case1501 {Sleuth2}

Logging and Water Quality

Description

Data from an observational study of nitrate levels measured at three week intervals for five years in two watersheds. One of the watersheds was undisturbed and the other had been logged with a patchwork pattern.

Usage

case1501

Format

A data frame with 88 observations on the following 3 variables.

Week

week after the start of the study

Patch

residual nitrate level in the logged watershed (ppm) (see Display 15.3 of Statistical Sleuth)

Nocut

residual nitrate level in the undisturbed watershed (ppm)

Source

Ramsey, F.L. and Schafer, D.W. (2002). The Statistical Sleuth: A Course in Methods of Data Analysis (2nd ed), Duxbury.

References

Harr, R.D., Friderksen, R.L., and Rothacher, J. (1979). Changes in Streamflow Following Timber Harvests in Southwestern Oregon, USDA/USFS Research Paper PNW-249, Pacific NW Forest and Range Experiment Station, Portland, Oregon.

Examples

str(case1501)

par(mfrow=c(2,1)) # Make 2 plots on one page
plot(Nocut ~ Week, case1501)
plot(Patch ~ Week, case1501)
par(mfrow=c(1,1))
lag.plot(case1501$Nocut,do.lines=FALSE) 
lag.plot(case1501$Patch,do.lines=FALSE)

# Compute pooled estimate of first autocorrelation coefficient
# First auto covariance, Nocut
ac1nocut <- acf(case1501$Nocut,lag.max=1,type="covariance",plot=FALSE)$acf[2] 
n <- length(case1501$Nocut)
# Zeroth autocovariance for Nocut
ac0nocut <- var(case1501$Nocut[2:n])*(n-2)/(n-1)
# First auto covariance, Patch
ac1patch <- acf(case1501$Patch,lag.max=1,type="covariance",plot=FALSE)$acf[2]
# Zeroth autocovariance for PATCH
ac0patch <- var(case1501$Patch [2:n])*(n-2)/(n-1)

ac1pool <- (ac1nocut + ac1patch)/2
ac0pool <- (ac0nocut + ac0patch)/2

acorr1 <- ac1pool/ac0pool
acorr1  # Pooled estimate of first lag serial coefficient