62 rows and 2 columns.

An object of class data.frame with 23 rows and 2 columns.

An object of class data.frame with 23 rows and 2 columns.

An object of class data.frame with 32 rows and 2 columns.

An object of class data.frame with 48 rows and 5 columns.

An object of class data.frame with 13 rows and 2 columns.

An object of class data.frame with 66 rows and 2 columns.

An object of class data.frame with 102 rows and 7 columns.

An object of class data.frame with 14 rows and 4 columns.

An object of class data.frame with 44 rows and 2 columns.

An object of class data.frame with 172 rows and 2 columns.

An object of class data.frame with 33 rows and 4 columns.

An object of class data.frame with 114 rows and 3 columns.

An object of class data.frame with 15 rows and 3 columns.

An object of class data.frame with 20 rows and 4 columns.

An object of class data.frame with 15 rows and 3 columns.

An object of class data.frame with 21 rows and 3 columns.

An object of class data.frame with 15 rows and 5 columns.

An object of class data.frame with 26 rows and 13 columns.

An object of class data.frame with 34 rows and 7 columns.

An object of class data.frame with 96 rows and 8 columns.

An object of class data.frame with 70 rows and 5 columns.

An object of class data.frame with 28 rows and 3 columns.

An object of class data.frame with 27 rows and 3 columns.

An object of class data.frame with 40 rows and 3 columns.

An object of class data.frame with 31 rows and 4 columns.

An object of class data.frame with 12 rows and 3 columns.

An object of class data.frame with 47 rows and 3 columns.

An object of class data.frame with 129 rows and 3 columns.

An object of class data.frame with 30 rows and 3 columns.

An object of class data.frame with 18 rows and 3 columns.

An object of class data.frame with 37 rows and 3 columns.

An object of class data.frame with 41 rows and 10 columns.

An object of class data.frame with 19 rows and 9 columns.

An object of class data.frame with 20 rows and 2 columns.

An object of class data.frame with 303 rows and 2 columns.

An object of class data.frame with 10 rows and 4 columns.

An object of class data.frame with 34 rows and 2 columns.

An object of class data.frame with 70 rows and 2 columns.

An object of class data.frame with 12 rows and 2 columns.

An object of class data.frame with 43 rows and 5 columns.

An object of class data.frame with 67 rows and 2 columns.

An object of class data.frame with 18 rows and 3 columns.

An object of class data.frame with 50 rows and 2 columns.

An object of class data.frame with 31 rows and 3 columns.

An object of class data.frame with 45 rows and 3 columns.

An object of class data.frame with 18 rows and 2 columns.

An object of class data.frame with 44 rows and 5 columns.

An object of class data.frame with 20 rows and 6 columns.

An object of class data.frame with 20 rows and 3 columns.

An object of class data.frame with 18 rows and 3 columns.

An object of class data.frame with 9 rows and 6 columns.

An object of class data.frame with 31 rows and 2 columns.

An object of class data.frame with 17 rows and 2 columns.

An object of class data.frame with 55 rows and 4 columns.

An object of class data.frame with 77 rows and 4 columns.

Conditional and/or Marginal Probabilities

Description

Add conditional and/or marginal probabilities to a two-way contingency table.

Usage

addProbs(A, margin = seq_len(nd), fmt = "%d (%.1f%%)")

Arguments

Details

Function addProbs provides the joint, marginal (using margin = 1:2) and conditional (using margin = 1L or margin = 2L) probabilities of a two-dimensional contingency table.

Value

Function addProbs returns an 'addProbs' object, which inherits from table and noquote.

Note

margin.table (which is to be renamed as marginSums) is much slower than colSums.

The use of argument margin is the same as addmargins, and different from proportions!

See Also

rowSums colSums proportions

Examples

addProbs(table(warpbreaks$tension))

storage.mode(VADeaths) = 'integer'
addProbs(VADeaths)
addProbs(VADeaths, margin = 1L)
rowSums(proportions(VADeaths, margin = 1L))
addmargins(VADeaths, margin = 1L)

Boolean Test-&-Disease or Risk-&-Disease Table

Description

To create a Boolean test-&-disease or risk-&-disease table.

Usage

binTab(x, ...)

## S3 method for class 'matrix'
binTab(x, ...)

## S3 method for class 'table'
binTab(x, ...)

## S3 method for class 'formula'
binTab(formula, data, ...)

Arguments

Details

Function binTab creates a 2\times 2 test-&-disease contingency table with layout

or a 2\times 2 risk-&-disease contingency table with layout

The endpoint (i.e., disease) must be on the rows and the test/risk on the columns.

Value

Function binTab returns a two-by-two integer matrix.

See Also

Function caret::confusionMatrix does not provide confidence intervals of sensitivity, specificity, etc.

Examples

binTab(matrix(c(7L, 3L, 8L, 6L), nrow = 2L))
binTab(matrix(c(7L, 3L, 8L, 6L), nrow = 2L, dimnames = list(X = c('a','b'), NULL)))
binTab(~ (mag < 4.5) + (depth > 400), data = quakes)

S4 Class freqs

Description

S4 Class freqs

Slots

.Data

integer vector, frequency counts

data.name

character integer, name of the data, only used in output

Predictive Values

Description

Positive and negative predictive values.

Usage

ppv(prevalence, sensitivity, specificity)

npv(prevalence, sensitivity, specificity)

Arguments

Details

Function ppv calculates positive predictive values.

Function npv calculates negative predictive values.

Value

Functions ppv and npv return double scalar or vector.

Print Boolean Test-&-Disease and/or Risk-&-Disease Table

Description

Print Boolean test-&-disease and/or risk-&-disease table.

Usage

## S3 method for class 'binTab'
print(x, prevalence, ansi = identical(.Platform$GUI, "RStudio"), ...)

Arguments

Details

Function print.binTab prints the diagnostic test characteristics, e.g., sensitivity, specificity, predictive values, and diagnostic accuracy, together with their 95\% Clopper-Pearson exact confidence intervals.

Value

Function print.binTab does not have a returned value.

References

https://en.wikipedia.org/wiki/Diagnostic_odds_ratio

Examples

(x = array(c(95L, 10L, 31L, 82L), dim = c(2L, 2L)))
binTab(x)
print(binTab(x), prevalence = c(.0001, .001, .01))

Create R Markdown Script for binTab Object

Description

Method dispatch to binTab for S3 generic rmd_ (in a different master package).

Usage

rmd_.binTab(x, xnm = substitute(x), ...)

Arguments

Value

Function rmd_.binTab returns a character vector.

Show freqs Object

Description

Show freqs object

Usage

## S4 method for signature 'freqs'
show(object)

Arguments

Value

The show method for freqs object does not have a returned value.