Two-Sample Inferences: Two-Sample Inferences (Confidence Intervals and Tests)
In Harrindy/StatEngine: An R Package for the UofSC Course STAT 509 "Statistics for Engineers"

Description Usage Arguments Details Value Note Author(s) References Examples

Compute confidence intervals and conduct hypothesis testing on difference between two population means, population variances, and population proportions.

#CI for the difference in two pupulation means of a normal distribution
#when the population variances are known:
# if sample available
twosample.Zinterval(level,sigma1,sigma2,sample1,sample2)
# if stats are provided
twosample.Zinterval(level,sigma1,sigma2,barx1,barx2,n1,n2)

#Test on the difference in two pupulation means of a normal distribution
#when the population variances are known:
# if sample available
twosample.Ztest(Delta0,H1,alpha,sigma1,sigma2,sample1,sample2)
# if stats are provided
twosample.Ztest(Delta0,H1,alpha,sigma1,sigma2,barx1,barx2,n1,n2)

#CI for the difference in two pupulation means of a normal distribution
#when the population variances are unknown (pooled=yes or no)
# if sample available
twosample.Tinterval(level, pooled,sample1,sample2)
# if stats are provided
twosample.Tinterval(level, pooled,barx1,barx2,n1,n2,s1,s2)

#Test on the difference in two pupulation means of a normal distribution
#when the population variances are unknown:
# if sample available
twosample.Ttest(Delta0,H1,alpha,pooled=yes,sample1,sample2)
# if stats are provided
twosample.Ttest(Delta0,H1,alpha,pooled=yes,barx1,barx2,n1,n2,s1,s2)

#CI for the ratio between two pupulation variances of a normal distribution
# if sample available
Finterval(level, sample1,sample2)
# if stats are provided
Finterval(level, n1,n2,s1,s2)

#Test on the ratio between two pupulation variances of a normal distribution
# if sample available
Ftest(H1,alpha,sample1,sample2)
# if stats are provided
Ftest(H1,alpha,n1,n2,s1,s2)

`level`	the confidence level
`sample1`	a vector of the observed sample from the first population
`sample2`	a vector of the observed sample from the second population
`sigma1`	the known population standard deviation of the first population
`sigma2`	the known population standard deviation of the second population
`s1,s2`	the sample standard deviations
`barx1,barx2`	the sample means
`n1,n2`	the sample sizes
`X1,X2`	number of observations belongs to a class of interest
`Delta0`	the hypothesized value of mu1-mu2
`H1`	type of alternative: "two","left", or "right"
`alpha`	the significance level
`pooled`	"yes" or "no"

Compute confidence intervals and conduct hypothesis testing on difference between two population means, population variances, and population proportions.

`interval`	As long as the function has "interval", the outcome contains a two-sided CI and the two one-sided confidence bounds.
`test`	As long as the function has "test", it produces the test results of using three approaches.

deweiwang@stat.sc.edu

Dewei Wang

Chapter 10 of the textbook "Applied Statistics and Probability for Engineers" 7th edition

#two-sample Zinterval
#must include the = sign
twosample.Zinterval(level=0.9,sigma1=1,sigma2=1.5,barx1=87.6,barx2=74.5,n1=10,n2=12)

#two-sample Ztest
twosample.Ztest(Delta0=0,H1="right",alpha=0.05, sigma1=8,sigma2=8,
                barx1=121,barx2=112,n1=10,n2=10)

#two-sample Tinterval
#must include the = sign
twosample.Tinterval(level=0.95,pooled="no",s1=5,s2=4,barx1=90,barx2=87,n1=10,n2=15)

#two-sample Ttest
catalyst1=c(91.50,94.18,92.18,95.39,91.79,89.07,94.72,89.21)
catalyst2=c(89.19,90.95,90.46,93.21,97.19,97.04,91.07,92.75)
data.summary(catalyst1)
data.summary(catalyst2)
twosample.Tinterval(level=0.95,pooled="yes",
                    sample1=catalyst1,sample2=catalyst2)
twosample.Ttest(Delta0=0,H1="two",alpha=0.05, pooled="yes",
                sample1=catalyst1,sample2=catalyst2)


C50=c(0.047, 0.060, 0.061, 0.064, 0.080, 0.090, 0.118, 0.165, 0.183)
C60=c(0.062, 0.105, 0.118, 0.137, 0.153, 0.197, 0.210, 0.250, 0.335)
data.summary(C50)
data.summary(C60)
twosample.Tinterval(level=0.95,pooled="no",
                    sample1=C50,sample2=C60)
twosample.Ttest(Delta0=0,H1="left",alpha=0.05, pooled="no",
                sample1=C50,sample2=C60)


#Paired T-test
Karlsrube=c(1.186,1.151,1.322,1.229,1.200,1.402,1.365,1.537,1.559)
   Lehigh=c(1.061,0.992,1.063,1.062,1.065,1.178,1.037,1.086,1.052)
   data.summary(Karlsrube-Lehigh)
Tinterval(level=0.95,sample=Karlsrube-Lehigh)
Ttest(mu0=0, H1="two",alpha=0.05,sample=Karlsrube-Lehigh)

#F-interval
Finterval(level=0.9,n1=11,n2=16,s1=5.1,s2=4.7)
Ftest(H1="two",alpha=0.1,n1=11,n2=16,s1=5.1,s2=4.7)

#two-sample proportion Z-interval
twosample.Propinterval(level=0.95, n1=85,n2=85,X1=10,X2=8)
twosample.Propinterval(level=0.95, n1=100,n2=100,X1=27,X2=19)
twosample.Proptest(H1="right",alpha=0.05,n1=100,n2=100,X1=27,X2=19)