# Rproject11_Tablets_TwoSampleT.r
# 1.0 Read in data ----
# See Example 12.2A of Rice
#
# Measurements of chlorpheniramine maleate in tablets made by seven laboratories
# Nominal dosage equal to 4mg
# 10 measurements per laboratory
#
# Sources of variability
# within labs
# between labs
# Note: read.table has trouble parsing header row
if (FALSE){tablets1=read.table(file="Rice 3e Datasets/ASCII Comma/Chapter 12/tablets1.txt",
sep=",",stringsAsFactors = FALSE, quote="\'",
header=TRUE)
}
# Read in matrix and label columns
tablets1=read.table(file="Rice 3e Datasets/ASCII Comma/Chapter 12/tablets1.txt",
sep=",",stringsAsFactors = FALSE, skip=1,
header=FALSE)
dimnames(tablets1)[[2]]<-paste("Lab",c(1:7),sep="")
tablets1
## Lab1 Lab2 Lab3 Lab4 Lab5 Lab6 Lab7
## 1 4.13 3.86 4.00 3.88 4.02 4.02 4.00
## 2 4.07 3.85 4.02 3.88 3.95 3.86 4.02
## 3 4.04 4.08 4.01 3.91 4.02 3.96 4.03
## 4 4.07 4.11 4.01 3.95 3.89 3.97 4.04
## 5 4.05 4.08 4.04 3.92 3.91 4.00 4.10
## 6 4.04 4.01 3.99 3.97 4.01 3.82 3.81
## 7 4.02 4.02 4.03 3.92 3.89 3.98 3.91
## 8 4.06 4.04 3.97 3.90 3.89 3.99 3.96
## 9 4.10 3.97 3.98 3.97 3.99 4.02 4.05
## 10 4.04 3.95 3.98 3.90 4.00 3.93 4.06
# Replicate Figure 12.1 of Rice
boxplot(tablets1)
![](data:image/png;base64,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)
# 2.1 Define a function to implement Two-sample t test ----
fcn.TwoSampleTTest<-function(x,y, conf.level=0.95, digits0=4){
# conf.level=0.95; digits0=4
x.mean=mean(x)
y.mean=mean(y)
x.var=var(x)
y.var=var(y)
x.n=length(x)
y.n=length(y)
sigmasq.pooled=((x.n-1)*x.var + (y.n-1)*y.var)/(x.n + y.n -2)
# Print out statistics for each sample and pooled estimate of standard deviation
cat("Sample Statistics:\n")
print(t(data.frame(
x.mean,
x.n,
x.stdev=sqrt(x.var),
y.mean,
y.n,
y.stdev=sqrt(y.var),
sigma.pooled=sqrt(sigmasq.pooled)
)))
cat("\n t test Computations")
mean.diff=x.mean-y.mean
mean.diff.sterr=sqrt(sigmasq.pooled)*sqrt( 1/x.n + 1/y.n)
mean.diff.tstat=mean.diff/mean.diff.sterr
tstat.df=x.n + y.n -2
mean.diff.tstat.pvalue=2*pt(-abs(mean.diff.tstat), df=tstat.df)
print(t(data.frame(
mean.diff=mean.diff,
mean.diff.sterr=mean.diff.sterr,
tstat=mean.diff.tstat,
df=tstat.df,
pvalue=mean.diff.tstat.pvalue)))
# Confidence interval for difference
alphahalf=(1-conf.level)/2.
t.critical=qt(1-alphahalf, df=tstat.df)
mean.diff.confInterval=mean.diff +c(-1,1)*mean.diff.sterr*t.critical
cat(paste("\n", 100*conf.level, " Percent Confidence Interval:\n "))
cat(paste(c(
"[", round(mean.diff.confInterval[1],digits=digits0),
",", round(mean.diff.confInterval[2],digits=digits0),"]"), collapse=""))
# invisible(return(NULL))
}
# 2.2 Apply function fcn.TwoSampleTTest ----
# Compare Lab7 to Lab4
fcn.TwoSampleTTest(tablets1$Lab7, tablets1$Lab4)
## Sample Statistics:
## [,1]
## x.mean 3.99800000
## x.n 10.00000000
## x.stdev 0.08482662
## y.mean 3.92000000
## y.n 10.00000000
## y.stdev 0.03333333
## sigma.pooled 0.06444636
##
## t test Computations [,1]
## mean.diff 0.07800000
## mean.diff.sterr 0.02882129
## tstat 2.70633286
## df 18.00000000
## pvalue 0.01445587
##
## 95 Percent Confidence Interval:
## [0.0174,0.1386]
# Compare output to t.test
t.test(tablets1$Lab7, tablets1$Lab4, var.equal=TRUE)
##
## Two Sample t-test
##
## data: tablets1$Lab7 and tablets1$Lab4
## t = 2.7063, df = 18, p-value = 0.01446
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 0.01744872 0.13855128
## sample estimates:
## mean of x mean of y
## 3.998 3.920
# 3.1 Conduct One-Way ANOVA ----
# Analysis of Variance with R function aov()
# Create vector variables
# yvec = Dependent variable
yvec=as.vector(data.matrix(tablets1))
# xvec.factor.Lab = Independent variable (of factor type in R)
xvec.factor.Lab=as.factor(as.vector(col(data.matrix(tablets1))))
table(xvec.factor.Lab)
## xvec.factor.Lab
## 1 2 3 4 5 6 7
## 10 10 10 10 10 10 10
plot(as.numeric(xvec.factor.Lab), yvec)
![](data:image/png;base64,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)
# One-way ANOVA using r function aov()
tablets1.aov<-aov(yvec ~ xvec.factor.Lab)
tablets1.aov.summary<-summary(tablets1.aov)
# Replicate Table in Example 12.2.A, p. 483 of Rice
print(tablets1.aov.summary)
## Df Sum Sq Mean Sq F value Pr(>F)
## xvec.factor.Lab 6 0.1247 0.020790 5.66 9.45e-05 ***
## Residuals 63 0.2314 0.003673
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# Construct model tables
tablets1.aov.model.tables<-model.tables(tablets1.aov, type="means",se=TRUE)
print(tablets1.aov.model.tables)
## Tables of means
## Grand mean
##
## 3.984571
##
## xvec.factor.Lab
## xvec.factor.Lab
## 1 2 3 4 5 6 7
## 4.062 3.997 4.003 3.920 3.957 3.955 3.998
##
## Standard errors for differences of means
## xvec.factor.Lab
## 0.0271
## replic. 10
# Validate standard error for difference of means
ResidualsMeanSq=0.003673
J=nrow(tablets1)
sqrt(ResidualsMeanSq/J) # standard error of each mean
## [1] 0.01916507
sqrt(ResidualsMeanSq/J)*sqrt(2) # standard error of difference of two means
## [1] 0.02710351
#tablets1.aov.model.tables<-model.tables(tablets1.aov, type="effects",se=TRUE)
#print(tablets1.aov.model.tables)
# 3.2 Confidence intervals for pairwise differences ----
# Create confidence intervals on differences between means
# Studentized range statistic
# Tukey's 'Honest Significant Difference' method
# Apply R function TukeyHSD():
TukeyHSD(tablets1.aov)
## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = yvec ~ xvec.factor.Lab)
##
## $xvec.factor.Lab
## diff lwr upr p adj
## 2-1 -0.065 -0.147546752 0.017546752 0.2165897
## 3-1 -0.059 -0.141546752 0.023546752 0.3226101
## 4-1 -0.142 -0.224546752 -0.059453248 0.0000396
## 5-1 -0.105 -0.187546752 -0.022453248 0.0045796
## 6-1 -0.107 -0.189546752 -0.024453248 0.0036211
## 7-1 -0.064 -0.146546752 0.018546752 0.2323813
## 3-2 0.006 -0.076546752 0.088546752 0.9999894
## 4-2 -0.077 -0.159546752 0.005546752 0.0830664
## 5-2 -0.040 -0.122546752 0.042546752 0.7578129
## 6-2 -0.042 -0.124546752 0.040546752 0.7140108
## 7-2 0.001 -0.081546752 0.083546752 1.0000000
## 4-3 -0.083 -0.165546752 -0.000453248 0.0478900
## 5-3 -0.046 -0.128546752 0.036546752 0.6204148
## 6-3 -0.048 -0.130546752 0.034546752 0.5720976
## 7-3 -0.005 -0.087546752 0.077546752 0.9999964
## 5-4 0.037 -0.045546752 0.119546752 0.8178759
## 6-4 0.035 -0.047546752 0.117546752 0.8533629
## 7-4 0.078 -0.004546752 0.160546752 0.0760155
## 6-5 -0.002 -0.084546752 0.080546752 1.0000000
## 7-5 0.041 -0.041546752 0.123546752 0.7362355
## 7-6 0.043 -0.039546752 0.125546752 0.6912252
#
# Compare Tukey HSD confidence interval for Lab7 vs Lab4
fcn.TwoSampleTTest(tablets1$Lab7,tablets1$Lab4)
## Sample Statistics:
## [,1]
## x.mean 3.99800000
## x.n 10.00000000
## x.stdev 0.08482662
## y.mean 3.92000000
## y.n 10.00000000
## y.stdev 0.03333333
## sigma.pooled 0.06444636
##
## t test Computations [,1]
## mean.diff 0.07800000
## mean.diff.sterr 0.02882129
## tstat 2.70633286
## df 18.00000000
## pvalue 0.01445587
##
## 95 Percent Confidence Interval:
## [0.0174,0.1386]
# Note P-value from t-test is 0.0144 while TukeyHSD is 0.076
# 4. Implement One-Way Anova with lm() ----
lmfit.oneway.Lab=lm(yvec ~ xvec.factor.Lab,x=TRUE, y=TRUE)
lmfit.oneway.Lab.summary<-summary(lmfit.oneway.Lab)
print(lmfit.oneway.Lab.summary)
##
## Call:
## lm(formula = yvec ~ xvec.factor.Lab, x = TRUE, y = TRUE)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.1880 -0.0245 0.0060 0.0410 0.1130
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.06200 0.01917 211.948 < 2e-16 ***
## xvec.factor.Lab2 -0.06500 0.02710 -2.398 0.019449 *
## xvec.factor.Lab3 -0.05900 0.02710 -2.177 0.033248 *
## xvec.factor.Lab4 -0.14200 0.02710 -5.239 1.99e-06 ***
## xvec.factor.Lab5 -0.10500 0.02710 -3.874 0.000257 ***
## xvec.factor.Lab6 -0.10700 0.02710 -3.948 0.000201 ***
## xvec.factor.Lab7 -0.06400 0.02710 -2.361 0.021316 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.06061 on 63 degrees of freedom
## Multiple R-squared: 0.3503, Adjusted R-squared: 0.2884
## F-statistic: 5.66 on 6 and 63 DF, p-value: 9.453e-05
# Compare regression output from lm() with anova output from aov()
print(tablets1.aov.summary)
## Df Sum Sq Mean Sq F value Pr(>F)
## xvec.factor.Lab 6 0.1247 0.020790 5.66 9.45e-05 ***
## Residuals 63 0.2314 0.003673
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# Residual standard error equals root (Mean Sq for Residuals)
print(lmfit.oneway.Lab.summary$sigma)
## [1] 0.06060541
print((lmfit.oneway.Lab.summary$sigma)^2)
## [1] 0.003673016
# Compare to Mean Sq for Residuals in tablets1.aov.summary
# F-statistic/degrees of freedom/P-values are same