R/t_test.R
In jrpriceUPS/Math160UPS: Suite of Functions for Math 160 Classes at the University of Puget Sound
Defines functions
t_test
Documented in
t_test
#' t-test
#'
#' This function asks you a sequence of questions in order to execute a t-test. It finds a confidence interval and a p-value, produces a plot, and indicates how this could be queried directly from R.
#' @export
#' @examples
#'
#'
#'
#'
#' > x = c(1, 2, 3, 4, 5, 6, 7)
#' > t_test()
#' Do you have a single population or are you comparing populations?
#' Possible answers are 'single' and 'comparing'.
#' single
#' Do you have the whole dataset or do you just have the statistics (mean, standard deviation)?
#' Possible answers are 'whole' or 'stats'.
#' whole
#' What is the name of your variable?
#' x
#' The statistics for your dataset are:
#' xbar = 4
#' s = 2.160247
#' n = 7
#' df = 7 - 1 = 6
#'
#' What is the theoretical mean you are testing against (called mu_0)?
#' (If you only want a confidence interval, type 'NA')
#' 3
#' What is your desired confidence level?
#' .95
#' Your t-statistic is:
#' t = (4-3)/(2.160247/sqrt(7)) = 1.224745
#'
#' The probability of getting this result or more extreme for xbar
#' if mu really is 3 is
#' p = 0.2665697
#'
#' You can get this result by typing:
#' 2*(1-pt(1.22474487139159,6))
#'
#'
#' The 95% confidence interval for the population mean is
#' 2.002105 < mu < 5.997895
#'
#' You can get this result by finding:
#' tstar = 1-qt((1-0.95)/2,6) = 2.446912
#'
#' and then calculating:
#' 4 - 2.446912 x 2.160247/sqrt(7) and 4 + 2.446912 x 2.160247/sqrt(7)
#'
#'
#' Or, since you have the whole dataset, you could just type:
#' t.test(x,mu = 3,conf.level = 0.95)
#'
#'
#'
#'> t_test()
#'Do you have a single population or are you comparing populations?
#' Possible answers are 'single' and 'comparing'.
#'single
#'Do you have the whole dataset or do you just have the statistics (mean, standard deviation)?
#' Possible answers are 'whole' or 'stats'.
#'stats
#'What is your sample mean?
#' 4
#'What is your sample standard deviation?
#' 2.16
#'What is your sample size?
#' 7
#'What is the theoretical mean you are testing against (called mu_0)?
#' (If you only want a confidence interval, type 'NA')
#'3
#'What is your desired confidence level?
#' .95
#'Your t-statistic is:
#' t = (4-3)/(2.16/sqrt(7)) = 1.224885
#'
#'The probability of getting this result or more extreme for xbar
#'if mu really is 3 is
#'p = 0.2665206
#'
#'You can get this result by typing:
#' 2*(1-pt(1.22488486623361,6))
#'
#'
#'The 95% confidence interval for the population mean is
#'2.002333 < mu < 5.997667
#'
#'You can get this result by finding:
#' tstar = 1-qt((1-0.95)/2,6) = 2.446912
#'
#'and then calculating:
#' 4 - 2.446912 x 2.16/sqrt(7) and 4 + 2.446912 x 2.16/sqrt(7)
#'
#'
#'
#'
#'
#'
#' > t_test()
#' Do you have a single population or are you comparing populations?
#' Possible answers are 'single' and 'comparing'.
#' comparing
#' Do you have the whole dataset or do you just have the statistics (mean, standard deviation)?
#' Possible answers are 'whole' or 'stats'.
#' whole
#' Is this a matched-pairs comparison in which the same subjects are measured twice?
#' yes
#' What is the name of the variable for the first set of measurements?
#' x
#' What is the name of the variable for the second set of measurements?
#' y
#' The statistics for your datasets are:
#' n = 7
#' xbar1 = 4
#' s1 = 2.160247
#'
#' xbar2 = 8.842857
#' s2 = 4.595236
#'
#' The statistics for the difference are:
#' xbar = 4.842857
#' s = 2.445988
#' n = 7
#' df = 7 - 1 = 6
#'
#' What is your desired confidence level?
#' .95
#' Your t-statistic is:
#' t = 4.842857/(2.445988/sqrt(7)) = 5.238372
#'
#' The probability of getting this result or more extreme for xbar2 - xbar1 if there really is no difference is
#' p = 0.001941435
#'
#' You can get this result by typing:
#' 2*(1-pt(5.23837230565063,6))
#'
#'
#' The 95% confidence interval for the difference in population means is
#' 2.580696 < mu2 - mu1 < 7.105019
#'
#' You can get this result by finding:
#' tstar = 1-qt((1-0.95)/2,6) = 2.446912
#'
#' and then calculating:
#' (8.84285714285714-4) - 2.446912 x 2.445988/sqrt(7) and (8.84285714285714-4) + 2.446912 x 2.445988/sqrt(7)
#'
#'
#' Or, since you have the whole dataset, you could just type:
#' t.test(y,x, paired = TRUE, conf.level = 0.95)
#'
#'
#'
#'
#'
#'
#' > t_test()
#' Do you have a single population or are you comparing populations?
#' Possible answers are 'single' and 'comparing'.
#' comparing
#' Do you have the whole dataset or do you just have the statistics (mean, standard deviation)?
#' Possible answers are 'whole' or 'stats'.
#' whole
#' Is this a matched-pairs comparison in which the same subjects are measured twice?
#' no
#' What is the name of the variable for the first set of measurements?
#' x
#' What is the name of the variable for the second set of measurements?
#' y
#' The statistics for your datasets are:
#' n1 = 7
#' xbar1 = 4
#' s1 = 2.160247
#'
#' n2 = 7
#' xbar2 = 8.842857
#' s2 = 4.595236
#'
#' The statistics for the difference are:
#' xbar = 4.842857
#' s = sqrt(2.160247^2/7 + 4.595236^2/7) = 1.919183
#' df = 8.5285
#'
#' What is your desired confidence level?
#' .95
#' Your t-statistic is:
#' t = (4.84285714285714)/(1.919183) = 2.523395
#'
#' The probability of getting this result or more extreme for xbar2 - xbar1 if there really is no difference is
#' p = 0.03391985
#'
#' You can get this result by typing:
#' 2*(1-pt(2.52339452856832,8.52849965837585))
#'
#'
#' The 95% confidence interval for the difference in population means is
#' 0.4644978 < mu2 - mu1 < 9.221216
#'
#' You can get this result by finding:
#' tstar = 1-qt((1-0.95)/2,8.5285) = 2.281366
#'
#' and then calculating:
#' (8.84285714285714-4) - 2.281366 x 1.919183 and (8.84285714285714-4) + 2.281366 x 1.919183
#'
#'
#' Or, since you have the whole dataset, you could just type:
#' t.test(y,x, conf.level = 0.95)
t_test <- function(){
cat("Are you executing a one-sample t-test or a two-sample t-test?\nPossible answers are 'one' and 'two'.\n")
compare = readline()
while(!(compare %in% c('one','1','One','two','2','Two'))){
cat("Please choose either 'one' or 'two'.\n")
compare = readline()
}
if(compare %in% c('one','1','One')){compare = "single"}
if(compare %in% c('two','2','Two')){compare = "comparing"}
cat("Do you have the whole dataset or do you just have the statistics (mean, standard deviation)?\nPossible answers are 'whole' or 'stats'.\n")
vec = readline()
if(compare=="comparing"){
if(vec=="stats"){
cat("What is the sample mean of the first set of measurements? \n")
xbar1 = as.numeric(readline())
cat("What is the sample mean of the second set of measurements? \n")
xbar2 = as.numeric(readline())
cat("What is the sample standard deviation of the first set of measurements? \n")
s1 = as.numeric(readline())
cat("What is the sample standard deviation of the second set of measurements? \n")
s2 = as.numeric(readline())
cat("What is the sample size of the first set of measurements? \n")
n1 = as.numeric(readline())
cat("What is the sample size of the second set of measurements? \n")
n2 = as.numeric(readline())
xbar = xbar2-xbar1
df = n1+n2-2
s = sqrt(s1^2/n1+s2^2/n2)
cat("The statistics for the difference are: ")
cat("\n")
cat(paste("xbar = ",format(xbar,scientific=FALSE)))
cat("\n")
cat(paste("s = sqrt(",format(s1,scientific=FALSE),"^2/",format(n1,scientific=FALSE)," + ",format(s2,scientific=FALSE),"^2/",format(n2,scientific=FALSE),") = ",format(s,scientific=FALSE),sep=""))
cat("\n")
cat(paste("df = ",format(n1,scientific=FALSE),"+",format(n2,scientific=FALSE),"- 2 = ",format(n1+n2-2,scientific=FALSE)))
cat("\n")
cat("\n")
}
if(vec=="whole"){
cat("What is the name of the variable for the first set of measurements? \n")
varname1 = readline()
cat("What is the name of the variable for the second set of measurements? \n")
varname2 = readline()
if(grepl("$", varname1, fixed=TRUE)){
names = strsplit(varname1,"\\$")
frame = get(names[[1]][1])
data1 = frame[[names[[1]][2]]]
} else{
data1 = get(varname1)}
data1 = data1[!is.na(data1)]
xbar1 = mean(data1)
s1 = sd(data1)
n1 = length(data1)
if(grepl("$", varname2, fixed=TRUE)){
names = strsplit(varname2,"\\$")
frame = get(names[[1]])
data2 = frame[[names[[1]][2]]]
} else{
data2 = get(varname2)}
data2 = data2[!is.na(data2)]
xbar2 = mean(data2)
s2 = sd(data2)
n2 = length(data2)
xbar = mean(data2)-mean(data1)
s = sqrt(sd(data1)^2/n1 + sd(data2)^2/n2)
test_result = t.test(data1,data2)
df = as.numeric(test_result$parameter)
cat("The statistics for your datasets are: ")
cat("\n")
cat(paste("n1 = ",format(n1,scientific=FALSE)))
cat("\n")
cat(paste("xbar1 = ",format(xbar1,scientific=FALSE)))
cat("\n")
cat(paste("s1 = ",format(s1,scientific=FALSE)))
cat("\n")
cat("\n")
cat(paste("n2 = ",format(n2,scientific=FALSE)))
cat("\n")
cat(paste("xbar2 = ",format(xbar2,scientific=FALSE)))
cat("\n")
cat(paste("s2 = ",format(s2,scientific=FALSE)))
cat("\n")
cat("\n")
cat("The statistics for the difference are: ")
cat("\n")
cat(paste("xbar = ",format(xbar,scientific=FALSE)))
cat("\n")
cat(paste("s = sqrt(",format(s1,scientific=FALSE),"^2/",format(n1,scientific=FALSE)," + ",format(s2,scientific=FALSE),"^2/",format(n2,scientific=FALSE),") = ",format(s,scientific=FALSE),sep=""))
cat("\n")
cat(paste("df = ",format(df,scientific=FALSE),sep=""))
cat("\n")
cat("\n")
}
cat("What is your desired confidence level? \n")
conf_level = as.numeric(readline())
while(conf_level<0 | conf_level>1){cat('Please choose a confidence level between 0 and 1\n')
cat("What is your desired confidence level? \n")
conf_level = as.numeric(readline("What is your desired confidence level? "))
}
sidedness = "both"
if(sidedness!="NA"){
t = xbar/s
out = conduct_t_test(t,df,sidedness)}
# new version with no one-sided confidence intervals:
tstar = -qt((1-conf_level)/2,df)
thing_to_type2 = paste("tstar = 1-qt((1-",format(conf_level,scientific=FALSE),")/2,",format(df,scientific=FALSE),") = ",format(tstar,scientific=FALSE),sep="")
thing_to_type3 = paste("(",toString(xbar2),"-",toString(xbar1),") - ",format(tstar,scientific=FALSE)," x ",format(s,scientific=FALSE),sep="")
thing_to_type4 = paste("(",toString(xbar2),"-",toString(xbar1),") + ",format(tstar,scientific=FALSE)," x ",format(s,scientific=FALSE),sep="")
lower = xbar - tstar*s
upper = xbar + tstar*s
if(sidedness!="NA"){
sidedness_type = paste("The probability of getting this result or more extreme for xbar2 - xbar1 if there really is no difference is",sep="")
cat("Your t-statistic is:")
cat("\n")
cat(paste("t = (",toString(xbar),")/(",format(s,scientific=FALSE),") = ",format(t,scientific=FALSE),sep=""))
cat("\n")
cat("\n")
cat(sidedness_type)
cat("\n")
cat(paste("p = ",format(out$prob,scientific=FALSE)))
cat("\n")
cat("\n")
cat("You can get this result by typing:")
cat("\n")
cat(out$p_value_type)
cat("\n")
cat("\n")
cat("\n")}
cat(paste("The ",toString(conf_level*100),"% confidence interval for the difference in population means is",sep=""))
cat("\n")
cat(paste(format(lower,scientific=FALSE)," < mu2 - mu1 < ",format(upper,scientific=FALSE)))
cat("\n")
cat("\n")
cat("You can get this result by finding:")
cat("\n")
cat(thing_to_type2)
cat("\n")
cat("\n")
cat("and then calculating:")
cat("\n")
cat(paste(thing_to_type3," and ",thing_to_type4))
if(vec=="whole"){
cat("\n")
cat("\n")
cat("\n")
cat("Or, since you have the whole dataset, you could just type:")
cat("\n")
cat(paste("t.test(",varname2,",",varname1,", conf.level = ", toString(conf_level), ")",sep=""))
}
}
if(compare=="single"){
if(vec=="stats"){
cat("What is your sample mean? \n")
xbar = as.numeric(readline())
cat("What is your sample standard deviation? \n")
s = as.numeric(readline())
cat("What is your sample size? \n")
n = as.numeric(readline())
df = n-1
}
if(vec=="whole"){
cat("What is the name of your variable? \n")
varname = readline()
if(grepl("$", varname, fixed=TRUE)){
names = strsplit(varname,"\\$")
frame = get(names[[1]][1])
data = frame[[names[[1]][2]]]
} else{
data = get(varname)}
data = data[!is.na(data)]
xbar = mean(data)
s = sd(data)
n = length(data)
cat("The statistics for your dataset are: ")
cat("\n")
cat(paste("xbar = ",format(xbar,scientific=FALSE)))
cat("\n")
cat(paste("s = ",format(s,scientific=FALSE)))
cat("\n")
cat(paste("n = ",format(n,scientific=FALSE)))
cat("\n")
cat(paste("df = ",format(n,scientific=FALSE),"- 1 = ",format(n-1,scientific=FALSE)))
cat("\n")
cat("\n")
}
cat("What is the theoretical mean you are testing against (called mu_0)?\n")
cat("(If you only want a confidence interval, type 'NA')\n")
mu_0 = readline()
if(mu_0!="NA"){mu_0 = as.numeric(mu_0)}
cat("What is your desired confidence level? \n")
conf_level = as.numeric(readline())
while(conf_level<0 | conf_level>1){cat('Please choose a confidence level between 0 and 1\n')
cat("What is your desired confidence level? \n")
conf_level = as.numeric(readline())
}
sidedness = "both"
if(mu_0!="NA"){
t = (xbar - mu_0)/(s/sqrt(n))
df = n-1
out = conduct_t_test(t,df,sidedness)}
# new version with no one-sided confidence intervals
tstar = -qt((1-conf_level)/2,df)
thing_to_type2 = paste("tstar = 1-qt((1-",format(conf_level,scientific=FALSE),")/2,",format(df,scientific=FALSE),") = ",format(tstar,scientific=FALSE),sep="")
thing_to_type3 = paste(toString(xbar)," - ",format(tstar,scientific=FALSE)," x ",format(s,scientific=FALSE),"/sqrt(",toString(n),")",sep="")
thing_to_type4 = paste(toString(xbar)," + ",format(tstar,scientific=FALSE)," x ",format(s,scientific=FALSE),"/sqrt(",toString(n),")",sep="")
lower = xbar - tstar*s/sqrt(n)
upper = xbar + tstar*s/sqrt(n)
# if(sidedness == "both"){
#
# tstar = -qt((1-conf_level)/2,df)
#
# thing_to_type2 = paste("tstar = 1-qt((1-",format(conf_level,scientific=FALSE),")/2,",format(df,scientific=FALSE),") = ",format(tstar,scientific=FALSE),sep="")
# thing_to_type3 = paste(toString(xbar)," - ",format(tstar,scientific=FALSE)," x ",format(s,scientific=FALSE),"/sqrt(",toString(n),")",sep="")
# thing_to_type4 = paste(toString(xbar)," + ",format(tstar,scientific=FALSE)," x ",format(s,scientific=FALSE),"/sqrt(",toString(n),")",sep="")
#
# lower = xbar - tstar*s/sqrt(n)
# upper = xbar + tstar*s/sqrt(n)
# }
#
# if(sidedness == "less"){
#
# tstar = qt(conf_level,df)
#
# thing_to_type2 = paste("tstar = qt(",format(conf_level,scientific=FALSE),",",format(df,scientific=FALSE),") = ",format(tstar,scientific=FALSE),sep="")
# thing_to_type3 = "-Infinity"
# thing_to_type4 = paste(toString(xbar)," + ",format(tstar,scientific=FALSE)," x ",format(s,scientific=FALSE),"/sqrt(",toString(n),")",sep="")
#
# lower = -Inf
# upper = xbar + tstar*s/sqrt(n)
# }
#
# if(sidedness == "greater"){
# tstar = qt(conf_level,df)
#
# thing_to_type2 = paste("tstar = qt(",format(conf_level,scientific=FALSE),",",format(df,scientific=FALSE),") = ",format(tstar,scientific=FALSE),sep="")
# thing_to_type3 = paste(toString(xbar)," - ",format(tstar,scientific=FALSE)," x ",format(s,scientific=FALSE),"/sqrt(",toString(n),")",sep="")
# thing_to_type4 = "Infinity"
#
# lower = xbar - tstar*s/sqrt(n)
# upper = Inf
#
# }
if(mu_0!="NA"){
cat("Your t-statistic is:")
cat("\n")
cat(paste("t = (",format(xbar,scientific=FALSE),"-",format(mu_0,scientific=FALSE),")/(",format(s,scientific=FALSE),"/sqrt(",format(n,scientific=FALSE),")) = ",format(t,scientific=FALSE),sep=""))
cat("\n")
cat("\n")
cat(paste("The probability of getting this result or more extreme for xbar\nif mu really is ",toString(mu_0)," is",sep=""))
cat("\n")
cat(paste("p = ",format(out$prob,scientific=FALSE)))
cat("\n")
cat("\n")
cat("You can get this result by typing:")
cat("\n")
cat(out$p_value_type)
cat("\n")
cat("\n")
cat("\n")}
cat(paste("The ",toString(conf_level*100),"% confidence interval for the population mean is",sep=""))
cat("\n")
cat(paste(format(lower,scientific=FALSE)," < mu < ",format(upper,scientific=FALSE)))
cat("\n")
cat("\n")
cat("You can get this result by finding:")
cat("\n")
cat(thing_to_type2)
cat("\n")
cat("\n")
cat("and then calculating:")
cat("\n")
cat(paste(thing_to_type3," and ",thing_to_type4))
if(vec=="whole"){
cat("\n")
cat("\n")
cat("\n")
cat("Or, since you have the whole dataset, you could just type:")
cat("\n")
if(sidedness=="both"){
cat(paste("t.test(",varname,",mu = ",format(mu_0,scientific=FALSE),",conf.level = ",toString(conf_level),")",sep=""))
}
}
}
}
jrpriceUPS/Math160UPS documentation built on April 28, 2024, 12:41 p.m.
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Defines functions t_test
Documented in t_test
#' t-test
#'
#' This function asks you a sequence of questions in order to execute a t-test. It finds a confidence interval and a p-value, produces a plot, and indicates how this could be queried directly from R.
#' @export
#' @examples
#'
#'
#'
#'
#' > x = c(1, 2, 3, 4, 5, 6, 7)
#' > t_test()
#' Do you have a single population or are you comparing populations?
#' Possible answers are 'single' and 'comparing'.
#' single
#' Do you have the whole dataset or do you just have the statistics (mean, standard deviation)?
#' Possible answers are 'whole' or 'stats'.
#' whole
#' What is the name of your variable?
#' x
#' The statistics for your dataset are:
#' xbar = 4
#' s = 2.160247
#' n = 7
#' df = 7 - 1 = 6
#'
#' What is the theoretical mean you are testing against (called mu_0)?
#' (If you only want a confidence interval, type 'NA')
#' 3
#' What is your desired confidence level?
#' .95
#' Your t-statistic is:
#' t = (4-3)/(2.160247/sqrt(7)) = 1.224745
#'
#' The probability of getting this result or more extreme for xbar
#' if mu really is 3 is
#' p = 0.2665697
#'
#' You can get this result by typing:
#' 2*(1-pt(1.22474487139159,6))
#'
#'
#' The 95% confidence interval for the population mean is
#' 2.002105 < mu < 5.997895
#'
#' You can get this result by finding:
#' tstar = 1-qt((1-0.95)/2,6) = 2.446912
#'
#' and then calculating:
#' 4 - 2.446912 x 2.160247/sqrt(7) and 4 + 2.446912 x 2.160247/sqrt(7)
#'
#'
#' Or, since you have the whole dataset, you could just type:
#' t.test(x,mu = 3,conf.level = 0.95)
#'
#'
#'
#'> t_test()
#'Do you have a single population or are you comparing populations?
#' Possible answers are 'single' and 'comparing'.
#'single
#'Do you have the whole dataset or do you just have the statistics (mean, standard deviation)?
#' Possible answers are 'whole' or 'stats'.
#'stats
#'What is your sample mean?
#' 4
#'What is your sample standard deviation?
#' 2.16
#'What is your sample size?
#' 7
#'What is the theoretical mean you are testing against (called mu_0)?
#' (If you only want a confidence interval, type 'NA')
#'3
#'What is your desired confidence level?
#' .95
#'Your t-statistic is:
#' t = (4-3)/(2.16/sqrt(7)) = 1.224885
#'
#'The probability of getting this result or more extreme for xbar
#'if mu really is 3 is
#'p = 0.2665206
#'
#'You can get this result by typing:
#' 2*(1-pt(1.22488486623361,6))
#'
#'
#'The 95% confidence interval for the population mean is
#'2.002333 < mu < 5.997667
#'
#'You can get this result by finding:
#' tstar = 1-qt((1-0.95)/2,6) = 2.446912
#'
#'and then calculating:
#' 4 - 2.446912 x 2.16/sqrt(7) and 4 + 2.446912 x 2.16/sqrt(7)
#'
#'
#'
#'
#'
#'
#' > t_test()
#' Do you have a single population or are you comparing populations?
#' Possible answers are 'single' and 'comparing'.
#' comparing
#' Do you have the whole dataset or do you just have the statistics (mean, standard deviation)?
#' Possible answers are 'whole' or 'stats'.
#' whole
#' Is this a matched-pairs comparison in which the same subjects are measured twice?
#' yes
#' What is the name of the variable for the first set of measurements?
#' x
#' What is the name of the variable for the second set of measurements?
#' y
#' The statistics for your datasets are:
#' n = 7
#' xbar1 = 4
#' s1 = 2.160247
#'
#' xbar2 = 8.842857
#' s2 = 4.595236
#'
#' The statistics for the difference are:
#' xbar = 4.842857
#' s = 2.445988
#' n = 7
#' df = 7 - 1 = 6
#'
#' What is your desired confidence level?
#' .95
#' Your t-statistic is:
#' t = 4.842857/(2.445988/sqrt(7)) = 5.238372
#'
#' The probability of getting this result or more extreme for xbar2 - xbar1 if there really is no difference is
#' p = 0.001941435
#'
#' You can get this result by typing:
#' 2*(1-pt(5.23837230565063,6))
#'
#'
#' The 95% confidence interval for the difference in population means is
#' 2.580696 < mu2 - mu1 < 7.105019
#'
#' You can get this result by finding:
#' tstar = 1-qt((1-0.95)/2,6) = 2.446912
#'
#' and then calculating:
#' (8.84285714285714-4) - 2.446912 x 2.445988/sqrt(7) and (8.84285714285714-4) + 2.446912 x 2.445988/sqrt(7)
#'
#'
#' Or, since you have the whole dataset, you could just type:
#' t.test(y,x, paired = TRUE, conf.level = 0.95)
#'
#'
#'
#'
#'
#'
#' > t_test()
#' Do you have a single population or are you comparing populations?
#' Possible answers are 'single' and 'comparing'.
#' comparing
#' Do you have the whole dataset or do you just have the statistics (mean, standard deviation)?
#' Possible answers are 'whole' or 'stats'.
#' whole
#' Is this a matched-pairs comparison in which the same subjects are measured twice?
#' no
#' What is the name of the variable for the first set of measurements?
#' x
#' What is the name of the variable for the second set of measurements?
#' y
#' The statistics for your datasets are:
#' n1 = 7
#' xbar1 = 4
#' s1 = 2.160247
#'
#' n2 = 7
#' xbar2 = 8.842857
#' s2 = 4.595236
#'
#' The statistics for the difference are:
#' xbar = 4.842857
#' s = sqrt(2.160247^2/7 + 4.595236^2/7) = 1.919183
#' df = 8.5285
#'
#' What is your desired confidence level?
#' .95
#' Your t-statistic is:
#' t = (4.84285714285714)/(1.919183) = 2.523395
#'
#' The probability of getting this result or more extreme for xbar2 - xbar1 if there really is no difference is
#' p = 0.03391985
#'
#' You can get this result by typing:
#' 2*(1-pt(2.52339452856832,8.52849965837585))
#'
#'
#' The 95% confidence interval for the difference in population means is
#' 0.4644978 < mu2 - mu1 < 9.221216
#'
#' You can get this result by finding:
#' tstar = 1-qt((1-0.95)/2,8.5285) = 2.281366
#'
#' and then calculating:
#' (8.84285714285714-4) - 2.281366 x 1.919183 and (8.84285714285714-4) + 2.281366 x 1.919183
#'
#'
#' Or, since you have the whole dataset, you could just type:
#' t.test(y,x, conf.level = 0.95)
t_test <- function(){
cat("Are you executing a one-sample t-test or a two-sample t-test?\nPossible answers are 'one' and 'two'.\n")
compare = readline()
while(!(compare %in% c('one','1','One','two','2','Two'))){
cat("Please choose either 'one' or 'two'.\n")
compare = readline()
}
if(compare %in% c('one','1','One')){compare = "single"}
if(compare %in% c('two','2','Two')){compare = "comparing"}
cat("Do you have the whole dataset or do you just have the statistics (mean, standard deviation)?\nPossible answers are 'whole' or 'stats'.\n")
vec = readline()
if(compare=="comparing"){
if(vec=="stats"){
cat("What is the sample mean of the first set of measurements? \n")
xbar1 = as.numeric(readline())
cat("What is the sample mean of the second set of measurements? \n")
xbar2 = as.numeric(readline())
cat("What is the sample standard deviation of the first set of measurements? \n")
s1 = as.numeric(readline())
cat("What is the sample standard deviation of the second set of measurements? \n")
s2 = as.numeric(readline())
cat("What is the sample size of the first set of measurements? \n")
n1 = as.numeric(readline())
cat("What is the sample size of the second set of measurements? \n")
n2 = as.numeric(readline())
xbar = xbar2-xbar1
df = n1+n2-2
s = sqrt(s1^2/n1+s2^2/n2)
cat("The statistics for the difference are: ")
cat("\n")
cat(paste("xbar = ",format(xbar,scientific=FALSE)))
cat("\n")
cat(paste("s = sqrt(",format(s1,scientific=FALSE),"^2/",format(n1,scientific=FALSE)," + ",format(s2,scientific=FALSE),"^2/",format(n2,scientific=FALSE),") = ",format(s,scientific=FALSE),sep=""))
cat("\n")
cat(paste("df = ",format(n1,scientific=FALSE),"+",format(n2,scientific=FALSE),"- 2 = ",format(n1+n2-2,scientific=FALSE)))
cat("\n")
cat("\n")
}
if(vec=="whole"){
cat("What is the name of the variable for the first set of measurements? \n")
varname1 = readline()
cat("What is the name of the variable for the second set of measurements? \n")
varname2 = readline()
if(grepl("$", varname1, fixed=TRUE)){
names = strsplit(varname1,"\\$")
frame = get(names[[1]][1])
data1 = frame[[names[[1]][2]]]
} else{
data1 = get(varname1)}
data1 = data1[!is.na(data1)]
xbar1 = mean(data1)
s1 = sd(data1)
n1 = length(data1)
if(grepl("$", varname2, fixed=TRUE)){
names = strsplit(varname2,"\\$")
frame = get(names[[1]])
data2 = frame[[names[[1]][2]]]
} else{
data2 = get(varname2)}
data2 = data2[!is.na(data2)]
xbar2 = mean(data2)
s2 = sd(data2)
n2 = length(data2)
xbar = mean(data2)-mean(data1)
s = sqrt(sd(data1)^2/n1 + sd(data2)^2/n2)
test_result = t.test(data1,data2)
df = as.numeric(test_result$parameter)
cat("The statistics for your datasets are: ")
cat("\n")
cat(paste("n1 = ",format(n1,scientific=FALSE)))
cat("\n")
cat(paste("xbar1 = ",format(xbar1,scientific=FALSE)))
cat("\n")
cat(paste("s1 = ",format(s1,scientific=FALSE)))
cat("\n")
cat("\n")
cat(paste("n2 = ",format(n2,scientific=FALSE)))
cat("\n")
cat(paste("xbar2 = ",format(xbar2,scientific=FALSE)))
cat("\n")
cat(paste("s2 = ",format(s2,scientific=FALSE)))
cat("\n")
cat("\n")
cat("The statistics for the difference are: ")
cat("\n")
cat(paste("xbar = ",format(xbar,scientific=FALSE)))
cat("\n")
cat(paste("s = sqrt(",format(s1,scientific=FALSE),"^2/",format(n1,scientific=FALSE)," + ",format(s2,scientific=FALSE),"^2/",format(n2,scientific=FALSE),") = ",format(s,scientific=FALSE),sep=""))
cat("\n")
cat(paste("df = ",format(df,scientific=FALSE),sep=""))
cat("\n")
cat("\n")
}
cat("What is your desired confidence level? \n")
conf_level = as.numeric(readline())
while(conf_level<0 | conf_level>1){cat('Please choose a confidence level between 0 and 1\n')
cat("What is your desired confidence level? \n")
conf_level = as.numeric(readline("What is your desired confidence level? "))
}
sidedness = "both"
if(sidedness!="NA"){
t = xbar/s
out = conduct_t_test(t,df,sidedness)}
# new version with no one-sided confidence intervals:
tstar = -qt((1-conf_level)/2,df)
thing_to_type2 = paste("tstar = 1-qt((1-",format(conf_level,scientific=FALSE),")/2,",format(df,scientific=FALSE),") = ",format(tstar,scientific=FALSE),sep="")
thing_to_type3 = paste("(",toString(xbar2),"-",toString(xbar1),") - ",format(tstar,scientific=FALSE)," x ",format(s,scientific=FALSE),sep="")
thing_to_type4 = paste("(",toString(xbar2),"-",toString(xbar1),") + ",format(tstar,scientific=FALSE)," x ",format(s,scientific=FALSE),sep="")
lower = xbar - tstar*s
upper = xbar + tstar*s
if(sidedness!="NA"){
sidedness_type = paste("The probability of getting this result or more extreme for xbar2 - xbar1 if there really is no difference is",sep="")
cat("Your t-statistic is:")
cat("\n")
cat(paste("t = (",toString(xbar),")/(",format(s,scientific=FALSE),") = ",format(t,scientific=FALSE),sep=""))
cat("\n")
cat("\n")
cat(sidedness_type)
cat("\n")
cat(paste("p = ",format(out$prob,scientific=FALSE)))
cat("\n")
cat("\n")
cat("You can get this result by typing:")
cat("\n")
cat(out$p_value_type)
cat("\n")
cat("\n")
cat("\n")}
cat(paste("The ",toString(conf_level*100),"% confidence interval for the difference in population means is",sep=""))
cat("\n")
cat(paste(format(lower,scientific=FALSE)," < mu2 - mu1 < ",format(upper,scientific=FALSE)))
cat("\n")
cat("\n")
cat("You can get this result by finding:")
cat("\n")
cat(thing_to_type2)
cat("\n")
cat("\n")
cat("and then calculating:")
cat("\n")
cat(paste(thing_to_type3," and ",thing_to_type4))
if(vec=="whole"){
cat("\n")
cat("\n")
cat("\n")
cat("Or, since you have the whole dataset, you could just type:")
cat("\n")
cat(paste("t.test(",varname2,",",varname1,", conf.level = ", toString(conf_level), ")",sep=""))
}
}
if(compare=="single"){
if(vec=="stats"){
cat("What is your sample mean? \n")
xbar = as.numeric(readline())
cat("What is your sample standard deviation? \n")
s = as.numeric(readline())
cat("What is your sample size? \n")
n = as.numeric(readline())
df = n-1
}
if(vec=="whole"){
cat("What is the name of your variable? \n")
varname = readline()
if(grepl("$", varname, fixed=TRUE)){
names = strsplit(varname,"\\$")
frame = get(names[[1]][1])
data = frame[[names[[1]][2]]]
} else{
data = get(varname)}
data = data[!is.na(data)]
xbar = mean(data)
s = sd(data)
n = length(data)
cat("The statistics for your dataset are: ")
cat("\n")
cat(paste("xbar = ",format(xbar,scientific=FALSE)))
cat("\n")
cat(paste("s = ",format(s,scientific=FALSE)))
cat("\n")
cat(paste("n = ",format(n,scientific=FALSE)))
cat("\n")
cat(paste("df = ",format(n,scientific=FALSE),"- 1 = ",format(n-1,scientific=FALSE)))
cat("\n")
cat("\n")
}
cat("What is the theoretical mean you are testing against (called mu_0)?\n")
cat("(If you only want a confidence interval, type 'NA')\n")
mu_0 = readline()
if(mu_0!="NA"){mu_0 = as.numeric(mu_0)}
cat("What is your desired confidence level? \n")
conf_level = as.numeric(readline())
while(conf_level<0 | conf_level>1){cat('Please choose a confidence level between 0 and 1\n')
cat("What is your desired confidence level? \n")
conf_level = as.numeric(readline())
}
sidedness = "both"
if(mu_0!="NA"){
t = (xbar - mu_0)/(s/sqrt(n))
df = n-1
out = conduct_t_test(t,df,sidedness)}
# new version with no one-sided confidence intervals
tstar = -qt((1-conf_level)/2,df)
thing_to_type2 = paste("tstar = 1-qt((1-",format(conf_level,scientific=FALSE),")/2,",format(df,scientific=FALSE),") = ",format(tstar,scientific=FALSE),sep="")
thing_to_type3 = paste(toString(xbar)," - ",format(tstar,scientific=FALSE)," x ",format(s,scientific=FALSE),"/sqrt(",toString(n),")",sep="")
thing_to_type4 = paste(toString(xbar)," + ",format(tstar,scientific=FALSE)," x ",format(s,scientific=FALSE),"/sqrt(",toString(n),")",sep="")
lower = xbar - tstar*s/sqrt(n)
upper = xbar + tstar*s/sqrt(n)
# if(sidedness == "both"){
#
# tstar = -qt((1-conf_level)/2,df)
#
# thing_to_type2 = paste("tstar = 1-qt((1-",format(conf_level,scientific=FALSE),")/2,",format(df,scientific=FALSE),") = ",format(tstar,scientific=FALSE),sep="")
# thing_to_type3 = paste(toString(xbar)," - ",format(tstar,scientific=FALSE)," x ",format(s,scientific=FALSE),"/sqrt(",toString(n),")",sep="")
# thing_to_type4 = paste(toString(xbar)," + ",format(tstar,scientific=FALSE)," x ",format(s,scientific=FALSE),"/sqrt(",toString(n),")",sep="")
#
# lower = xbar - tstar*s/sqrt(n)
# upper = xbar + tstar*s/sqrt(n)
# }
#
# if(sidedness == "less"){
#
# tstar = qt(conf_level,df)
#
# thing_to_type2 = paste("tstar = qt(",format(conf_level,scientific=FALSE),",",format(df,scientific=FALSE),") = ",format(tstar,scientific=FALSE),sep="")
# thing_to_type3 = "-Infinity"
# thing_to_type4 = paste(toString(xbar)," + ",format(tstar,scientific=FALSE)," x ",format(s,scientific=FALSE),"/sqrt(",toString(n),")",sep="")
#
# lower = -Inf
# upper = xbar + tstar*s/sqrt(n)
# }
#
# if(sidedness == "greater"){
# tstar = qt(conf_level,df)
#
# thing_to_type2 = paste("tstar = qt(",format(conf_level,scientific=FALSE),",",format(df,scientific=FALSE),") = ",format(tstar,scientific=FALSE),sep="")
# thing_to_type3 = paste(toString(xbar)," - ",format(tstar,scientific=FALSE)," x ",format(s,scientific=FALSE),"/sqrt(",toString(n),")",sep="")
# thing_to_type4 = "Infinity"
#
# lower = xbar - tstar*s/sqrt(n)
# upper = Inf
#
# }
if(mu_0!="NA"){
cat("Your t-statistic is:")
cat("\n")
cat(paste("t = (",format(xbar,scientific=FALSE),"-",format(mu_0,scientific=FALSE),")/(",format(s,scientific=FALSE),"/sqrt(",format(n,scientific=FALSE),")) = ",format(t,scientific=FALSE),sep=""))
cat("\n")
cat("\n")
cat(paste("The probability of getting this result or more extreme for xbar\nif mu really is ",toString(mu_0)," is",sep=""))
cat("\n")
cat(paste("p = ",format(out$prob,scientific=FALSE)))
cat("\n")
cat("\n")
cat("You can get this result by typing:")
cat("\n")
cat(out$p_value_type)
cat("\n")
cat("\n")
cat("\n")}
cat(paste("The ",toString(conf_level*100),"% confidence interval for the population mean is",sep=""))
cat("\n")
cat(paste(format(lower,scientific=FALSE)," < mu < ",format(upper,scientific=FALSE)))
cat("\n")
cat("\n")
cat("You can get this result by finding:")
cat("\n")
cat(thing_to_type2)
cat("\n")
cat("\n")
cat("and then calculating:")
cat("\n")
cat(paste(thing_to_type3," and ",thing_to_type4))
if(vec=="whole"){
cat("\n")
cat("\n")
cat("\n")
cat("Or, since you have the whole dataset, you could just type:")
cat("\n")
if(sidedness=="both"){
cat(paste("t.test(",varname,",mu = ",format(mu_0,scientific=FALSE),",conf.level = ",toString(conf_level),")",sep=""))
}
}
}
}
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